This handout is designed to help writers develop and use logical arguments in writing. This handout helps writers analyze the arguments of others and generate their own arguments. However, it is important to remember that logic is only one aspect of a successful argument. Non-logical arguments , statements that cannot be logically proven or disproved, are important in argumentative writing—such as appeals to emotions or values. Illogical arguments , on the other hand, are false and must be avoided.
Logic is a formal system of analysis that helps writers invent, demonstrate, and prove arguments. It works by testing propositions against one another to determine their accuracy. People often think they are using logic when they avoid emotion or make arguments based on their common sense, such as "Everyone should look out for their own self-interests" or "People have the right to be free." However, unemotional or common sense statements are not always equivalent to logical statements. To be logical, a proposition must be tested within a logical sequence.
The most famous logical sequence, called the syllogism , was developed by the Greek philosopher Aristotle. His most famous syllogism is:
Premise 1: All men are mortal. Premise 2: Socrates is a man. Conclusion: Therefore, Socrates is mortal.
In this sequence, premise 2 is tested against premise 1 to reach the logical conclusion. Within this system, if both premises are considered valid, there is no other logical conclusion than determining that Socrates is a mortal.
This guide provides some vocabulary and strategies for determining logical conclusions.
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1 What is Logic?
Matthew Knachel
There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response goes roughly like this: we manifest our rationality by engaging in activities that involve reasoning —making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on.
This reasoning activity can be done well and it can be done badly; it can be done correctly or incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad.
Good reasoning is not necessarily effective reasoning. In fact, as we shall see in a subsequent chapter on logical fallacies, bad reasoning is pervasive and often extremely effective—in the sense that people are often persuaded by it. In logic, the standard of goodness is not effectiveness in the sense of persuasiveness, but rather correctness according to logical rules.
For example, consider Hitler. He persuaded an entire nation to go along with a variety of proposals that were not only false but downright evil. You won’t be surprised to hear that if you examine it critically, his reasoning does not pass logical muster. Hitler’s arguments were effective, but not logically correct. Moreover, his persuasive techniques go beyond reasoning in the sense of backing up claims with reasons. Hitler relied on threats, emotional manipulation, unsupported assertions, etc. There are many rhetorical tricks one can use to persuade.
In logic, we study the rules and techniques that allow us to distinguish good, correct reasoning from bad, incorrect reasoning.
Since there are a variety of different types of reasoning and methods with which to evaluate each of these types, plus various diverging views on what constitutes correct reasoning, there are many approaches to the logical enterprise. We talk of logic, but also of logics . A logic is just a set of rules and techniques for distinguishing good reasoning from bad. A logic must formulate precise standards for evaluating reasoning and develop methods for applying those standards to particular instances.
Basic Notions
Reasoning involves claims or statements—making them and backing them up with reasons, drawing out their consequences. Propositions are the things we claim, state, assert.
Propositions are the kinds of things that can be true or false. They are expressed by declarative sentences . We use such sentences to make all sorts of assertions, from routine matters of fact (“the Earth revolves around the Sun”), to grand metaphysical theses (“reality is an unchanging, featureless, unified Absolute”), to claims about morality (“it is wrong to eat meat”).
It is important to distinguish sentences in the declarative mood, which express propositions, from sentences in other moods, which do not. Interrogative sentences, for example, ask questions (“Is it raining?”), and imperative sentences issue commands (“Don’t drink kerosene.”). It makes no sense to ask whether these kinds of sentences express truths or falsehoods, so they do not express propositions.
We also distinguish propositions from the sentences that express them, because a single proposition can be expressed by different sentences. “It’s raining” and “es regnet” both express the proposition that it’s raining; one sentence does it in English, the other in German. Also, “John loves Mary” and “Mary is loved by John” both express the same proposition.
The fundamental unit of reasoning is the argument. In logic, by “argument” we don’t mean a disagreement, a shouting match; rather, we define the term precisely:
Argument = a set of propositions, one of which, the conclusion, is (supposed to be) supported by the others, the premises.
If we’re reasoning by making claims and backing them up with reasons, then the claim that’s being backed up is the conclusion of an argument; the reasons given to support it are the argument’s premises. If we’re reasoning by drawing an inference from a set of statements, then the inference we draw is the conclusion of an argument, and the statements from which it’s drawn are the premises.
We include the parenthetical hedge—“supposed to be”—in the definition to make room for bad arguments. A bad argument, very roughly speaking, is one where the premises fail to support the conclusion; a good argument’s premises actually do support the conclusion.
Analysis of Arguments
The following passage expresses an argument:
So does this passage:
Again, the ultimate purpose of logic is to evaluate arguments—to distinguish the good from the bad. To do so requires distinctions, definitions, principles, and techniques that will be outlined in subsequent chapters. For now, we will focus on identifying and reconstructing arguments.
The first task is to explicate arguments—to state explicitly their premises and conclusions. A perspicuous way to do this is simply to list declarative sentences expressing the relevant propositions, with a line separating the premises from the conclusion, thus:
McDonald’s pays their workers very low wages.
The animals that provide McDonald’s meat are raised in deplorable conditions.
McDonald’s food is very unhealthy.
[latex]/ \therefore[/latex] You shouldn’t eat at McDonald’s. [1]
This is an explication of the first argumentative passage above. To identify the conclusion of an argument, it is helpful to ask oneself, “What is this person trying to convince me to believe by saying these things? What is the ultimate point of this passage?” The answer is pretty clear in this case. Another clue as to what’s going on in the passage is provided by the word “because” in the third sentence. Along with other words, like “since” and “for,” it indicates the presence of a premise. We can call such words premise markers . The symbol “/∴” can be read as shorthand for “therefore.” Along with expressions like “consequently,” “thus,” “it follows that” and “which implies that,” “therefore” is an indicator that the argument’s conclusion is about to follow. We call such locutions conclusion markers . Such a marker is not present in the first argument, but we do see one in the second, which may be explicated thus:
The universe is vast and complex.
The universe displays an astonishing degree of order.
The planets orbit the sun according to regular laws.
Animals’ minutest parts are arranged precisely to serve their purposes.
Such order and complexity cannot arise at random.
[latex]/ \therefore[/latex] The universe must be the product of a designer of enormous power and intellect: God.
Several points of comparison to our first explication are worthy of note here. First, as mentioned, we were alerted of the conclusion by the word “therefore.” Second, this passage required much more paraphrase than the first. The second sentence is interrogative, not declarative, and so it does not express a proposition. Since arguments are, by definition, collections of propositions, we must restrict ourselves to declarative sentences when explicating them. Since the answer to the second sentence’s rhetorical question is clearly “yes,” we paraphrase as shown. The third sentence expresses two propositions, so in our explication we separate them; each one is a premise.
So sometimes, when we explicate an argument, we have to take what’s present in the argumentative passage and change it slightly, so that all of the sentences we write down express the propositions present in the argument. This is paraphrasing. At other times, we have to do even more. For example, we may have to introduce propositions which are not explicitly mentioned within the argumentative passage, but are undoubtedly used within the argument’s reasoning.
There’s a Greek word for argumentative passages that leave certain propositions unstated: enthymemes . Here’s an example:
There’s an implicit premise lurking in the background here—something that hasn’t been said, but which needs to be true for the argument to go through. We need a claim that connects the premise to the conclusion—that bridges the gap between them. Something like this: An all-loving God would not allow innocent people to suffer. Or maybe: widespread suffering is incompatible with the idea of an all-loving deity. The premise points to suffering, while the conclusion is about God; these propositions connect those two claims. A complete explication of the argumentative passage would make a proposition like this explicit:
Many innocent people all over the world are suffering.
An all-loving God would not allow innocent people to suffer.
[latex]/ \therefore[/latex] There cannot be an all-loving God.
This is the mark of the kinds of tacit premises we want to uncover: if they’re false, they undermine the argument. Often, premises like this are unstated for a reason: they’re controversial claims on their own, requiring evidence to support them; so the arguer leaves them out, preferring not to get bogged down. [2] When we draw them out, however, we can force a more robust dialectical exchange, focusing the argument on the heart of the matter. In this case, a discussion about the compatibility of God’s goodness and evil in the world would be in order. There’s a lot to be said on that topic. Philosophers and theologians have developed elaborate arguments over the centuries to defend the idea that God’s goodness and human suffering are in fact compatible. [3]
So far, our analysis of arguments has not been particularly deep. We have noted the importance of identifying the conclusion and clearly stating the premises, but we have not looked into the ways in which sets of premises can support their conclusions. We have merely noted that, collectively, premises provide support for conclusions. We have not looked at how they do so, what kinds of relationships they have with one another. This requires deeper analysis.
Often, different premises will support a conclusion—or another premise—individually, without help from any others. Consider this simple argument:
Propositions 1 and 2 support the conclusion, proposition 3—and they do so independently. Each gives us a reason for believing that the war was unjust, and each stands as a reason even if we were to suppose that the other were not true; this is the mark of independent premises .
It can be helpful, especially when arguments are more complex, to draw diagrams that depict the relationships among premises and conclusion. We could depict the argument above as follows:
In such a diagram, the circled numbers represent the propositions and the arrows represent the relationship of support from one proposition to another. Since propositions 1 and 2 each support 3 independently, they get their own arrows.
Other relationships among premises are possible. Sometimes, premises provide support for conclusions only indirectly, by giving us a reason to believe some other premise, which is intermediate between the two claims. Consider the following argument:
In this example, proposition 1 provides support for proposition 2 (the word “hence” is a clue), while proposition 2 directly supports the conclusion in 3. We would depict the relationships among these propositions thus:
Sometimes premises must work together to provide support for another claim, not because one of them provides reason for believing the other, but because neither provides the support needed on its own; we call such propositions joint premises . Consider the following:
In this argument, neither premise 1 nor premise 2 supports the conclusion on its own; rather, the second premise, as it were, provides a key that unlocks the conclusion from the conditional premise 1. We can indicate such interdependence diagrammatically with brackets, thus:
Diagramming arguments in this way can be helpful both in understanding how they work and informing any attempt to critically engage with them. One can see clearly in the first argument that any considerations put forward contrary to one of the independent premises will not completely undermine support for the conclusion, as there is still another premise providing it with some degree of support. In the second argument, though, reasons telling against the second premise would cut off support for the conclusion at its root; and anything contrary to the first premise will leave the second in need of support. And in the third argument, considerations contrary to either of the joint premises will undermine support for the conclusion. Especially when arguments are more complex, such visual aids can help us recognize all of the inferences contained within the argument.
Perhaps it will be useful to conclude by considering a slightly more complex argument. Let’s consider the nature of numbers:
The conclusion of this argument is the last proposition, that numbers are abstract objects. Notice that the first premise gives us a choice between this claim and an alternative—that they are concrete. The second premise denies that alternative, and so premises 1 and 2 are working together to support the conclusion:
Now we need to make room in our diagram for propositions 3 and 4. They are there to give us reasons for believing that numbers are not concrete objects. First, by asserting that numbers aren’t located in space like concrete objects are, and second by asserting that numbers don’t interact with other objects, like concrete objects do. These are separate, independent reasons for believing they aren’t concrete, so we end up with this diagram:
Logic and Philosophy
At the heart of the logical enterprise is a philosophical question: What makes a good argument? That is, what is it for a set of claims to provide support for some other claim? Or maybe: When are we justified in drawing inferences? To answer these questions, logicians have developed a wide variety of logical systems, covering different types of arguments, and applying different principles and techniques. Many of the tools developed in logic can be applied beyond the confines of philosophy. The mathematician proving a theorem, the computer scientist programming a computer, the linguist modeling the structure of language—all these are using logical methods. Because logic has such wide application, and because of the formal/mathematical sophistication of many logical systems, it occupies a unique place in the philosophical curriculum. A class in logic is typically unlike other philosophy classes in that very little time is spent directly engaging with and attempting to answer the “big questions”; rather, one very quickly gets down to the business of learning logical formalisms. The questions logic is trying to answer are important philosophical questions, but the techniques developed to answer them are worthy of study on their own.
This does not mean, however, that we should think of logic and philosophy as merely tangentially related; on the contrary, they are deeply intertwined. For all the formal bells and whistles featured in the latest high-end logical system, at bottom it is part of an effort to answer the fundamental question of what follows from what. Moreover, logic is useful to the practicing philosopher in at least three other ways.
Philosophers attempt to answer deep, vexing questions—about the nature of reality, what constitutes a good life, how to create a just society, and so on. They give their answers to these questions, and they back those answers up with reasons. Then other philosophers consider their arguments and reply with elaborations and criticisms—arguments of their own. Philosophy is conducted and makes progress by way of exchanging arguments. Since they are the primary tool of their trade, philosophers better know a little something about what makes for good arguments! Logic, therefore, is essential to the practice of philosophy.
But logic is not merely a tool for evaluating philosophical arguments; it has altered the course of the ongoing philosophical conversation. As logicians developed formal systems to model the structure of an ever-wider range of discursive practices, philosophers have been able to apply their insights directly to traditional philosophical problems and recognize previously hidden avenues of inquiry. Since the turn of the 20th century especially, the proliferation of novel approaches in logic has sparked a revolution in the practice of philosophy. It is not too much of an exaggeration to say that much of the history of philosophy in the 20th century constituted an ongoing attempt to grapple with new developments in logic, and the philosophical focus on language that they seemed to demand. No philosophical topic—from metaphysics to ethics to epistemology and beyond—was untouched by this revolution.
Finally, logic itself is the source of fascinating philosophical questions. The basic question at its heart—what is it for a claim to follow from others?—ramifies out in myriad directions, providing fertile ground for philosophical speculation. There is logic, and then there is philosophy of logic . Logic is said to be “formal,” for example. What does that mean? It’s a surprisingly difficult question to answer. [5] Our simplest logical formulations of conditional sentences (those involving “if”), lead to apparent paradoxes. [6] How should those be resolved? Should our formalisms be altered to better capture the natural-language meanings of conditionals? What is the proper relationship between logical systems and natural languages, anyway?
Traditionally, most logicians have accepted that logic should be “bivalent”: every proposition is either true or false. But natural languages contain vague terms whose boundaries of applicability are not always clear. For example, “bald”: for certain subjects, we might be inclined to say that they’re well on their way to full-on baldness, but not quite there yet; on the other hand, we would be reluctant to say that they’re not-bald. There are in-between cases. For such cases, we might want to say, for example, that the proposition that Fredo is bald is neither true nor false. Some logicians have developed logics that are not bivalent, to deal with this sort of linguistic phenomenon. Some add a third truth-value: “neither” or “undetermined,” for instance. Others introduce infinite degrees of truth (this is called “fuzzy logic”). These logics deviate from traditional approaches. Are they therefore wrong in some sense? Or are they right, and the traditionalists wrong? Or are we even asking a sensible question when we ask whether a particular logical system is right or wrong? Can we be so-called logical “pluralists,” accepting a variety of incompatible logics, depending, for example, on whether they’re useful?
These sorts of questions are beyond the scope of this introductory text, of course. They’re included to give you a sense of just how far one can take the study of logic. The task for now, though, is to begin that study.
First, explicate the following arguments, paraphrasing as necessary and only including tacit premises when explicitly instructed to do so. Next, diagram the arguments.
Numbers, if they exist at all, must be either concrete or abstract objects. Concrete objects–like planets and people–are able to interact with other things in cause-and-effect relations. Numbers lack this ability. Therefore, numbers are abstract objects. [ You will need to add an implicit intermediate premise here! ]
Abolish the death penalty! Why? It is immoral. Numerous studies have shown that there is racial bias in its application. The rise of DNA testing has exonerated scores of inmates on death row; who knows how many innocent people have been killed in the past? The death penalty is also impractical. Revenge is counterproductive: “An eye for an eye leaves the whole world blind,” as Gandhi said. Moreover, the costs of litigating death penalty cases, with their endless appeals, are enormous.
A just economic system would feature an equitable distribution of resources and an absence of exploitation. Capitalism is an unjust economic system. Under capitalism, the typical distribution of wealth is highly skewed in favor of the rich. And workers are exploited: despite their essential role in producing goods for the market, most of the profits from the sales of those goods go to the owners of firms, not their workers.
The mind and the brain are not identical. How can things be identical if they have different properties? There is a property that the mind and brain do not share: the brain is divisible, but the mind is not. Like all material things, the brain can be divided into parts—different halves, regions, neurons, etc. But the mind is a unity. It is my thinking essence, in which I can discern no separate parts. [7]
Every able-bodied adult ought to participate in the workforce. The more people working, the greater the nation’s wealth, which benefits everyone economically. In addition, there is no replacement for the dignity workers find on the job. The government should therefore issue tax credits to encourage people to enter the workforce. [ Include in your explication a tacit premise, not explicitly stated in the passage, but necessary to support the conclusion. ]
The symbols preceding the conclusion, "[latex]/ \therefore[/latex]" represent the word "therefore." ↵
This is not always the reason. Some claims are left tacit simply because everybody accepts them and to state them explicitly would be a waste of time. If we argue, “Elephants are mammals, and so warm-blooded,” we omit the claim that all mammals are warm-blooded for this innocent reason. ↵
These arguments even have a special name: they’re called “theodicies.” ↵
An extremely compressed version of Plato’s objections to poetry in Book X of The Republic . ↵
John MacFarlane, in his widely read PhD dissertation, spends over 300 pages on that question. See: MacFarlane, J. 2000. “What Does It Mean to Say That Logic Is Formal?” University of Pittsburgh. ↵
For a concise explanation, see the Wikipedia entry on paradoxes of material implication . ↵
A simplified version of an argument from Rene Descartes. ↵
The unambiguated meaning of declarative sentences.
Sentences which communicate that something is, or is not, the case. For example, “Bob won the 50m freestyle.” Declarative sentences can be contrasted with those that pose questions, called interrogative sentences , and those which deliver commands, known as imperative sentences . (Declarative sentences are also known as indicative sentences)
Words that generally indicate what follows is a premise, e.g. “given that,” “as,” “since.”
Words that generally indicate that what follows is a conclusion, e.g. “therefore,” “thus,” “consequently.”
Arguments which leave certain premises unstated.
Premises which aim to provide sufficient support on their own for the truth of the conclusion.
Premises which attempt to directly support not the conclusion of an argument, but another premise.
Premises which only provide support for the truth of the conclusion when combined.
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24 What is Logic?
Kirsten DeVries
Logic, in its most basic sense, is the study of how ideas reasonably fit together. In other words, when you apply logic, you must be concerned with analyzing ideas and arguments by using reason and rational thinking, not emotions or mysticism or belief. As a dedicated field of study, logic belongs primarily to math, philosophy, and computer science; in these fields, one can get professional training in logic. However, all academic disciplines employ logic: to evaluate evidence, to analyze arguments, to explain ideas, and to connect evidence to arguments. One of the most important uses of logic is in composing and evaluating arguments.
The study of logic divides into two main categories: formal and informal. Formal logic is the formal study of logic. In other words, in math or philosophy or computer science, if you were to take a class on logic, you would likely be learning formal logic. The purpose of formal logic is to eliminate any imprecision or lack of objectivity in evaluating arguments. Logicians, scholars who study and apply logic, have devised a number of formal techniques that accomplish this goal for certain classes of arguments. These techniques can include truth tables, Venn diagrams, proofs, syllogisms, and formulae. The different branches of formal logic include, but are not limited to, propositional logic, categorical logic, and first order logic.
Informal logic is logic applied outside of formal study and is most often used in college, business, and life. According to The Stanford Encyclopedia of Philosophy ,
For centuries, the study of logic has inspired the idea that its methods might be harnessed in efforts to understand and improve thinking, reasoning, and argument as they occur in real life contexts: in public discussion and debate; in education and intellectual exchange; in interpersonal relations; and in law, medicine, and other professions. Informal logic is the attempt to build a logic suited to this purpose. It combines the study of argument, evidence, proof and justification with an instrumental outlook which emphasizes its usefulness in the analysis of real life arguing.
When people apply the principles of logic to employ and evaluate arguments in real life situations and studies, they are using informal logic.
Why Is Logic Important?
Logic is one of the most respected elements of scholarly and professional thinking and writing. Consider that logic teaches us how to recognize good and bad arguments—not just arguments about logic, any argument. Nearly every undertaking in life will ultimately require that you evaluate an argument, perhaps several. You are confronted with a question: “Should I buy this car or that car?” “Should I go to this college or that college?” “Did that scientific experiment show what the scientist claims it did?” “Should I vote for the candidate who promises to lower taxes, or for the one who says she might raise them?” Your life is a long parade of choices.
When answering such questions, to make the best choices, you often have only one tool: an argument. You listen to the reasons for and against various options and must choose among them. Thus, the ability to evaluate arguments is an ability useful in everything that you will do—in your work, your personal life, and your deepest reflections. This is the job of logic.
If you are a student, note that nearly every discipline–be it a science, one of the humanities, or a study like business–relies upon arguments. Evaluating arguments is the most fundamental skill common to math, physics, psychology, history, literary studies, and any other intellectual endeavor. Logic alone tells you how to evaluate the arguments of any discipline.
The alternative to developing logic skills is to be always at the mercy of bad reasoning and, as a result, bad choices. Worse, you can be manipulated by deceivers. Speaking in Canandaigua, New York, on August 3, 1857, the escaped slave and abolitionist leader Frederick Douglass observed,
Power concedes nothing without a demand. It never did and it never will. Find out just what any people will quietly submit to and you have found out the exact measure of injustice and wrong which will be imposed upon them, and these will continue till they are resisted with either words or blows, or with both. The limits of tyrants are prescribed by the endurance of those whom they oppress.
Add this to Frederick Douglass’s words: If you find out just how much a person can be deceived, that is just how far she will be deceived. The limits of tyrants are also prescribed by the reasoning abilities of those they aim to oppress. What logic teaches you is how to demand and recognize good reasoning, and, hence, avoid deceit. You are only as free as your powers of reasoning enable.
The remaining part of this logic section will concern two types of logical arguments— inductive and deductive —and the tests of those arguments, including validity , soundness , reliability , and strength , so that you can check your own arguments and evaluate the arguments of others, no matter if those arguments come from the various academic disciplines, politics, the business world, or just discussions with friends and family.
What Is Deductive Argument?
A deductive argument is an argument whose conclusion is supposed to follow from its premises with absolute certainty, thus leaving no possibility that the conclusion doesn’t follow from the premises. If a deductive argument fails to guarantee the truth of the conclusion, then the deductive argument can no longer be called a deductive argument.
The Tests of Deductive Arguments: Validity and Soundness
So far in this chapter, you have learned what arguments are and how to determine their structure, including how to reconstruct arguments in standard form. But what makes an argument good or bad? There are four main ways to test arguments, two of which are for deductive arguments. The first test for deductive arguments is validity , a concept that is central to logical thinking. Validity relates to how well the premises support the conclusion and is the golden standard that every deductive argument should aim for. A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true. Another way to put this is as a conditional statement: A valid argument is an argument in which if the premises are true, the conclusion must be true. Here is an example of a valid argument:
Violet is a dog.
Therefore, Violet is a mammal. (from 1)
You might wonder whether it is true that Violet is a dog (maybe she’s a lizard or a buffalo—you have no way of knowing from the information given). But, for the purposes of validity, it doesn’t matter whether premise 1 is actually true or false. All that matters for validity is whether the conclusion follows from the premise. You can see that the conclusion—that Violet is a mammal—does seem to follow from the premise—that Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. This argument is clearly valid because if you assume that “Violet is a dog” is true, then, since all dogs are mammals, it follows that “Violet is a mammal” must also be true. Thus, whether an argument is valid has nothing to do with whether the premises of the argument are actually true. Here is an example where the premises are clearly false, yet the argument is valid:
Everyone born in France can speak French.
Barack Obama was born in France.
Therefore, Barack Obama can speak French. (from 1-2)
This is a valid argument. Why? Because when you assume the truth of the premises (everyone born in France can speak French, and Barack Obama was born in France) the conclusion (Barack Obama can speak French) must be true. Notice that this is so even though none of these statements is actually true. Not everyone born in France can speak French (think about people who were born there but then moved somewhere else where they didn’t speak French and never learned it), and Barack Obama was not born in France, but it is also false that Obama can speak French. However, the argument is still valid even though neither the premises nor the conclusion is actually true. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true.
To better understand the concept of validity, examine this example of an invalid argument:
George was President of the United States.
Therefore, George was elected President of the United States. (from 1)
This argument is invalid because it is possible for the premise to be true and yet the conclusion false. Here is a counterexample to the argument. Gerald Ford was President of the United States, but he was never elected president because Ford replaced Richard Nixon when Nixon resigned in the wake of the Watergate scandal. Therefore, it does not follow that just because someone is President of the United States that he was elected President of the United States. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. This means that the argument is invalid. If an argument is invalid, it will always be possible to construct a counterexample to show that it is invalid (as demonstrated in the Gerald Ford scenario). A counterexample is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.
Determine whether the following arguments are valid by using an informal test of validity. In other words, ask whether you can imagine a scenario in which the premises are both true and yet the conclusion is false. For each argument do the following: (1) If the argument is valid, explain your reasoning, and (2) if the argument is invalid, provide a counterexample. Remember, this is a test of validity, so you may assume all premises are true (even if you know or suspect they are not in real life) for the purposes of this assignment.
1. Katie is a human being. Therefore, Katie is smarter than a chimpanzee.
2. Bob is a fireman. Therefore, Bob has put out fires.
3. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.
4. Monica is a French teacher. Therefore, Monica knows how to teach French.
5. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.
7. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.
8. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.
9. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.
10. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.
A good deductive argument is not only valid but also sound . A sound argument is a valid argument that has all true premises. That means that the conclusion, or claim, of a sound argument will always be true because if an argument is valid, the premises transmit truth to the conclusion on the assumption of the truth of the premises. If the premises are actually true, as they are in a sound argument, and since all sound arguments are valid, we know that the conclusion of a sound argument is true. The relationship between soundness and validity is easy to specify: all sound arguments are valid arguments, but not all valid arguments are sound arguments .
Professors will expect sound arguments in college writing. Philosophy professors, for the sake of pursuing arguments based on logic alone, may allow students to pursue unsound arguments, but nearly all other professors will want sound arguments. How do you make sure that all the premises of your argument are true? How can we know that Violet is a dog or that littering is harmful to animals and people? Answers to these questions come from evidence , often in the form of research.
One way to counter another’s argument is to question his premises and test them for soundness. If you find that one or more premise is unsound, you can add that information–and your explanations–to the support of your own argument.
One way to test the accuracy of a premise is to apply the following questions:
Is there a sufficient amount of data?
What is the quality of the data?
Has additional data been missed?
Is the data relevant?
Are there additional possible explanations?
Determine whether the starting claim is based upon a sample that is both representative and sufficiently large, and ask yourself whether all relevant factors have been taken into account in the analysis of data that leads to a generalization.
Another way to evaluate a premise is to determine whether its source is credible. Ask yourself,
Are the authors identified?
What are their backgrounds?
Was the claim something you found on an undocumented website?
Did you find it in a popular publication or a scholarly one?
How complete, how recent, and how relevant are the studies or statistics discussed in the source?
What Is Inductive Argument?
In contrast to a deductive argument, an inductive argument is an argument whose conclusion is supposed to follow from its premises with a high level of probability, which means that although it is possible that the conclusion doesn’t follow from its premises, it is unlikely that this is the case. Here is an example of an inductive argument:
Tweets is a healthy, normally functioning bird and since most healthy, normally functioning birds fly, Tweets most likely flies.
Notice that the conclusion, “Tweets probably flies,” contains the words “most likely.” This is a clear indicator that the argument is supposed to be inductive, not deductive. Here is the argument in standard form:
Tweets is a healthy, normally functioning bird. ( premise )
Most healthy, normally functioning birds fly. ( premise )
Therefore, Tweets probably flies. ( conclusion )
Given the information provided by the premises, the conclusion does seem to be well supported. That is, the premises provide strong reasons for accepting the conclusion. The inductive argument’s conclusion is a strong one, even though we can imagine a scenario in which the premises are true and yet the conclusion is false.
Remember, inductive arguments cannot guarantee the truth of the conclusion, which means they will look like invalid deductive arguments. Indeed, they are. There will be counterexamples for inductive arguments because an inductive argument never promises absolute truth. We measure inductive arguments by degrees of probability and plausibility , not absolute categories like validity and soundness. Validity and soundness do not allow for a sliding scale of degrees. They are absolute conditions: There is no such thing as being partially valid or somewhat sound.
Do not let this difference between deductive and inductive arguments cause you to privilege deductive and revile inductive because inductive arguments cannot guarantee truth. That is an unfair measure, and it is not practical. The truth is that most arguments we create and evaluate in life are inductive arguments. It might be helpful to think of deductive arguments as those created in perfect lab conditions, where all the ideal parameters can be met. Life is much messier than that, and we rarely get ideal conditions. One main reason is that we rarely ever have all the information we need to form an absolutely true conclusion. When new information is discovered, a scientist or historian or psychologist or business executive or a college student should investigate how it affects previous ideas and arguments, knowing that those previous ideas may need to be adjusted based on new information. For example, suppose that we added the following premise to our earlier argument:
Tweets is 6 feet tall and can run 30 mph. ( premise )
When we add this premise, the conclusion that Tweets can fly would no longer be likely because any bird that is 6 feet tall and can run 30 mph, is not a kind of bird that can fly. That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly.
The Tests of Inductive Arguments: Reliability and Strength
Inductive arguments can never lead to absolute certainty, which is one reason scholars keep studying and trying to add to knowledge. This does not mean, however, that any inductive argument will be a good one. Inductive arguments must still be evaluated and tested, and the two main tests are reliability and strength .
Test of reliability , much like that of validity for deductive arguments, tests an inductive argument’s reason, its internal logic. In other words, just because an inductive argument cannot guarantee a true conclusion doesn’t mean that it should not be logically constructed. One cannot make just any sort of claim, particularly one that does not have a reliable basis. Reliability, unlike validity, can be measured by degree. More reliable arguments are ones that have a more solid basis in reason. Consider this example:
Ninety-seven percent of Banana TM computers work without any glitches. ( premise )
Max has a Banana TM computer. ( premise )
Therefore, Max’s computer works without any glitches. ( conclusion )
This argument has a high degree of reliability. While it may well be true that Max has one of the three percent of computers that have glitches, it is much more likely, given the initial premise that he does not. If the initial premise changes, however, so does the reliability of the argument:
Thirty-three percent of Banana TM computers work without any glitches.
Max has a Banana TM computer.
Therefore, Max’s computer works without any glitches.
Note how the degree of reliability has gone done dramatically. The argument can now be considered unreliable since the conclusion that Max’s computer will work without glitches is improbable given the premises provided. The conclusion still could be true, but it has tipped toward unlikely.
The second test of inductive arguments is strength . Strength, like reliability, can be measured by degree. Strong arguments must have the following conditions: (1) They must be reliable arguments; (2) they draw upon multiple lines of reasoning as support and/or a collection of data. Indeed, the more the data and the more the reasons for a conclusion, the stronger the argument. Consider the following argument:
Susie has walked by Mack the dog every day for ten days. ( premise )
Mack the dog has never bitten Susie. ( premise )
Thus, when Susie walks by Mack the dog today, he will not bite her. ( conclusion )
This argument is reasonable; we can see that the premises may logically lead to the conclusion. However, the argument is not very strong as Susie has only walked by the dog for ten days. Is that enough data to make the conclusion a likely one? What if we had more data, like so—
Susie has walked by Mack the dog every day for five years.
Mack the dog has never bitten Susie.
Thus, when Susie walks by Mack the dog today, he will not bite her.
This argument, with more data to consider (five years of information instead of just ten days), is much stronger. An argument also gets stronger when reasons are added:
Mack’s owners trained him to be friendly to people. ( additional premise )
Mack the dog’s breed is not known for aggression. ( additional premise )
This argument is even stronger. Not only does it have more data, but it also has additional reasons for Mack’s gentle nature.
Remember these tests when writing your own essays. You are most likely going to be using inductive arguments, and you should make them as reliable and strong as you can because you can bet your professors will be evaluating your arguments by those criteria as well.
What Are Logical Fallacies, and Why Should You Avoid Them?
Fallacies are errors or tricks of reasoning. A fallacy is an error of reasoning if it occurs accidentally; it is a trick of reasoning if a speaker or writer uses it to deceive or manipulate his audience. Fallacies can be either formal or informal .
Whether a fallacy is an error or a trick, whether it is formal or informal, its use undercuts the validity and soundness of any argument. At the same time, fallacious reasoning can damage the credibility of the speaker or writer and improperly manipulate the emotions of the audience or reader. This is a consideration you must keep in mind as a writer who is trying to maintain credibility ( ethos ) with the reader. Moreover, being able to recognize logical fallacies in the speech and writing of others can greatly benefit you as both a college student and a participant in civic life. Not only does this awareness increase your ability to think and read critically—and thus not be manipulated or fooled—but it also provides you with a strong basis for counter arguments.
Even more important, using faulty reasoning is unethical and irresponsible. Using logical fallacies can be incredibly tempting. The unfortunate fact is they work. Every day—particularly in politics and advertising—we can see how using faults and tricks of logic effectively persuade people to support certain individuals, groups, and ideas and, conversely, turn them away from others. Furthermore, logical fallacies are easy to use. Instead of doing the often difficult work of carefully supporting an argument with facts, logic, and researched evidence, the lazy debater turns routinely to the easy path of tricky reasoning. Human beings too often favor what is easy and effective, even if morally questionable, over what is ethical, particularly if difficult. However, your college professors’ task is not to teach you how to join the Dark Side. Their job is to teach you how to write, speak, and argue effectively and ethically . To do so, you must recognize and avoid the logical fallacies.
What Are Formal Fallacies?
Most formal fallacies are errors of logic: The conclusion does not really “follow from” (is not supported by) the premises. Either the premises are untrue, or the argument is invalid. Below is an example of an invalid deductive argument:
Premise : All black bears are omnivores.
Premise : All raccoons are omnivores.
Conclusion : All raccoons are black bears.
Bears are a subset of omnivores. Raccoons also are a subset of omnivores. But these two subsets do not overlap, and that fact makes the conclusion illogical. The argument is invalid—that is, the relationship between the two premises does not support the conclusion.
“Raccoons are black bears” is instantaneously recognizable as fallacious and may seem too silly to be worth bothering about. However, that and other forms of poor logic play out on a daily basis, and they have real world consequences. Below is an example of a common fallacious argument:
Premise : All Arabs are Muslims.
Premise : All Iranians are Muslims.
Conclusion : All Iranians are Arabs.
This argument fails on two levels. First, the premises are untrue because, although many Arabs and Iranians are Muslim, not all are. Second, the two ethnic groups (Iranians and Arabs) are sets that do not overlap; nevertheless, the two groups are confounded because they (largely) share one quality in common (being Muslim). One only has to look at comments on the web to realize that the confusion is widespread and that it influences attitudes and opinions about US foreign policy. The logical problems make this both an invalid and an unsound argument.
What Are Informal Fallacies?
Informal fallacies take many forms and are widespread in everyday discourse. Very often they involve bringing irrelevant information into an argument, or they are based on assumptions that, when examined, prove to be incorrect. Formal fallacies are created when the relationship between premises and conclusion does not hold up or when premises are unsound; informal fallacies are more dependent on misuse of language and of evidence.
It is easy to find lists of informal fallacies, but that does not mean that it is always easy to spot them.
How Can You Check for Logical Fallacies?
One way to go about evaluating an argument for fallacies is to return to the concept of the three fundamental appeals: ethos , logos , and pathos . As a quick reminder,
Ethos is an appeal to ethics, authority, and/or credibility.
Logos is an appeal to logic.
Pathos is an appeal to emotion.
Once you have refreshed your memory of the basics, you may begin to understand how ethos, logos, and pathos can be used appropriately to strengthen your argument or inappropriately to manipulate an audience through the use of fallacies. Classifying fallacies as fallacies of ethos, logos, or pathos will help you to understand their nature and to recognize them. Please keep in mind, however, that some fallacies may fit into multiple categories. For more details and examples on errors in the rhetorical appeals, see Chapter 2, “Rhetorical Analysis.”
Fallacies of ethos relate to credibility. These fallacies may unfairly build up the credibility of the author (or his allies) or unfairly attack the credibility of the author’s opponent (or her allies). Some fallacies give an unfair advantage to the claims of the speaker or writer or an unfair disadvantage to his opponent’s claims. These are fallacies of logos . Fallacies of pathos rely excessively upon emotional appeals, attaching positive associations to the author’s argument and negative ones to his opponent’s position.
Key Takeaways: Logic
Logic —shows how ideas fit together by using reason.
Formal Logic —a formal and rigorous study of logic, such as in math and philosophy.
Informal Logic —the application of logic to arguments of all types: in scholarship, in business, and in life. Informal logic is what this part of the chapter covers.
Deductive Argument —guarantees a true conclusion based on the premises. The tests for deductive arguments are validity and soundness.
Validity —a way to evaluate a deductive argument; a valid argument is one which, if the premises are true, the conclusion must be true.
Soundness —the second way to evaluate a deductive argument; a sound argument is one where the argument is valid AND the premises have been shown to be true (via support).
Inductive Argument —cannot guarantee a true conclusion but can only assert what is most likely to be true based on the premises and the support. The tests for inductive arguments are reliability and strength.
Reliability —a test of reason for inductive arguments. Inductive arguments must still be reasonable, must still have a reliable basis in logic.
Strength —another test for inductive arguments. Inductive arguments are stronger when they have more reasons and more data to support them.
Logical Fallacy —a flaw or trick of logic to be avoided at all costs. Fallacies can be formal or informal. See the Repository of Logical Fallacies below for individual examples.
Hermione Granger got it right when, facing the potion-master's test in Harry Potter, she said: "This isn't magic - it's logic - a puzzle. A lot of the greatest wizards haven't got an ounce of logic; they'd be stuck here forever."
In the real world, we are better off. We use Logic in just about everything we do. We use it in our professional lives - in proving mathematical theorems, in debugging computer programs, in medical diagnosis, and in legal reasoning. And we use it in our personal lives - in solving puzzles, in playing games, and in doing school assignments, not just in Math but also in History and English and other subjects.
Just because we use Logic does not mean we are necessarily good at it. Thinking correctly and effectively requires training in Logic, just as writing well requires training in English and composition. Without explicit training, we are likely to be unsure of our conclusions; we are prone to make mistakes; and we are apt to be fooled by others.
The ancient Greeks thought Logic sufficiently important that it was one of the three subjects in the Greek educational Trivium, along with Grammar and Rhetoric. Oddly, Logic occupies a relatively small place in the modern school curriculum. We have courses in the Sciences and various branches of Mathematics, but very few secondary schools offer courses in Logic; and it is not required in most university programs.
Given the importance of the subject, this is surprising. Calculus is important to physics. And it is widely taught at the high school level. Logic is important in all of these disciplines, and it is essential in computer science. Yet it is rarely offered as a standalone course, making it more difficult for students to succeed and get better quality jobs.
This course is a basic introduction to Logic. It is intended primarily for university students. However, it has been used by motivated secondary school students and post-graduate professionals interested in honing their logical reasoning skills.
There are just two prerequisites. The course presumes that the student understands sets and set operations, such as union, intersection, and complement. The course also presumes that the student is comfortable with symbolic mathematics, at the level of high-school algebra. Nothing else is required.
This chapter is an overview of the course. We start with a look at the essential elements of logic - logical sentences, logical entailment, and logical proofs. We then see some of the problems with the use of natural language and see how those problems can be mitigated through the use of Symbolic Logic. Finally, we discuss the automation of logical reasoning and some of the computer applications that this makes possible.
1.2 Logical Sentences
For many, Logic is an esoteric subject. It is used primarily by mathematicians in proving complicated theorems in geometry or number theory. It is all about writing formal proofs to be published in scholarly papers that have little to do with everyday life. Nothing could be further from the truth.
As an example of using Logic in everyday life, consider the interpersonal relations of a small group of friends. There are just four members - Abby, Bess, Cody, and Dana. Some of the girls like each other, but some do not.
The figure on the left below shows one set of possibilities. The checkmark in the first row here means that Abby likes Cody, while the absence of a checkmark means that Abby does not like the other girls (including herself). Bess likes Cody too. Cody likes everyone but herself. And Dana also likes the popular Cody. Of course, this is not the only possible state of affairs. The figure on the right shows another possible world. In this world, every girl likes exactly two other girls, and every girl is liked by just two girls.
Let's assume that we do not know the likes and dislikes of the girls ourselves but we have informants who are willing to tell us about them. Each informant knows a little about the likes and dislikes of the girls, but no one knows everything.
This is where Logic comes in. By writing logical sentences , each informant can express exactly what he or she knows - no more, no less. The following sentences are examples of different types of logical sentences. The first sentence is straightforward; it tells us directly that Dana likes Cody. The second and third sentences tell us what is not true without saying what is true. The fourth sentence says that one condition holds or another but does not say which. The fifth sentence gives a general fact about the girls Abby likes. The sixth sentence expresses a general fact about Cody's likes. The last sentence says something about everyone.
Dana likes Cody.
Abby does like Dana.
Dana does like Abby.
Bess likes Cody Dana.
Abby likes that Bess likes.
Cody likes who likes her.
likes herself
Looking at the worlds above, we see that all of these sentences are true in the world on the left. By contrast, several of the sentences are false in the world on the right. Hence, we can rule out the second world.
Of course, in general, there are more than two possible worlds to consider. As it turns out, there are quite a few possibilities. Given four girls, there are sixteen possible instances of the likes relation - Abby likes Abby, Abby likes Bess, Abby likes Cody, Abby likes Dana, Bess likes Abby, and so forth. Each of these sixteen can be either true or false. There are 2 16 (65,536) possible combinations of these true-false possibilities, and so there are 2 16 possible worlds.
Logical sentences like the ones above constrain the possible ways the world could be. Each sentence divides the set of possible worlds into two subsets, those in which the sentence is true and those in which the sentence is false, as suggested by the following figure. Believing a sentence is tantamount to believing that the world is in the first set.
Given two sentences, we know the world must be in the intersection of the set of worlds in which the first sentence is true and the set of worlds in which the second sentence is true.
Ideally, when we have enough sentences, we know exactly how things stand.
Effective communication requires a language that allows us to express what we know, no more and no less. If we know the state of the world, then we should write enough sentences to communicate this to others. If we do not know which of various ways the world could be, we need a language that allows us to express only what we know, i.e. which worlds are possible and which are not. The language of Logic gives us a means to express incomplete information when that is all we have and to express complete information when full information is available.
1.3 Logical Entailment
Once we know which world is correct, we can see that some sentences must be true even though they are not included in the premises we are given. For example, in the first world we saw above, we can see that Bess likes Cody, even though we are not told this fact explicitly. Similarly, we can see that Abby does not like Bess.
Unfortunately, things are not always so simple. Although logical sentences can sometimes pinpoint a specific world from among many possible worlds, this is not always the case. Sometimes, a collection of sentences only partially constrains the world. For example, there are four different worlds that satisfy the sentences in the previous section.
In situations like this, which world should we use in answering questions? The good news it that sometimes it does not matter. Even though a set of sentences does not determine a unique world, there are some sentences that have the same truth value in every world that satisfies the given sentences, and we can use that value in answering questions.
This is logical entailment . We say that a set of premises logically entails a conclusion if and only if every world that satisfies the premises also satisfies the conclusion.
What can we conclude from the bits of information in our sample logical sentences? Quite a bit, as it turns out. In our example, we see that Bess likes Cody in all four worlds. We also see Bess does not like Abby in all four worlds. Does Dana like Bess? Since there are different values in different worlds, we cannot say yes and we cannot say no. All we can say is Maybe. In the real world, either Dana likes Bess or she doesn't. However, we do not have enough information to say which case is correct.
Model checking is the process of examining the set of all worlds to determine logical entailment. To check whether a set of sentences logically entails a conclusion, we use our premises to determine which worlds are possible and then examine those worlds to see whether or not they satisfy our conclusion. If the number of worlds is not too large, this method works well.
Unfortunately, in general, there are many, many possible worlds; and, in some cases, the number of possible worlds is infinite, in which case model checking is impossible. So what do we do? The answer is logical reasoning and logical proofs.
1.4 Logical Proofs
Logical proofs are analogous to derivations in algebra. We can try solving algebraic equations by randomly trying different values for the variables in those equations. However, we can usually get to an answer faster by manipulating our equations syntactically. Logical reasoning is similar. Rather than checking all worlds, we simply apply syntactic operations to the premises we are given to generate conclusions.
One of Aristotle's great contributions to philosophy was the identification of syntactic operations that . Such operations are typically called rules of inference . By applying rules of inference to premises, we produce conclusions that are entailed by those premises. A proof is a sequence of such rule applications. We can think of individual reasoning steps as the atoms out of which proof molecules are built.
As an example of a rule of inference, consider the reasoning step shown below. We know that all Accords are Hondas, and we know that all Hondas are Japanese cars. Consequently, we can conclude that all Accords are Japanese cars.
Now consider another example. We know that all borogoves are slithy toves, and we know that all slithy toves are mimsy. Consequently, we can conclude that all borogoves are mimsy. What's more, in order to reach this conclusion, we do not need to know anything about borogoves or slithy toves or what it means to be mimsy.
What is interesting about these examples is that they share the same reasoning structure, viz. the pattern shown below.
Two things are worthy of note here. First of all, correctness in logical reasoning is determined by the logical operators in our sentences, not the objects and relationships mentioned in those sentences. Second, the conclusion is guaranteed to be true only if the premises are true.
The philosopher Bertrand Russell summed this situation up as follows. Logic may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true . We do not need to know anything about the concepts in our premises except for the information expressed in those premises. Furthermore, while our conclusion must be true if our premises are true, it can be false if one or more of our premises is false.
The existence of reasoning patterns is fundamental in Logic but raises important questions. Which rules of inference are correct? Are there many such patterns or just a few?
Let us consider the first of these questions. Obviously, there are patterns that are just plain wrong in the sense that they can lead to incorrect conclusions. Consider, as an example, the faulty reasoning pattern shown below.
Now let us take a look at an instance of this pattern. If we replace x by Toyotas and y by cars and z by made in America , we get the following line of argument, leading to a conclusion that happens to be correct.
On the other hand, if we replace x by Toyotas and y by cars and z by Porsches , we get a line of argument leading to a conclusion that is questionable.
What distinguishes a correct pattern from one that is incorrect is that it must always lead to correct conclusions, i.e. they must be correct so long as the premises on which they are based are correct. As we will see, this is the defining criterion for what we call deduction .
Now, it is noteworthy that there are patterns of reasoning that are not always correct but are sometimes useful. There is induction, abduction, analogy, and so forth.
Induction is reasoning from the particular to the general. The example shown below illustrates this. In this case, the induction is incomplete. Although we have seen many ravens, we have not seen them all. However, if we see enough cases in which something is true and we never see a case in which it is false, we tend to conclude that it is always true. Unfortunately, when induction is incomplete, as in this case, it is not sound. There might be an albino raven that we have not yet seen.
Now try red Hondas.
Incomplete induction is the basis for Science (and machine learning). Deduction is the subject matter of Logic. Science aspires to discover / propose new knowledge. Logic aspires to apply and/or analyze existing knowledge.
This distinction was at the heart of a famous disagreement between the physicist Albert Einstein and his contemporary Niels Bohr in which Bohr derided Einstein's emphasis on deduction rather than induction. He reputedly told Einstein: You are not thinking; you are just being logical. Bohr was a fan of induction and thought that Einstein placed too much emphasis on deduction.
Of all types of reasoning, deduction is the only one that guarantees its conclusions in all cases, it produces only those conclusions that are logically entailed by one's premises.
In talking about Logic, we now have two notions - logical entailment and provability. A set of premises logically entails a conclusion if and only if every possible world that satisfies the premises also satisfies the conclusion. A sentence is provable from a set of premises if and only if there is a finite sequence of sentences in which every element is either a premise or the result of applying a deductive rule of inference to earlier members in the sequence.
These concepts are quite different. One is based on possible worlds; the other is based on symbolic manipulation of expressions. Yet, for "well-behaved" logics, it turns out that logical entailment and provability are identical - a set of premises logically entails a conclusion if and only if the conclusion is provable from the premises. Even if the number of worlds is infinite , it is possible in such logics to produce a finite proof of the conclusion, i.e. we can determine logical entailment without going through all possible worlds. This is a very big deal.
1.5 Symbolic Logic
So far, we have illustrated everything with sentences in English. While natural language works well in many circumstances, it is not without its problems. Natural language sentences can be complex; they can be ambiguous; and failing to understand the meaning of a sentence can lead to errors in reasoning.
As an example of ambiguity, suppose I were to write the sentence There's a girl in the room with a telescope . See the following figure for two possible meanings of this sentence. Am I saying that there is a girl in a room containing a telescope? Or am I saying that there is a girl in the room and she is holding a telescope?
Such complexities and ambiguities can sometimes be humorous if they lead to interpretations the author did not intend. See the examples below for some infamous newspaper headlines with multiple interpretations. Using a formal language eliminates such unintentional ambiguities (and, for better or worse, avoids any unintentional humor as well).
Crowds Rushing to See Pope Trample 6 to Death
Journal Star, Peoria, 1980
Scientists Grow Frog Eyes and Ears
British Left Waffles On Falkland Islands
The Daily Camera, Boulder, 2000
Food Stamp Recipients Turn to Plastic
Indian Ocean Talks
The Miami Herald, 1991
The Plain Dealer, 1977
Fried Chicken Cooked in Microwave Wins Trip
The Oregonian, Portland, 1981
As an illustration of errors that arise in reasoning with sentences in natural language, consider the following examples. In the first, we use the transitivity of the better relation to derive a conclusion about the relative quality of champagne and soda from the relative quality of champagne and beer and the relative quality or beer and soda. So far so good.
Champagne is better than beer.
Beer is better than soda.
Therefore, champagne is better than soda.
This makes sense. It is an example of a general rule about the transitivity of the better relation. If x is better than y and y is better than z, then x better than z.
x is better than y.
y is better than z.
Therefore, x is better than z.
Now, consider what happens when we apply this rule in the case illustrated below. Bad sex is better than nothing. Nothing is better than good sex. Therefore, bad sex is better than good sex. Really?
Bad sex is better than nothing.
Nothing is better than good sex.
Therefore, bad sex is better than good sex.
The form of the argument is the same as in the previous example, but the conclusion is somewhat less believable. The problem in this case is that the use of nothing here is syntactically similar to the use of beer in the preceding example, but in English it means something entirely different.
Logic eliminates these difficulties through the use of a formal language for encoding information. Given the syntax and semantics of this formal language, we can give a precise definition for the notion of logical conclusion. Moreover, we can establish precise reasoning rules that produce all and only logical conclusions.
In this regard, there is a strong analogy between the methods of Formal Logic and those of high school algebra. To illustrate this analogy, consider the following algebra problem.
Xavier is three times as old as Yolanda. Xavier's age and Yolanda's age add up to twelve. How old are Xavier and Yolanda?
Typically, the first step in solving such a problem is to express the information in the form of equations. If we let x represent the age of Xavier and y represent the age of Yolanda, we can capture the essential information of the problem as shown below.
- 3 = 0
+ = 12
Using the methods of algebra, we can then manipulate these expressions to solve the problem. First we subtract the second equation from the first.
- 3 = 0
+ = 12
-4 = -12
Next, we divide each side of the resulting equation by -4 to get a value for y . Then substituting back into one of the preceding equations, we get a value for x .
= 9
= 3
Now, consider the following logic problem.
If Mary loves Pat, then Mary loves Quincy. If it is Monday and raining, then Mary loves Pat or Quincy. If it is Monday and raining, does Mary love Quincy?
As with the algebra problem, the first step is formalization. Let p represent the possibility that Mary loves Pat; let q represent the possibility that Mary loves Quincy; let m represent the possibility that it is Monday; and let r represent the possibility that it is raining.
With these abbreviations, we can represent the essential information of this problem with the following logical sentences. The first says that p implies q , i.e. if Mary loves Pat, then Mary loves Quincy. The second says that m and r implies p or q , i.e. if it is Monday and raining, then Mary loves Pat or Mary loves Quincy.
⇒
∧
⇒
∨
As with Algebra, Formal Logic defines certain operations that we can use to manipulate expressions. The operation shown below is a variant of what is called Propositional Resolution . The expressions above the line are the premises of the rule, and the expression below is the conclusion.
∧ ... ∧
⇒
∨ ... ∨
∧ ... ∧
⇒
∨ ... ∨
∧ ... ∧ ∧ ∧ ... ∧
⇒
∨ ... ∨ ∨ ∨ ... ∨
There are two elaborations of this operation. (1) If a proposition on the left hand side of one sentence is the same as a proposition on the right hand side of the other sentence, it is okay to drop the two symbols, with the proviso that only one such pair may be dropped. (2) If a constant is repeated on the same side of a single sentence, all but one of the occurrences can be deleted.
We can use this operation to solve the problem of Mary's love life. Looking at the two premises above, we notice that p occurs on the left-hand side of one sentence and the right-hand side of the other. Consequently, we can cancel the p and thereby derive the conclusion that, if is Monday and raining, then Mary loves Quincy or Mary loves Quincy.
⇒
∧
⇒
∨
∧
⇒
∨
Dropping the repeated symbol on the right hand side, we arrive at the conclusion that, if it is Monday and raining, then Mary loves Quincy.
∧
⇒
∨
∧
⇒
This example is interesting in that it showcases our formal language for encoding logical information. As with algebra, we use symbols to represent relevant aspects of the world in question, and we use operators to connect these symbols in order to express information about the things those symbols represent.
The example also introduces one of the most important operations in Formal Logic, viz. Resolution (in this case a restricted form of Resolution). Resolution has the property of being complete for an important class of logic problems, i.e. it is the only operation necessary to solve any problem in the class.
1.6 Automation
The existence of a formal language for representing information and the existence of a corresponding set of mechanical manipulation rules together have an important consequence, viz. the possibility of automated reasoning using digital computers.
The idea is simple. We use our formal representation to encode the premises of a problem as data structures in a computer, and we program the computer to apply our mechanical rules in a systematic way. The rules are applied until the desired conclusion is attained or until it is determined that the desired conclusion cannot be attained. (Unfortunately, in some cases, this determination cannot be made; and the procedure never halts. Nevertheless, as discussed in later chapters, the idea is basically sound.)
Although the prospect of automated reasoning has achieved practical realization only in the last few decades, it is interesting to note that the concept itself is not new. In fact, the idea of building machines capable of logical reasoning has a long tradition.
One of the first individuals to give voice to this idea was Leibnitz. He conceived of "a universal algebra by which all knowledge, including moral and metaphysical truths, can some day be brought within a single deductive system". Having already perfected a mechanical calculator for arithmetic, he argued that, with this universal algebra, it would be possible to build a machine capable of rendering the consequences of such a system mechanically.
Boole gave substance to this dream in the 1800s with the invention of Boolean algebra and with the creation of a machine capable of computing accordingly.
The early twentieth century brought additional advances in Logic, notably the invention of the predicate calculus by Russell and Whitehead and the proof of the corresponding completeness and incompleteness theorems by Godel in the 1930s.
The advent of the digital computer in the 1940s gave increased attention to the prospects for automated reasoning. Research in artificial intelligence led to the development of efficient algorithms for logical reasoning, highlighted by Robinson's invention of resolution theorem proving in the 1960s.
Today, the prospect of automated reasoning has moved from the realm of possibility to that of practicality, with the creation of logic technology in the form of automated reasoning systems, such as Vampire, Prover9, the Prolog Technology Theorem Prover, and others.
The emergence of this technology has led to the application of logic technology in a wide variety of areas. The following paragraphs outline some of these uses.
Mathematics. Automated reasoning programs can be used to check proofs and, in some cases, to produce proofs or portions of proofs.
Engineering. Engineers can use the language of Logic to write specifications for their products and to encode their designs. Automated reasoning tools can be used to simulate designs and in some cases validate that these designs meet their specification. Such tools can also be used to diagnose failures and to develop testing programs.
Database Systems. By conceptualizing database tables as sets of simple sentences, it is possible to use Logic in support of database systems. For example, the language of Logic can be used to define virtual views of data in terms of explicitly stored tables, and it can be used to encode constraints on databases. Automated reasoning techniques can be used to compute new tables, to detect problems, and to optimize queries.
Data Integration The language of Logic can be used to relate the vocabulary and structure of disparate data sources, and automated reasoning techniques can be used to integrate the data in these sources.
Law and Business. The language of Logic can be used to encode regulations and business rules, and automated reasoning techniques can be used to analyze such regulations for inconsistency and overlap.
1.7 Reading Guide
Although Logic is a single field of study, there is more than one logic in this field. In the three main units of this book, we look at three different types of logic, each more sophisticated than the one before.
Propositional Logic is the logic of propositions. Symbols in the language represent "conditions" in the world, and complex sentences in the language express interrelationships among these conditions. The primary operators are Boolean connectives, such as and , or , and not .
Relational Logic expands upon Propositional Logic by providing a means for explicitly talking about individual objects and their interrelationships (not just monolithic conditions). In order to do so, we expand our language to include object constants and relation constants, variables and quantifiers.
Functional Logic takes us one step further by providing a means for describing worlds with infinitely many objects. The resulting logic is much more powerful than Propositional Logic and Relational Logic. Unfortunately, as we shall see, some of the nice computational properties of the first two logics are lost as a result.
Each logic introduces new issues and capabilities. Despite their differences, there are many commonalities among these logics. In particular, in each case, there is a language with a formal syntax and a precise semantics; there is a notion of logical entailment; and there are legal rules for manipulating expressions in the language.
These similarities allow us to compare the logics and to gain an appreciation of the fundamental tradeoff between expressiveness and computational complexity. On the one hand, the introduction of additional linguistic complexity makes it possible to say things that cannot be said in more restricted languages. On the other hand, the introduction of additional linguistic flexibility has adverse effects on computability. As we proceed though the material, our attention will range from the completely computable case of Propositional Logic to a variant that is not at all computable.
There are also some topics that are relevant to Logic but are out of scope for this course, such as probability, metaknowledge (knowledge about knowledge), and paradoxes (e.g. This sentence is false. ). Also, negation as failure ( knowing not versus not knowing , non-deductive reasoning methods (like induction), and paraconsistent reasoning (i.e. reasoning from inconsistent premises). We touch on these extensions in this course, but we do not talk about them in any depth.
One final comment. In the hopes of preventing difficulties, it is worth pointing out a potential source of confusion. This book exists in the meta world. It contains sentences about sentences; it contains proofs about proofs. In some places, we use similar mathematical symbology both for sentences in Logic and sentences about Logic. Wherever possible, we try to be clear about this distinction, but the potential for confusion remains. Unfortunately, this comes with the territory. We are using Logic to study Logic. It is our most powerful intellectual tool.
Logic is the study of information encoded in the form of logical sentences. Each logical sentence divides the set of all possible world into two subsets - the set of worlds in which the sentence is true and the set of worlds in which the set of sentences is false. A set of premises logically entails a conclusion if and only if the conclusion is true in every world in which all of the premises are true. Deduction is a form of symbolic reasoning that produces conclusions that are logically entailed by premises (distinguishing it from other forms of reasoning, such as induction , abduction , and analogical reasoning ). A proof is a sequence of simple, more-or-less obvious deductive steps that justifies a conclusion that may not be immediately obvious from given premises. In Logic, we usually encode logical information as sentences in formal languages; and we use rules of inference appropriate to these languages. Such formal representations and methods are useful for us to use ourselves. Moreover, they allow us to automate the process of deduction, though the computability of such implementations varies with the complexity of the sentences involved.
Exercise 1.1: Consider the state of the Sorority World depicted below.
Abby
Bess
Cody
Dana
Abby
Bess
Cody
Dana
For each of the following sentences, say whether or not it is true in this state of the world.
( )
( )
( )
( )
( )
Exercise 1.2: Consider the state of the Sorority World depicted below.
Exercise 1.3: Consider the state of the Sorority World depicted below.
Exercise 1.4: Come up with a table of likes and dislikes for the Sorority World that makes all of the following sentences true. Note that there is more than one such table.
Exercise 1.5: Consider a set of Sorority World premises that are true in the four states of Sorority World shown in Section 1.4. For each of the following sentences, say whether or not it is logically entailed by these premises.
( )
( )
( )
Exercise 1.6: Consider the sentences shown below.
Everybody likes somebody.
Bess likes everyone Abby likes.
Bess does not like Dana.
Nobody likes herself.
Say whether each of the following sentences is logically entailed by these sentences.
( )
( )
( )
( )
Exercise 1.7: Say whether or not the following reasoning patterns are logically correct.
( )
( )
( )
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Introduction
Nature and varieties of logic
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Intensional logic
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philosophy of logic
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Routledge Encyclopedia of Philosophy - Philosophy of Logic
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philosophy of logic , the study, from a philosophical perspective, of the nature and types of logic , including problems in the field and the relation of logic to mathematics and other disciplines .
The term logic comes from the Greek word logos . The variety of senses that logos possesses may suggest the difficulties to be encountered in characterizing the nature and scope of logic. Among the partial translations of logos , there are “sentence,” “discourse,” “reason,” “rule,” “ratio,” “account” (especially the account of the meaning of an expression), “rational principle,” and “definition.” Not unlike this proliferation of meanings, the subject matter of logic has been said to be the “laws of thought ,” “the rules of right reasoning,” “the principles of valid argumentation,” “the use of certain words labelled ‘logical constants’,” “truths (true propositions) based solely on the meanings of the terms they contain,” and so on.
Logic as a discipline
It is relatively easy to discern some order in the above embarrassment of explanations. Some of the characterizations are in fact closely related to each other. When logic is said, for instance, to be the study of the laws of thought , these laws cannot be the empirical (or observable) regularities of actual human thinking as studied in psychology; they must be laws of correct reasoning , which are independent of the psychological idiosyncrasies of the thinker. Moreover, there is a parallelism between correct thinking and valid argumentation : valid argumentation may be thought of as an expression of correct thinking, and the latter as an internalization of the former. In the sense of this parallelism, laws of correct thought will match those of correct argumentation. The characteristic mark of the latter is, in turn, that they do not depend on any particular matters of fact. Whenever an argument that takes a reasoner from p to q is valid, it must hold independently of what he happens to know or believe about the subject matter of p and q . The only other source of the certainty of the connection between p and q , however, is presumably constituted by the meanings of the terms that the propositions p and q contain. These very same meanings will then also make the sentence “If p , then q ” true irrespective of all contingent matters of fact. More generally, one can validly argue from p to q if and only if the implication “If p , then q ” is logically true— i.e., true in virtue of the meanings of words occurring in p and q , independently of any matter of fact.
Logic may thus be characterized as the study of truths based completely on the meanings of the terms they contain.
In order to accommodate certain traditional ideas within the scope of this formulation, the meanings in question may have to be understood as embodying insights into the essences of the entities denoted by the terms, not merely codifications of customary linguistic usage.
The following proposition (from Aristotle), for instance, is a simple truth of logic: “If sight is perception, the objects of sight are objects of perception.” Its truth can be grasped without holding any opinions as to what, in fact, the relationship of sight to perception is. What is needed is merely an understanding of what is meant by such terms as “if–then,” “is,” and “are,” and an understanding that “object of” expresses some sort of relation.
The logical truth of Aristotle ’s sample proposition is reflected by the fact that “The objects of sight are objects of perception” can validly be inferred from “Sight is perception.”
Many questions nevertheless remain unanswered by this characterization. The contrast between matters of fact and relations between meanings that was relied on in the characterization has been challenged, together with the very notion of meaning. Even if both are accepted, there remains a considerable tension between a wider and a narrower conception of logic. According to the wider interpretation, all truths depending only on meanings belong to logic. It is in this sense that the word logic is to be taken in such designations as “epistemic logic” (logic of knowledge), “doxastic logic” (logic of belief), “deontic logic” (logic of norms), “the logic of science,” “inductive logic,” and so on. According to the narrower conception, logical truths obtain (or hold) in virtue of certain specific terms, often called logical constants . Whether they can be given an intrinsic characterization or whether they can be specified only by enumeration is a moot point. It is generally agreed, however, that they include (1) such propositional connectives as “not,” “and,” “or,” and “if–then” and (2) the so-called quantifiers “(∃ x )” (which may be read: “For at least one individual, call it x , it is true that”) and “(∀ x )” (“For each individual , call it x , it is true that”). The dummy letter x is here called a bound ( individual) variable. Its values are supposed to be members of some fixed class of entities, called individuals, a class that is variously known as the universe of discourse, the universe presupposed in an interpretation, or the domain of individuals. Its members are said to be quantified over in “(∃ x )” or “(∀ x ).” Furthermore, (3) the concept of identity (expressed by =) and (4) some notion of predication (an individual’s having a property or a relation’s holding between several individuals) belong to logic. The forms that the study of these logical constants take are described in greater detail in the article logic, in which the different kinds of logical notation are also explained. Here, only a delineation of the field of logic is given.
When the terms in (1) alone are studied, the field is called propositional logic. When (1), (2), and (4) are considered, the field is the central area of logic that is variously known as first-order logic, quantification theory, lower predicate calculus , lower functional calculus, or elementary logic. If the absence of (3) is stressed, the epithet “without identity” is added, in contrast to first-order logic with identity, in which (3) is also included.
Borderline cases between logical and nonlogical constants are the following (among others): (1) Higher order quantification, which means quantification not over the individuals belonging to a given universe of discourse, as in first-order logic, but also over sets of individuals and sets of n -tuples of individuals. (Alternatively, the properties and relations that specify these sets may be quantified over.) This gives rise to second-order logic. The process can be repeated. Quantification over sets of such sets (or of n -tuples of such sets or over properties and relations of such sets) as are considered in second-order logic gives rise to third-order logic; and all logics of finite order form together the (simple) theory of (finite) types. (2) The membership relation, expressed by ∊, can be grafted on to first-order logic; it gives rise to set theory . (3) The concepts of (logical) necessity and (logical) possibility can be added.
This narrower sense of logic is related to the influential idea of logical form. In any given sentence, all of the nonlogical terms may be replaced by variables of the appropriate type, keeping only the logical constants intact. The result is a formula exhibiting the logical form of the sentence. If the formula results in a true sentence for any substitution of interpreted terms (of the appropriate logical type) for the variables, the formula and the sentence are said to be logically true (in the narrower sense of the expression).
11.1 Developing Your Sense of Logic
Learning outcomes.
By the end of this section, you will be able to:
Identify key rhetorical concepts and thought patterns in a variety of texts.
Explain how patterns of thought function for different audiences, purposes, and situations.
For the purposes of this course, logic means “reasoning based on thought and evidence.” In practical terms, logic is the ability to analyze and evaluate persuasive or argument writing for effectiveness. By extension, it also means that you can learn to use logic in your own argumentative writing. Like any other new skill, you are likely to learn best when you have a starting point. Here are some suggestions for how to begin thinking and writing logically:
Approach a topic with an open mind.
Consider what you already know about the topic.
Consider what you want to know about the topic.
Find credible information about the topic.
Base your judgments of the topic on sound reasoning and evidence.
Once you have formed your opinions on a particular debatable subject, you must decide on the best way to organize them to share with others. Developing your skills in six widely used reasoning strategies , or patterns for thinking and writing, can help you determine the most logical and effective means of organizing information to make your points.
In this chapter, you will examine these six reasoning strategies—analogy, cause and effect, classification and division, comparison and contrast, problem and solution, and definition—that are often used in college classes. In addition, you will consider how writers’ personal views, cultural backgrounds, and purposes for writing help determine
which reasoning strategy suits their needs; and
what they decide to include in their writing.
As you progress in your college classes and beyond, you will find these reasoning strategies used in all genres of writing, both nonfiction (e.g., textbooks, how-to books) and fiction (e.g., novels, short stories). Understanding how these strategies work can help you recognize their common formats and analyze what you read; likewise, as a writer, understanding how these strategies work to reflect your thinking can help you determine the strategy you need to use.
Writers frequently use analogy as a strategy to compare two unlike subjects—one subject is familiar to readers, whereas the other is not. To explain or clarify the unfamiliar subject, the writer emphasizes the way or ways in which the two subjects are similar, even though they are dissimilar and unrelated in all other ways. Analogies are basically long forms of similes (short comparisons of unlike elements, based on the word like or as ) or metaphors (short comparisons without signal words). In the example paragraph, the writer explains unfamiliar aspects of the COVID-19 pandemic by comparing it with the more familiar concept of a robbery spree.
Model Paragraph
student sample text Examining COVID-19 is like examining a robbery case in this way: both require a great deal of investigation. Those investigating the causes behind the pandemic look for the history of how the virus spread, and those investigating a crime look for the backstory that might connect the victims and criminals. In addition, the two groups of investigators look at the reasons behind the focus of their study. Medical investigators look at why the virus spread throughout the world; police investigators look at why the crime spree took place in a particular area. Also, both types of investigators are trying to stop whatever or whoever is the focus of their investigation. Medical investigators want to stop the virus; police investigators want to stop the crimes. end student sample text
Cause and Effect
Cause-and-effect writing identifies and examines the reasons (causes) for and consequences (effects) of an action, event, or idea. Cause-and-effect writing often answers the question “Why?” and helps readers understand the connections between what happens because of—or as a result of—something else.
student sample text Ray’s grocery, Artie’s Hardware store, and Cradle and Teen department store all went out of business because a well-known superstore opened in Springdale. Customers who frequented Ray’s, an establishment that had been run by the same family for four generations, used to drive many miles to take advantage of the high quality of items in the meat and deli departments. After the opening of the superstore, however, those same customers found they could get similar items at a savings, even if the quality was not as high as the products at Ray’s. Customers at Artie’s Hardware often talked with owner Artie Shoeman about their hardware needs, but the store did not offer the same variety of items they could find in the superstore. The same was true for those who shopped at Cradle and Teen. The superstore featured lower prices and more variety, even if the items did not match the quality of the items at Cradle and Teen. end student sample text
Classification and Division
Classification and division are actually two closely related strategies, generally discussed together because of their similarity. When using the strategy of division, the writer identifies a single subject or group and explains categories within that subject or group. In other words, the writer divides the larger unit into component parts. When using the strategy of classification, writers do the opposite. They group various elements and place them into larger, more comprehensive categories rather than divide the whole into parts. In general, the reasoning strategy of classification and division looks at smaller elements as parts of a larger element and thus helps readers understand a general concept and the elements that it comprises.
Model Paragraphs
student sample text Extra material in the textbook can be divided into photographs, quotations, and tables. The photographs were all taken by the author and focus on various parts of the life cycle of the plants highlighted in the chapter. In addition, to add color and more information about the subject matter of each chapter, the author has inserted sidebar quotations from both famous and non-famous people. The tables the author has included help readers see more details about the progression of the plants’ spread across the country. end student sample text
student sample text After three months of training, the young dogs were placed into three categories: those who would go directly to permanent homes, those who would repeat the course, and those who would advance to the next level. The dogs that would be homed immediately were those who were far too social or far too active to be service dogs. The dogs that would repeat the course had possibilities as service dogs but needed more discipline and instruction. Their futures were yet to be decided. Those that advanced to the next level were obedient and focused and learned quickly. They displayed great promise as service dogs. end student sample text
Comparison and Contrast
Compare and contrast , one of the most frequently used reasoning strategies, analyzes two (sometimes more) subjects, examining the similarities (comparisons) and differences (contrasts) between them. Nearly everything you can think of can be a subject for comparison and contrast: objects, people, concepts, places, movies, literature, and styles, to name a few. To elaborate on the separate points, writers provide details about each element being compared or contrasted. Comparison and contrast helps readers analyze and evaluate subjects.
This strategy is helpful when the similarities or differences are not obvious and when a significant common thread exists between the subjects. For example, a contrast between an expensive, elegant restaurant and a fast-food restaurant would be useless because the differences are clearly obvious, despite the common thread—both are restaurants. However, not so obvious might be some similarities.
When subjects have no common thread or have obvious shared characteristics, any comparison or contrast makes little sense—like contrasting a fish and a shoe (no common thread) or comparing two fast-food restaurants (obvious similarities). However, a writer actually might find a common thread between a fish and a shoe (perhaps shine or texture or color), and a valid topic of contrast might be differences between the two fast-food restaurants.
student sample text Although they seem different on the surface, one way in which Romantic-period poetry and 1980s rap music are alike is the desire the writers had to create a new approach to their art. They wanted to represent simpler values that were more connected to the natural world, values to which a general audience could relate. For example, in William Wordsworth ’s “Daffodils,” the speaker can escape the depressing, industrialized urban world to find peace in nature by contemplating a field of flowers. Similarly, in the Sugarhill Gang ’s 1979 “Rapper’s Delight,” the band sings of how their beats can lift spirits and cause listeners to dance and forget their woes. However, Romantic-period poetry and 1980s rap music are different in the delivery style and form of the art; “Rapper’s Delight” is set to music, which is an integral part of the piece, but “Daffodils” is not. end student sample text
Problem and Solution
When using this reasoning strategy, writers introduce a predicament or challenging issue (the problem) and offer information about what was done or what should be done to remedy the predicament or issue (the solution). Problem-and-solution writing helps readers understand the complexities of some predicaments and the actions that can improve or eliminate them.
student sample text The issue of combating the spread of hate speech and misinformation on social media can be addressed if more social media providers improve their monitoring services. Aside from creating more algorithms that search for linked key words and phrases, social media providers should increase the number of professional monitors conducting active searches. Additionally, while many platforms such as Twitter and Facebook respond within a few days to reports of posts that violate their policies, more monitors could lessen the amount of time these posts are available. According to Facebook, inappropriate posts are investigated and removed within 24 to 48 hours (Facebook “Community Standards”). Some offenders have been reported multiple times for their platform violations, and social media sponsors should increase their monitoring of those offenders. Although such surveillance would increase the burden on the social media providers, it would help solve the growing challenge of online hate speech and misinformation. end student sample text
When using the reasoning strategy of definition , writers elaborate on the meaning of an idea, a word, or an expression, usually one that is controversial or that can be viewed in multiple ways. Beginning writers tend to think that definition writing looks only at the denotation , or dictionary definition. However, definition writing entails much more than relaying a dictionary definition. It also explains and elaborates on the connotations , the emotions and implications the topic evokes. Definition writing is especially useful for explaining and interpreting terms, ideas, or concepts that are easily or often confused or that have meanings beyond their denotations. Sometimes these meanings are personal interpretations and thus reflect a writer’s particular viewpoint. Additionally, this strategy is beneficial when writers want to explain or reinforce a term before making an argument about a larger concept.
student sample text In everyday speech, the word critical is often used to highlight negative aspects of a topic. If someone says a friend was critical of a new haircut, the implication is that the friend did not like the cut. However, when used in college classes, critical has an expanded meaning: noting both the negative and positive aspects of a topic, examining those aspects in depth, and then making decisions about the discoveries. Students directed to use critical thinking, critical reading, or critical writing should know they are expected to examine all sides of a topic fully, evaluate the validity of those sides, and then make sound judgments on the basis of their evaluation. end student sample text
In this chapter, you have learned about various reasoning strategies that you may use in academic and professional writing. Utilizing these strategies when you write can help you both evaluate and analyze text that you read and create more logical and persuasive arguments.
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Human beings have been thinking logically (and sometimes illogically) since the earliest era of human existence. However, they have not always been aware of the general principles that distinguish logical from illogical forms of thought. Logic, as an academic subject, is the systematic study of those principles. The logician asks, Which rules should we follow if we want our reasoning to be the best possible?
The rules of logic are guides to correct reasoning just as the rules of arithmetic are guides to correctly adding, subtracting, multiplying, and dividing numbers, the principles of photography are guides to taking good photos, and so on. You can improve your reasoning by studying the principles of logic, just as you can improve your number-crunching abilities by studying the principles of mathematics. Because correct reasoning can be applied to any subject matter whatsoever, the number of potential applications of logical theory is practically unlimited.
The Greek philosopher Aristotle (384–322 BC) wrote the first book on the standards of correct reasoning and later wrote four additional treatises on the subject. Thus, in five highly original (and extremely complex) works, collectively known as the Organon (Greek for “tool,” as in “general tool of thought”), Aristotle launched the study of the principles of correct reasoning and earned the title historians have conferred on him: founder of logic. [i] The noted twentieth-century logician and philosopher Benson Mates writes:
[W]e can say flatly that the history of logic begins with the Greek philosopher Aristotle . . . Although it is almost a platitude among historians that great intellectual advances are never the work of only one person (in founding the science of geometry Euclid made use of the results of Eudoxus and others; in the case of mechanics Newton stood upon the shoulders of Descartes, Galileo, and Kepler; and so on), Aristotle, according to all available evidence, created the science of logic absolutely ex nihilo. [ii]
Logic was first taught as an academic subject in the universities of ancient Athens, Greece during the fourth century BC, making it one of the oldest of all academic subjects. For twenty-five hundred years, it has been considered a core academic requirement at institutions of higher learning around the world. Logic remains part of the core curriculum around the world today because the principles of correct reasoning can help anyone reason more accurately, no matter what subject, making it an all-purpose “tool kit” for your mind.
Major Divisions of Logic
Formal logic studies the abstract patterns or forms of correct reasoning. Here the focus is on form rather than content, that is, on the logical structure of reasoning apart from what it is specifically about. Since ancient times, logicians have used special symbols and formulas, similar to those used in mathematics, to record the abstract logical forms they have discovered. This is why formal logic is sometimes also called “symbolic logic” or “mathematical logic.”
Informal logic studies the non-formal aspects of reasoning—qualities that cannot be accurately translated into abstract symbols. This is why informal logic for the most part dispenses with special symbols and formulas. In this division of logic, the focus is often reasoning expressed within everyday language.
Logical theory begins with the notion of an argument , which is defined as one or more statements, called “premises,” offered as evidence, or reason to believe, that a further statement, called the “conclusion,” is true. In plain terms, an argument is reasoning offered in support of a conclusion. Arguments are part of everyday life. You present one every time you put your reasoning into words to share it with others. In the following example, the premises are marked P1 and P2, and the conclusion is labeled C.
P1: All songwriters are poets.
P2: Bob Dylan is a songwriter.
C: Therefore, Bob Dylan is a poet.
The second building block of logical theory is the distinction, first noted by Aristotle, between deductive and inductive reasoning. A deductive argument aims to establish its conclusion with complete certainty, in such a way that if its premises all are true, then its conclusion must be true. Put another way, the underlying claim in the case of a deductive argument is that it is not even possible the premises all are true and the conclusion is false. For example:
P1. Tiny Tim played the ukulele.
P2. Anyone who plays the ukulele is a musician.
C. Consequently, Tiny Tim was a musician.
Deductive arguments aim for certainty and nothing less. If a deductive argument succeeds in its aim, it is a valid deductive argument. If it does not, it is an invalid deductive argument. A deductive argument is said to be sound if it is (a) valid and (b) all of its premises are true. The following deductive argument is clearly valid although it is not sound.
P1. All students are millionaires.
P2. All millionaires drink vodka.
C. Therefore, necessarily, all students drink vodka.
In contrast, the following argument is invalid (and hence also unsound).
P1. Ann and Sue are cousins.
P2. Sue and Rita are cousins.
C. So, Ann and Rita must be cousins.
The following argument hits the target—it is both valid and sound.
P1. All whales are mammals.
P2. All mammals are warm-blooded.
C. Ergo, all whales are warm-blooded.
Deductive logic is the study of the standards of correct deductive reasoning. Here is an example of a law of deductive logic. Let A, B, and C be variables ranging over terms that stand for categories—words such as cats, dogs, people, trucks, and so forth. Aristotle proved that the following form or pattern of reasoning, named Barbara by logicians in Europe during the Middle Ages, is a valid form, meaning that any argument—about any subject—that exactly follows this pattern is valid.
The Barbara Argument Form
All B are C.
All A are B.
Therefore, necessarily, all A are C.
Let’s test Barbara. If we replace the variable A with sparrows , the variable B with birds , and substitute animals for the variable C, we get the following “substitution instance” of the corresponding form:
P1. All birds are animals.
P2. All sparrows are birds.
C. Therefore, necessarily, all sparrows are animals.
This argument is clearly valid. Aristotle proved that any argument that exactly follows this form of reasoning is valid. For instance:
P1. All mammals are animals.
P2. All cats are mammals.
C. Therefore, necessarily, all cats are animals.
To return to Barbara for a moment, notice that the form is not about any particular subject—it is an abstract pattern with no material content. Barbara is all form and no content. Aristotle discovered that an argument’s validity is always a function of its form rather than its content. You can learn a lot about reasoning by studying valid argument forms. Logicians have catalogued hundreds of them. The study of logical forms is valuable, for if your argument follows a valid form, then it is guaranteed to be valid and therefore your conclusion must be true if your premises are true. As you may have guessed, formal logic and deductive logic overlap in the study of valid patterns of reasoning, of which there are many.
An inductive argument, on the other hand, does not aim to show that its conclusion is certain. Rather it aims to show that its conclusion is probably, though not definitely, true so that if its premises are true, it is likely that its conclusion is true. This argument aims to establish its conclusion with a probability less than one:
P1. Joe has eaten a Dick’s Deluxe burger for lunch every day for the past month.
C. So, it is very probable that he will have a Dick’s Deluxe for lunch tomorrow.
If an inductive argument achieves its aim, it is a strong argument . An inductive argument that does not achieve its aim is a weak argument . An inductive argument is said to be cogent if it is (a) strong, and (b) all of its premises are true. The following inductive argument is strong although it is surely not cogent:
P1. We interviewed one thousand people from all walks of life and every social group all over Seattle over a ten-week period, and 90 percent said they do not drink coffee.
C. Therefore, probably about 90 percent of Seattleites do not drink coffee.
The following argument is clearly weak:
P1. We interviewed one thousand people from all walks of life as they exited coffee shops in Seattle, and 98 percent said they drink coffee.
C. Therefore, probably about 98 percent of Seattleites drink coffee.
The following argument is better—it is strong as well as cogent:
P1. NASA announced that it found evidence of water on Mars.
P2. NASA is a scientifically reliable agency.
C. Therefore it is likely there is or was water on Mars.
Inductive logic is the study of the standards of good inductive reasoning. One inductive standard pertains to analogical arguments —arguments that take the following form:
A and B have many features in common.
A has attribute x and B is not known not to have attribute x .
Therefore, B probably has attribute x as well.
For instance:
P1. Monkey hearts are very similar to human hearts.
P2. Drug X cures heart disease in monkeys.
P3. Drug x is not known to not cure heart disease in humans.
C.Therefore, drug X will probably cure heart disease in humans.
Analogical arguments can be evaluated rationally. Here are three principles commonly used to judge their strength:
The more attributes A and B have in common, the stronger the argument, provided the common features are relevant to the conclusion.
The more differences there are between A and B, the weaker the argument, provided the differences are relevant to the conclusion.
The more specific or narrowly drawn the conclusion, the weaker the argument. The more general or widely drawn the conclusion, the stronger the argument.
Informal and inductive logic overlap in the study of the many non-formal aspects of inductive reasoning, which include guides to help us improve our assessments of probability.
Information Spillover
The history of ideas is fascinating because often one idea leads to another which leads to a completely unexpected discovery. Economists call this “information spillover” because freely traded ideas tend to give birth to new ideas that give birth to still more ideas that spill from mind to mind as the process cascades into ever widening circles of knowledge and understanding. Aristotle discovered logical principles so exact they could be expressed in symbols like those used in mathematics. Because they could be expressed so precisely, he was able to develop a system of logic similar to geometry. Recall that geometry begins with statements, called “axioms,” asserted as self-evident. With the addition of precise definitions, the geometer uses precise reasoning to derive further statements, called “theorems.” Aristotle’s system began in a similar way, with precise definitions and exact formulas asserted as self-evident. With the base established, he derived a multitude of theorems that branched out in many directions. When he was finished, his system of logical principles was as exact, and proven, as any system of mathematics of the day.
Some observers thought the rules of his system were too mechanical and abstract to be of any practical use. They were mistaken. Aristotle’s system of logic was actually the first step on the path to the digital computer. The first person to design a computing machine was a logician who, after reflecting on the exact and mechanical nature of Aristotle’s system of logical principles, raised one of the most seminal questions ever: Is it possible to design a machine whose gears, by obeying the “laws” of Aristotle’s logic, compute for us the exact, logically correct answer every time?
The logician who first asked the question that connected logic and computing was Raymond Lull (1232–1315), a philosopher, Aristotelian logician, and Catholic priest. Lull has been called the “father of the computer” because he was the first to conceive and design a logical computing machine. Lull’s device consisted of rotating cogwheels inscribed with logical symbols from Aristotle’s system, aligned to move in accord with the rules of logic. In theory, the operator would enter the premises of an argument by setting the dials, and the machine’s gears would then accurately crank out the logically correct conclusion.
Lull’s design may have been primitive, but for the first time in history someone had the idea of a machine that takes inputs, processes them mechanically on the basis of exact rules of logic, and outputs a logically correct answer. We usually associate computing with mathematics, but the first design for a computer was based not on math but on logic—the logic of Aristotle.
Ideas have consequences, and sometimes ideas that seem impractical have consequences that are quite practical. Lull was the first in a long succession of logical tinkerers, each seeking to design a more powerful computing machine. You have a cell phone in your hand right now thanks to the efforts of these innovators, each trained in logical theory. In addition to Lull, the list includes computer pioneers Leonardo da Vinci (1452–1519), Wilhelm Schickard (1592–1635), William Oughtred (1574–1660), Blaise Pascal (1623–1662), Gottfried Leibniz (1646–1716), Charles Babbage (1791–1871), Vannevar Bush (1890–1974), Howard Aiken (1900–1973), and Alan Turing (1912–1954).
Thus, a continuous line of thought can be traced from Aristotle’s logical treatises to the amazing advances in logic and computing theory of the nineteenth and twentieth centuries which led to the completion of the world’s first digital computer (at Iowa State College in 1937) and from there to the much smaller yet more powerful devices of today. It is no coincidence that the circuits inside every digital computer are called “logic gates.” In the logic classroom, this is my answer to those who suppose that abstract logical theory has no practical applications.
Computer science is only one spin-off of logical theory. The subject Aristotle founded remains as vital today as it was in ancient Athens. Aristotle probably had no idea how important his new subject would be—or how long the spillover and information overflow would continue.
What does all of this have to do with anything? In everyday life as well as in every academic subject, reason is our common currency. It follows that the ability to reason well is an essential life skill. But skills require knowledge as well as practice. Since logic is the study of the principles of correct reasoning, a familiarity with elementary logic and its applications can help anyone improve his or her life. Some people suppose logic is a useless subject; the truth may be the reverse—it may be the most useful subject of all.
[i] An editor applied the name Organon (“tool”) to Aristotle’s logical works after his death. The name reflects Aristotle’s claim that logic is an all-purpose tool of thought, a guide to the precise thinking needed to attain solidly proven truth on any subject.
[ii] Benson Mates, Elementary Logic , 2nd ed. (New York: Oxford University Press, 1972), 206. Ex nihilo is Latin for “out of nothing” and means “from scratch” in this context.
For a deeper look at the fundamentals of this subject, check out the free course “ Short Little Lessons in Logic ” published by Philosophy News. This course will teach you the fundamentals of logic in bite-sized lessons that you can learn at your own pace.
About the author
Paul Herrick received his Ph.D in philosophy from the University of Washington. Since 1983 he has taught philosophy at Shoreline Community College, in Shoreline, Washington, near Seattle. He is the author of Reason and Worldview. An Introduction to Western Philosophy , Think with Socrates: An Introduction to Critical Thinking, The Many Worlds of Logic, and Introduction to Logic .
Other articles by Paul Herrick
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This is a comprehensive introduction to the fundamentals of logic (both formal logic and critical reasoning), with exceptionally clear yet conversational explanations and a multitude of engaging examples and exercises. Herrick’s examples are on-point and fun, often bringing in real-life situations and popular culture. And more so than other logic textbooks, Introduction to Logic brings in the history of philosophy and logic through interesting boxes/sidebars and discussions, showing logic’s relation to philosophy.
Brief yet comprehensive, Think with Socrates: An Introduction to Critical Thinking uses the methods, ideas, and life of Socrates as a model for critical thinking. It offers a more philosophical, historical, and accessible introduction than longer textbooks while still addressing all of the key topics in logic and argumentation. Applying critical thinking to the Internet, mass media, advertising, personal experience, expert authority, the evaluation of sources, writing argumentative essays, and forming a worldview, Think with Socrates resonates with today’s students and teaches them how to apply critical thinking in the real world. At the same time, it covers the ancient intellectual roots and history of the field, placing critical thinking in its larger context to help students appreciate its perennial value.
A comprehensive look at major movements in philosophy and how those movements helped shape the way we think and behave.
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Introduction to Logic and Critical Thinking
(10 reviews)
Matthew Van Cleave, Lansing Community College
Copyright Year: 2016
Publisher: Matthew J. Van Cleave
Language: English
Formats Available
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Reviewed by "yusef" Alexander Hayes, Professor, North Shore Community College on 6/9/21
Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness. read more
Comprehensiveness rating: 5 see less
Formal and informal reasoning, argument structure, and fallacies are covered comprehensively, meeting the author's goal of both depth and succinctness.
Content Accuracy rating: 5
The book is accurate.
Relevance/Longevity rating: 5
While many modern examples are used, and they are helpful, they are not necessarily needed. The usefulness of logical principles and skills have proved themselves, and this text presents them clearly with many examples.
Clarity rating: 5
It is obvious that the author cares about their subject, audience, and students. The text is comprehensible and interesting.
Consistency rating: 5
The format is easy to understand and is consistent in framing.
Modularity rating: 5
This text would be easy to adapt.
Organization/Structure/Flow rating: 5
The organization is excellent, my one suggestion would be a concluding chapter.
Interface rating: 5
I accessed the PDF version and it would be easy to work with.
Grammatical Errors rating: 5
The writing is excellent.
Cultural Relevance rating: 5
This is not an offensive text.
Reviewed by Susan Rottmann, Part-time Lecturer, University of Southern Maine on 3/2/21
I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it... read more
Comprehensiveness rating: 4 see less
I reviewed this book for a course titled "Creative and Critical Inquiry into Modern Life." It won't meet all my needs for that course, but I haven't yet found a book that would. I wanted to review this one because it states in the preface that it fits better for a general critical thinking course than for a true logic course. I'm not sure that I'd agree. I have been using Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," and I think that book is a better introduction to critical thinking for non-philosophy majors. However, the latter is not open source so I will figure out how to get by without it in the future. Overall, the book seems comprehensive if the subject is logic. The index is on the short-side, but fine. However, one issue for me is that there are no page numbers on the table of contents, which is pretty annoying if you want to locate particular sections.
Content Accuracy rating: 4
I didn't find any errors. In general the book uses great examples. However, they are very much based in the American context, not for an international student audience. Some effort to broaden the chosen examples would make the book more widely applicable.
Relevance/Longevity rating: 4
I think the book will remain relevant because of the nature of the material that it addresses, however there will be a need to modify the examples in future editions and as the social and political context changes.
Clarity rating: 3
The text is lucid, but I think it would be difficult for introductory-level students who are not philosophy majors. For example, in Browne and Keeley's "Asking the Right Questions: A Guide to Critical Thinking," the sub-headings are very accessible, such as "Experts cannot rescue us, despite what they say" or "wishful thinking: perhaps the biggest single speed bump on the road to critical thinking." By contrast, Van Cleave's "Introduction to Logic and Critical Thinking" has more subheadings like this: "Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form" or "Propositional logic and the four basic truth functional connectives." If students are prepared very well for the subject, it would work fine, but for students who are newly being introduced to critical thinking, it is rather technical.
It seems to be very consistent in terms of its terminology and framework.
Modularity rating: 4
The book is divided into 4 chapters, each having many sub-chapters. In that sense, it is readily divisible and modular. However, as noted above, there are no page numbers on the table of contents, which would make assigning certain parts rather frustrating. Also, I'm not sure why the book is only four chapter and has so many subheadings (for instance 17 in Chapter 2) and a length of 242 pages. Wouldn't it make more sense to break up the book into shorter chapters? I think this would make it easier to read and to assign in specific blocks to students.
Organization/Structure/Flow rating: 4
The organization of the book is fine overall, although I think adding page numbers to the table of contents and breaking it up into more separate chapters would help it to be more easily navigable.
Interface rating: 4
The book is very simply presented. In my opinion it is actually too simple. There are few boxes or diagrams that highlight and explain important points.
The text seems fine grammatically. I didn't notice any errors.
The book is written with an American audience in mind, but I did not notice culturally insensitive or offensive parts.
Overall, this book is not for my course, but I think it could work well in a philosophy course.
Reviewed by Daniel Lee, Assistant Professor of Economics and Leadership, Sweet Briar College on 11/11/19
This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument read more
Comprehensiveness rating: 3 see less
This textbook is not particularly comprehensive (4 chapters long), but I view that as a benefit. In fact, I recommend it for use outside of traditional logic classes, but rather interdisciplinary classes that evaluate argument
To the best of my ability, I regard this content as accurate, error-free, and unbiased
The book is broadly relevant and up-to-date, with a few stray temporal references (sydney olympics, particular presidencies). I don't view these time-dated examples as problematic as the logical underpinnings are still there and easily assessed
Clarity rating: 4
My only pushback on clarity is I didn't find the distinction between argument and explanation particularly helpful/useful/easy to follow. However, this experience may have been unique to my class.
To the best of my ability, I regard this content as internally consistent
I found this text quite modular, and was easily able to integrate other texts into my lessons and disregard certain chapters or sub-sections
The book had a logical and consistent structure, but to the extent that there are only 4 chapters, there isn't much scope for alternative approaches here
No problems with the book's interface
The text is grammatically sound
Cultural Relevance rating: 4
Perhaps the text could have been more universal in its approach. While I didn't find the book insensitive per-se, logic can be tricky here because the point is to evaluate meaningful (non-trivial) arguments, but any argument with that sense of gravity can also be traumatic to students (abortion, death penalty, etc)
No additional comments
Reviewed by Lisa N. Thomas-Smith, Graduate Part-time Instructor, CU Boulder on 7/1/19
The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text,... read more
The text covers all the relevant technical aspects of introductory logic and critical thinking, and covers them well. A separate glossary would be quite helpful to students. However, the terms are clearly and thoroughly explained within the text, and the index is very thorough.
The content is excellent. The text is thorough and accurate with no errors that I could discern. The terminology and exercises cover the material nicely and without bias.
The text should easily stand the test of time. The exercises are excellent and would be very helpful for students to internalize correct critical thinking practices. Because of the logical arrangement of the text and the many sub-sections, additional material should be very easy to add.
The text is extremely clearly and simply written. I anticipate that a diligent student could learn all of the material in the text with little additional instruction. The examples are relevant and easy to follow.
The text did not confuse terms or use inconsistent terminology, which is very important in a logic text. The discipline often uses multiple terms for the same concept, but this text avoids that trap nicely.
The text is fairly easily divisible. Since there are only four chapters, those chapters include large blocks of information. However, the chapters themselves are very well delineated and could be easily broken up so that parts could be left out or covered in a different order from the text.
The flow of the text is excellent. All of the information is handled solidly in an order that allows the student to build on the information previously covered.
The PDF Table of Contents does not include links or page numbers which would be very helpful for navigation. Other than that, the text was very easy to navigate. All the images, charts, and graphs were very clear
I found no grammatical errors in the text.
Cultural Relevance rating: 3
The text including examples and exercises did not seem to be offensive or insensitive in any specific way. However, the examples included references to black and white people, but few others. Also, the text is very American specific with many examples from and for an American audience. More diversity, especially in the examples, would be appropriate and appreciated.
Reviewed by Leslie Aarons, Associate Professor of Philosophy, CUNY LaGuardia Community College on 5/16/19
This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an... read more
This is an excellent introductory (first-year) Logic and Critical Thinking textbook. The book covers the important elementary information, clearly discussing such things as the purpose and basic structure of an argument; the difference between an argument and an explanation; validity; soundness; and the distinctions between an inductive and a deductive argument in accessible terms in the first chapter. It also does a good job introducing and discussing informal fallacies (Chapter 4). The incorporation of opportunities to evaluate real-world arguments is also very effective. Chapter 2 also covers a number of formal methods of evaluating arguments, such as Venn Diagrams and Propositional logic and the four basic truth functional connectives, but to my mind, it is much more thorough in its treatment of Informal Logic and Critical Thinking skills, than it is of formal logic. I also appreciated that Van Cleave’s book includes exercises with answers and an index, but there is no glossary; which I personally do not find detracts from the book's comprehensiveness.
Overall, Van Cleave's book is error-free and unbiased. The language used is accessible and engaging. There were no glaring inaccuracies that I was able to detect.
Van Cleave's Textbook uses relevant, contemporary content that will stand the test of time, at least for the next few years. Although some examples use certain subjects like former President Obama, it does so in a useful manner that inspires the use of critical thinking skills. There are an abundance of examples that inspire students to look at issues from many different political viewpoints, challenging students to practice evaluating arguments, and identifying fallacies. Many of these exercises encourage students to critique issues, and recognize their own inherent reader-biases and challenge their own beliefs--hallmarks of critical thinking.
As mentioned previously, the author has an accessible style that makes the content relatively easy to read and engaging. He also does a suitable job explaining jargon/technical language that is introduced in the textbook.
Van Cleave uses terminology consistently and the chapters flow well. The textbook orients the reader by offering effective introductions to new material, step-by-step explanations of the material, as well as offering clear summaries of each lesson.
This textbook's modularity is really quite good. Its language and structure are not overly convoluted or too-lengthy, making it convenient for individual instructors to adapt the materials to suit their methodological preferences.
The topics in the textbook are presented in a logical and clear fashion. The structure of the chapters are such that it is not necessary to have to follow the chapters in their sequential order, and coverage of material can be adapted to individual instructor's preferences.
The textbook is free of any problematic interface issues. Topics, sections and specific content are accessible and easy to navigate. Overall it is user-friendly.
I did not find any significant grammatical issues with the textbook.
The textbook is not culturally insensitive, making use of a diversity of inclusive examples. Materials are especially effective for first-year critical thinking/logic students.
I intend to adopt Van Cleave's textbook for a Critical Thinking class I am teaching at the Community College level. I believe that it will help me facilitate student-learning, and will be a good resource to build additional classroom activities from the materials it provides.
Reviewed by Jennie Harrop, Chair, Department of Professional Studies, George Fox University on 3/27/18
While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters... read more
While the book is admirably comprehensive, its extensive details within a few short chapters may feel overwhelming to students. The author tackles an impressive breadth of concepts in Chapter 1, 2, 3, and 4, which leads to 50-plus-page chapters that are dense with statistical analyses and critical vocabulary. These topics are likely better broached in manageable snippets rather than hefty single chapters.
The ideas addressed in Introduction to Logic and Critical Thinking are accurate but at times notably political. While politics are effectively used to exemplify key concepts, some students may be distracted by distinct political leanings.
The terms and definitions included are relevant, but the examples are specific to the current political, cultural, and social climates, which could make the materials seem dated in a few years without intentional and consistent updates.
While the reasoning is accurate, the author tends to complicate rather than simplify -- perhaps in an effort to cover a spectrum of related concepts. Beginning readers are likely to be overwhelmed and under-encouraged by his approach.
Consistency rating: 3
The four chapters are somewhat consistent in their play of definition, explanation, and example, but the structure of each chapter varies according to the concepts covered. In the third chapter, for example, key ideas are divided into sub-topics numbering from 3.1 to 3.10. In the fourth chapter, the sub-divisions are further divided into sub-sections numbered 4.1.1-4.1.5, 4.2.1-4.2.2, and 4.3.1 to 4.3.6. Readers who are working quickly to master new concepts may find themselves mired in similarly numbered subheadings, longing for a grounded concepts on which to hinge other key principles.
Modularity rating: 3
The book's four chapters make it mostly self-referential. The author would do well to beak this text down into additional subsections, easing readers' accessibility.
The content of the book flows logically and well, but the information needs to be better sub-divided within each larger chapter, easing the student experience.
The book's interface is effective, allowing readers to move from one section to the next with a single click. Additional sub-sections would ease this interplay even further.
Grammatical Errors rating: 4
Some minor errors throughout.
For the most part, the book is culturally neutral, avoiding direct cultural references in an effort to remain relevant.
Reviewed by Yoichi Ishida, Assistant Professor of Philosophy, Ohio University on 2/1/18
This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic,... read more
This textbook covers enough topics for a first-year course on logic and critical thinking. Chapter 1 covers the basics as in any standard textbook in this area. Chapter 2 covers propositional logic and categorical logic. In propositional logic, this textbook does not cover suppositional arguments, such as conditional proof and reductio ad absurdum. But other standard argument forms are covered. Chapter 3 covers inductive logic, and here this textbook introduces probability and its relationship with cognitive biases, which are rarely discussed in other textbooks. Chapter 4 introduces common informal fallacies. The answers to all the exercises are given at the end. However, the last set of exercises is in Chapter 3, Section 5. There are no exercises in the rest of the chapter. Chapter 4 has no exercises either. There is index, but no glossary.
The textbook is accurate.
The content of this textbook will not become obsolete soon.
The textbook is written clearly.
The textbook is internally consistent.
The textbook is fairly modular. For example, Chapter 3, together with a few sections from Chapter 1, can be used as a short introduction to inductive logic.
The textbook is well-organized.
There are no interface issues.
I did not find any grammatical errors.
This textbook is relevant to a first semester logic or critical thinking course.
Reviewed by Payal Doctor, Associate Professro, LaGuardia Community College on 2/1/18
This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner... read more
This text is a beginner textbook for arguments and propositional logic. It covers the basics of identifying arguments, building arguments, and using basic logic to construct propositions and arguments. It is quite comprehensive for a beginner book, but seems to be a good text for a course that needs a foundation for arguments. There are exercises on creating truth tables and proofs, so it could work as a logic primer in short sessions or with the addition of other course content.
The books is accurate in the information it presents. It does not contain errors and is unbiased. It covers the essential vocabulary clearly and givens ample examples and exercises to ensure the student understands the concepts
The content of the book is up to date and can be easily updated. Some examples are very current for analyzing the argument structure in a speech, but for this sort of text understandable examples are important and the author uses good examples.
The book is clear and easy to read. In particular, this is a good text for community college students who often have difficulty with reading comprehension. The language is straightforward and concepts are well explained.
The book is consistent in terminology, formatting, and examples. It flows well from one topic to the next, but it is also possible to jump around the text without loosing the voice of the text.
The books is broken down into sub units that make it easy to assign short blocks of content at a time. Later in the text, it does refer to a few concepts that appear early in that text, but these are all basic concepts that must be used to create a clear and understandable text. No sections are too long and each section stays on topic and relates the topic to those that have come before when necessary.
The flow of the text is logical and clear. It begins with the basic building blocks of arguments, and practice identifying more and more complex arguments is offered. Each chapter builds up from the previous chapter in introducing propositional logic, truth tables, and logical arguments. A select number of fallacies are presented at the end of the text, but these are related to topics that were presented before, so it makes sense to have these last.
The text is free if interface issues. I used the PDF and it worked fine on various devices without loosing formatting.
1. The book contains no grammatical errors.
The text is culturally sensitive, but examples used are a bit odd and may be objectionable to some students. For instance, President Obama's speech on Syria is used to evaluate an extended argument. This is an excellent example and it is explained well, but some who disagree with Obama's policies may have trouble moving beyond their own politics. However, other examples look at issues from all political viewpoints and ask students to evaluate the argument, fallacy, etc. and work towards looking past their own beliefs. Overall this book does use a variety of examples that most students can understand and evaluate.
My favorite part of this book is that it seems to be written for community college students. My students have trouble understanding readings in the New York Times, so it is nice to see a logic and critical thinking text use real language that students can understand and follow without the constant need of a dictionary.
Reviewed by Rebecca Owen, Adjunct Professor, Writing, Chemeketa Community College on 6/20/17
This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current... read more
This textbook is quite thorough--there are conversational explanations of argument structure and logic. I think students will be happy with the conversational style this author employs. Also, there are many examples and exercises using current events, funny scenarios, or other interesting ways to evaluate argument structure and validity. The third section, which deals with logical fallacies, is very clear and comprehensive. My only critique of the material included in the book is that the middle section may be a bit dense and math-oriented for learners who appreciate the more informal, informative style of the first and third section. Also, the book ends rather abruptly--it moves from a description of a logical fallacy to the answers for the exercises earlier in the text.
The content is very reader-friendly, and the author writes with authority and clarity throughout the text. There are a few surface-level typos (Starbuck's instead of Starbucks, etc.). None of these small errors detract from the quality of the content, though.
One thing I really liked about this text was the author's wide variety of examples. To demonstrate different facets of logic, he used examples from current media, movies, literature, and many other concepts that students would recognize from their daily lives. The exercises in this text also included these types of pop-culture references, and I think students will enjoy the familiarity--as well as being able to see the logical structures behind these types of references. I don't think the text will need to be updated to reflect new instances and occurrences; the author did a fine job at picking examples that are relatively timeless. As far as the subject matter itself, I don't think it will become obsolete any time soon.
The author writes in a very conversational, easy-to-read manner. The examples used are quite helpful. The third section on logical fallacies is quite easy to read, follow, and understand. A student in an argument writing class could benefit from this section of the book. The middle section is less clear, though. A student learning about the basics of logic might have a hard time digesting all of the information contained in chapter two. This material might be better in two separate chapters. I think the author loses the balance of a conversational, helpful tone and focuses too heavily on equations.
Consistency rating: 4
Terminology in this book is quite consistent--the key words are highlighted in bold. Chapters 1 and 3 follow a similar organizational pattern, but chapter 2 is where the material becomes more dense and equation-heavy. I also would have liked a closing passage--something to indicate to the reader that we've reached the end of the chapter as well as the book.
I liked the overall structure of this book. If I'm teaching an argumentative writing class, I could easily point the students to the chapters where they can identify and practice identifying fallacies, for instance. The opening chapter is clear in defining the necessary terms, and it gives the students an understanding of the toolbox available to them in assessing and evaluating arguments. Even though I found the middle section to be dense, smaller portions could be assigned.
The author does a fine job connecting each defined term to the next. He provides examples of how each defined term works in a sentence or in an argument, and then he provides practice activities for students to try. The answers for each question are listed in the final pages of the book. The middle section feels like the heaviest part of the whole book--it would take the longest time for a student to digest if assigned the whole chapter. Even though this middle section is a bit heavy, it does fit the overall structure and flow of the book. New material builds on previous chapters and sub-chapters. It ends abruptly--I didn't realize that it had ended, and all of a sudden I found myself in the answer section for those earlier exercises.
The simple layout is quite helpful! There is nothing distracting, image-wise, in this text. The table of contents is clearly arranged, and each topic is easy to find.
Tiny edits could be made (Starbuck's/Starbucks, for one). Otherwise, it is free of distracting grammatical errors.
This text is quite culturally relevant. For instance, there is one example that mentions the rumors of Barack Obama's birthplace as somewhere other than the United States. This example is used to explain how to analyze an argument for validity. The more "sensational" examples (like the Obama one above) are helpful in showing argument structure, and they can also help students see how rumors like this might gain traction--as well as help to show students how to debunk them with their newfound understanding of argument and logic.
The writing style is excellent for the subject matter, especially in the third section explaining logical fallacies. Thank you for the opportunity to read and review this text!
Reviewed by Laurel Panser, Instructor, Riverland Community College on 6/20/17
This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as... read more
This is a review of Introduction to Logic and Critical Thinking, an open source book version 1.4 by Matthew Van Cleave. The comparison book used was Patrick J. Hurley’s A Concise Introduction to Logic 12th Edition published by Cengage as well as the 13th edition with the same title. Lori Watson is the second author on the 13th edition.
Competing with Hurley is difficult with respect to comprehensiveness. For example, Van Cleave’s book is comprehensive to the extent that it probably covers at least two-thirds or more of what is dealt with in most introductory, one-semester logic courses. Van Cleave’s chapter 1 provides an overview of argumentation including discerning non-arguments from arguments, premises versus conclusions, deductive from inductive arguments, validity, soundness and more. Much of Van Cleave’s chapter 1 parallel’s Hurley’s chapter 1. Hurley’s chapter 3 regarding informal fallacies is comprehensive while Van Cleave’s chapter 4 on this topic is less extensive. Categorical propositions are a topic in Van Cleave’s chapter 2; Hurley’s chapters 4 and 5 provide more instruction on this, however. Propositional logic is another topic in Van Cleave’s chapter 2; Hurley’s chapters 6 and 7 provide more information on this, though. Van Cleave did discuss messy issues of language meaning briefly in his chapter 1; that is the topic of Hurley’s chapter 2.
Van Cleave’s book includes exercises with answers and an index. A glossary was not included.
Reviews of open source textbooks typically include criteria besides comprehensiveness. These include comments on accuracy of the information, whether the book will become obsolete soon, jargon-free clarity to the extent that is possible, organization, navigation ease, freedom from grammar errors and cultural relevance; Van Cleave’s book is fine in all of these areas. Further criteria for open source books includes modularity and consistency of terminology. Modularity is defined as including blocks of learning material that are easy to assign to students. Hurley’s book has a greater degree of modularity than Van Cleave’s textbook. The prose Van Cleave used is consistent.
Van Cleave’s book will not become obsolete soon.
Van Cleave’s book has accessible prose.
Van Cleave used terminology consistently.
Van Cleave’s book has a reasonable degree of modularity.
Van Cleave’s book is organized. The structure and flow of his book is fine.
Problems with navigation are not present.
Grammar problems were not present.
Van Cleave’s book is culturally relevant.
Van Cleave’s book is appropriate for some first semester logic courses.
Table of Contents
Chapter 1: Reconstructing and analyzing arguments
1.1 What is an argument?
1.2 Identifying arguments
1.3 Arguments vs. explanations
1.4 More complex argument structures
1.5 Using your own paraphrases of premises and conclusions to reconstruct arguments in standard form
1.6 Validity
1.7 Soundness
1.8 Deductive vs. inductive arguments
1.9 Arguments with missing premises
1.10 Assuring, guarding, and discounting
1.11 Evaluative language
1.12 Evaluating a real-life argument
Chapter 2: Formal methods of evaluating arguments
2.1 What is a formal method of evaluation and why do we need them?
2.2 Propositional logic and the four basic truth functional connectives
2.3 Negation and disjunction
2.4 Using parentheses to translate complex sentences
2.5 “Not both” and “neither nor”
2.6 The truth table test of validity
2.7 Conditionals
2.8 “Unless”
2.9 Material equivalence
2.10 Tautologies, contradictions, and contingent statements
2.11 Proofs and the 8 valid forms of inference
2.12 How to construct proofs
2.13 Short review of propositional logic
2.14 Categorical logic
2.15 The Venn test of validity for immediate categorical inferences
2.16 Universal statements and existential commitment
2.17 Venn validity for categorical syllogisms
Chapter 3: Evaluating inductive arguments and probabilistic and statistical fallacies
3.1 Inductive arguments and statistical generalizations
3.2 Inference to the best explanation and the seven explanatory virtues
3.3 Analogical arguments
3.4 Causal arguments
3.5 Probability
3.6 The conjunction fallacy
3.7 The base rate fallacy
3.8 The small numbers fallacy
3.9 Regression to the mean fallacy
3.10 Gambler's fallacy
Chapter 4: Informal fallacies
4.1 Formal vs. informal fallacies
4.1.1 Composition fallacy
4.1.2 Division fallacy
4.1.3 Begging the question fallacy
4.1.4 False dichotomy
4.1.5 Equivocation
4.2 Slippery slope fallacies
4.2.1 Conceptual slippery slope
4.2.2 Causal slippery slope
4.3 Fallacies of relevance
4.3.1 Ad hominem
4.3.2 Straw man
4.3.3 Tu quoque
4.3.4 Genetic
4.3.5 Appeal to consequences
4.3.6 Appeal to authority
Answers to exercises Glossary/Index
Ancillary Material
About the book.
This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a “critical thinking textbook.”
About the Contributors
Matthew Van Cleave , PhD, Philosophy, University of Cincinnati, 2007. VAP at Concordia College (Moorhead), 2008-2012. Assistant Professor at Lansing Community College, 2012-2016. Professor at Lansing Community College, 2016-
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The four main types of essay | Quick guide with examples
The Four Main Types of Essay | Quick Guide with Examples
Published on September 4, 2020 by Jack Caulfield . Revised on July 23, 2023.
An essay is a focused piece of writing designed to inform or persuade. There are many different types of essay, but they are often defined in four categories: argumentative, expository, narrative, and descriptive essays.
Argumentative and expository essays are focused on conveying information and making clear points, while narrative and descriptive essays are about exercising creativity and writing in an interesting way. At university level, argumentative essays are the most common type.
Essay type
Skills tested
Example prompt
Has the rise of the internet had a positive or negative impact on education?
Explain how the invention of the printing press changed European society in the 15th century.
Write about an experience where you learned something about yourself.
Describe an object that has sentimental value for you.
In high school and college, you will also often have to write textual analysis essays, which test your skills in close reading and interpretation.
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Table of contents
Argumentative essays, expository essays, narrative essays, descriptive essays, textual analysis essays, other interesting articles, frequently asked questions about types of essays.
An argumentative essay presents an extended, evidence-based argument. It requires a strong thesis statement —a clearly defined stance on your topic. Your aim is to convince the reader of your thesis using evidence (such as quotations ) and analysis.
Argumentative essays test your ability to research and present your own position on a topic. This is the most common type of essay at college level—most papers you write will involve some kind of argumentation.
The essay is divided into an introduction, body, and conclusion:
The introduction provides your topic and thesis statement
The body presents your evidence and arguments
The conclusion summarizes your argument and emphasizes its importance
The example below is a paragraph from the body of an argumentative essay about the effects of the internet on education. Mouse over it to learn more.
A common frustration for teachers is students’ use of Wikipedia as a source in their writing. Its prevalence among students is not exaggerated; a survey found that the vast majority of the students surveyed used Wikipedia (Head & Eisenberg, 2010). An article in The Guardian stresses a common objection to its use: “a reliance on Wikipedia can discourage students from engaging with genuine academic writing” (Coomer, 2013). Teachers are clearly not mistaken in viewing Wikipedia usage as ubiquitous among their students; but the claim that it discourages engagement with academic sources requires further investigation. This point is treated as self-evident by many teachers, but Wikipedia itself explicitly encourages students to look into other sources. Its articles often provide references to academic publications and include warning notes where citations are missing; the site’s own guidelines for research make clear that it should be used as a starting point, emphasizing that users should always “read the references and check whether they really do support what the article says” (“Wikipedia:Researching with Wikipedia,” 2020). Indeed, for many students, Wikipedia is their first encounter with the concepts of citation and referencing. The use of Wikipedia therefore has a positive side that merits deeper consideration than it often receives.
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An expository essay provides a clear, focused explanation of a topic. It doesn’t require an original argument, just a balanced and well-organized view of the topic.
Expository essays test your familiarity with a topic and your ability to organize and convey information. They are commonly assigned at high school or in exam questions at college level.
The introduction of an expository essay states your topic and provides some general background, the body presents the details, and the conclusion summarizes the information presented.
A typical body paragraph from an expository essay about the invention of the printing press is shown below. Mouse over it to learn more.
The invention of the printing press in 1440 changed this situation dramatically. Johannes Gutenberg, who had worked as a goldsmith, used his knowledge of metals in the design of the press. He made his type from an alloy of lead, tin, and antimony, whose durability allowed for the reliable production of high-quality books. This new technology allowed texts to be reproduced and disseminated on a much larger scale than was previously possible. The Gutenberg Bible appeared in the 1450s, and a large number of printing presses sprang up across the continent in the following decades. Gutenberg’s invention rapidly transformed cultural production in Europe; among other things, it would lead to the Protestant Reformation.
A narrative essay is one that tells a story. This is usually a story about a personal experience you had, but it may also be an imaginative exploration of something you have not experienced.
Narrative essays test your ability to build up a narrative in an engaging, well-structured way. They are much more personal and creative than other kinds of academic writing . Writing a personal statement for an application requires the same skills as a narrative essay.
A narrative essay isn’t strictly divided into introduction, body, and conclusion, but it should still begin by setting up the narrative and finish by expressing the point of the story—what you learned from your experience, or why it made an impression on you.
Mouse over the example below, a short narrative essay responding to the prompt “Write about an experience where you learned something about yourself,” to explore its structure.
Since elementary school, I have always favored subjects like science and math over the humanities. My instinct was always to think of these subjects as more solid and serious than classes like English. If there was no right answer, I thought, why bother? But recently I had an experience that taught me my academic interests are more flexible than I had thought: I took my first philosophy class.
Before I entered the classroom, I was skeptical. I waited outside with the other students and wondered what exactly philosophy would involve—I really had no idea. I imagined something pretty abstract: long, stilted conversations pondering the meaning of life. But what I got was something quite different.
A young man in jeans, Mr. Jones—“but you can call me Rob”—was far from the white-haired, buttoned-up old man I had half-expected. And rather than pulling us into pedantic arguments about obscure philosophical points, Rob engaged us on our level. To talk free will, we looked at our own choices. To talk ethics, we looked at dilemmas we had faced ourselves. By the end of class, I’d discovered that questions with no right answer can turn out to be the most interesting ones.
The experience has taught me to look at things a little more “philosophically”—and not just because it was a philosophy class! I learned that if I let go of my preconceptions, I can actually get a lot out of subjects I was previously dismissive of. The class taught me—in more ways than one—to look at things with an open mind.
A descriptive essay provides a detailed sensory description of something. Like narrative essays, they allow you to be more creative than most academic writing, but they are more tightly focused than narrative essays. You might describe a specific place or object, rather than telling a whole story.
Descriptive essays test your ability to use language creatively, making striking word choices to convey a memorable picture of what you’re describing.
A descriptive essay can be quite loosely structured, though it should usually begin by introducing the object of your description and end by drawing an overall picture of it. The important thing is to use careful word choices and figurative language to create an original description of your object.
Mouse over the example below, a response to the prompt “Describe a place you love to spend time in,” to learn more about descriptive essays.
On Sunday afternoons I like to spend my time in the garden behind my house. The garden is narrow but long, a corridor of green extending from the back of the house, and I sit on a lawn chair at the far end to read and relax. I am in my small peaceful paradise: the shade of the tree, the feel of the grass on my feet, the gentle activity of the fish in the pond beside me.
My cat crosses the garden nimbly and leaps onto the fence to survey it from above. From his perch he can watch over his little kingdom and keep an eye on the neighbours. He does this until the barking of next door’s dog scares him from his post and he bolts for the cat flap to govern from the safety of the kitchen.
With that, I am left alone with the fish, whose whole world is the pond by my feet. The fish explore the pond every day as if for the first time, prodding and inspecting every stone. I sometimes feel the same about sitting here in the garden; I know the place better than anyone, but whenever I return I still feel compelled to pay attention to all its details and novelties—a new bird perched in the tree, the growth of the grass, and the movement of the insects it shelters…
Sitting out in the garden, I feel serene. I feel at home. And yet I always feel there is more to discover. The bounds of my garden may be small, but there is a whole world contained within it, and it is one I will never get tired of inhabiting.
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Though every essay type tests your writing skills, some essays also test your ability to read carefully and critically. In a textual analysis essay, you don’t just present information on a topic, but closely analyze a text to explain how it achieves certain effects.
Rhetorical analysis
A rhetorical analysis looks at a persuasive text (e.g. a speech, an essay, a political cartoon) in terms of the rhetorical devices it uses, and evaluates their effectiveness.
The goal is not to state whether you agree with the author’s argument but to look at how they have constructed it.
The introduction of a rhetorical analysis presents the text, some background information, and your thesis statement; the body comprises the analysis itself; and the conclusion wraps up your analysis of the text, emphasizing its relevance to broader concerns.
The example below is from a rhetorical analysis of Martin Luther King Jr.’s “I Have a Dream” speech . Mouse over it to learn more.
King’s speech is infused with prophetic language throughout. Even before the famous “dream” part of the speech, King’s language consistently strikes a prophetic tone. He refers to the Lincoln Memorial as a “hallowed spot” and speaks of rising “from the dark and desolate valley of segregation” to “make justice a reality for all of God’s children.” The assumption of this prophetic voice constitutes the text’s strongest ethical appeal; after linking himself with political figures like Lincoln and the Founding Fathers, King’s ethos adopts a distinctly religious tone, recalling Biblical prophets and preachers of change from across history. This adds significant force to his words; standing before an audience of hundreds of thousands, he states not just what the future should be, but what it will be: “The whirlwinds of revolt will continue to shake the foundations of our nation until the bright day of justice emerges.” This warning is almost apocalyptic in tone, though it concludes with the positive image of the “bright day of justice.” The power of King’s rhetoric thus stems not only from the pathos of his vision of a brighter future, but from the ethos of the prophetic voice he adopts in expressing this vision.
Literary analysis
A literary analysis essay presents a close reading of a work of literature—e.g. a poem or novel—to explore the choices made by the author and how they help to convey the text’s theme. It is not simply a book report or a review, but an in-depth interpretation of the text.
Literary analysis looks at things like setting, characters, themes, and figurative language. The goal is to closely analyze what the author conveys and how.
The introduction of a literary analysis essay presents the text and background, and provides your thesis statement; the body consists of close readings of the text with quotations and analysis in support of your argument; and the conclusion emphasizes what your approach tells us about the text.
Mouse over the example below, the introduction to a literary analysis essay on Frankenstein , to learn more.
Mary Shelley’s Frankenstein is often read as a crude cautionary tale about the dangers of scientific advancement unrestrained by ethical considerations. In this reading, protagonist Victor Frankenstein is a stable representation of the callous ambition of modern science throughout the novel. This essay, however, argues that far from providing a stable image of the character, Shelley uses shifting narrative perspectives to portray Frankenstein in an increasingly negative light as the novel goes on. While he initially appears to be a naive but sympathetic idealist, after the creature’s narrative Frankenstein begins to resemble—even in his own telling—the thoughtlessly cruel figure the creature represents him as. This essay begins by exploring the positive portrayal of Frankenstein in the first volume, then moves on to the creature’s perception of him, and finally discusses the third volume’s narrative shift toward viewing Frankenstein as the creature views him.
If you want to know more about AI tools , college essays , or fallacies make sure to check out some of our other articles with explanations and examples or go directly to our tools!
Ad hominem fallacy
Post hoc fallacy
Appeal to authority fallacy
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Sunk cost fallacy
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At high school and in composition classes at university, you’ll often be told to write a specific type of essay , but you might also just be given prompts.
Look for keywords in these prompts that suggest a certain approach: The word “explain” suggests you should write an expository essay , while the word “describe” implies a descriptive essay . An argumentative essay might be prompted with the word “assess” or “argue.”
The vast majority of essays written at university are some sort of argumentative essay . Almost all academic writing involves building up an argument, though other types of essay might be assigned in composition classes.
Essays can present arguments about all kinds of different topics. For example:
In a literary analysis essay, you might make an argument for a specific interpretation of a text
In a history essay, you might present an argument for the importance of a particular event
In a politics essay, you might argue for the validity of a certain political theory
An argumentative essay tends to be a longer essay involving independent research, and aims to make an original argument about a topic. Its thesis statement makes a contentious claim that must be supported in an objective, evidence-based way.
An expository essay also aims to be objective, but it doesn’t have to make an original argument. Rather, it aims to explain something (e.g., a process or idea) in a clear, concise way. Expository essays are often shorter assignments and rely less on research.
The key difference is that a narrative essay is designed to tell a complete story, while a descriptive essay is meant to convey an intense description of a particular place, object, or concept.
Narrative and descriptive essays both allow you to write more personally and creatively than other kinds of essays , and similar writing skills can apply to both.
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Unit 6: Argumentative Essay Writing
47 Logical Fallacies
Logical fallacies are errors in reasoning based on faulty logic . Good writers want to convince readers to agree with their arguments—their reasons and conclusions. If your arguments are not logical, readers won’t be convinced. Logic can help prove your point and disprove your opponent’s point—and perhaps change a reader’s mind about an issue. If you use faulty logic (logic not based on fact), readers will not believe you or take your position seriously.
Read about five of the most common logical fallacies and how to avoid them below:
Generalizations
Loaded words
Inappropriate authority figures
Either/or arguments
Slippery slope
Common Logical Fallacies
Below are five of the most common logical fallacies.
#1 Generalizations
Explanation: Hasty generalizations are just what they sound like—making quick judgments based on inadequate information. This kind of logical fallacy is a common error in argumentative writing.
Example 1: Ren didn’t want to study at a university. Instead, Ren decided to go to a technical school. Ren is now making an excellent salary repairing computers. Luis doesn’t want to study at a university. Therefore, Luis should go to a technical school to become financially successful.
Analysis: While they have something in common (they both want to go to school and earn a high salary), this fact alone does not mean Luis would be successful doing the same thing that their friend Ren did. There may be other specific information which is important as well, such as the fact that Ren has lots of experience with computers or that Luis has different skills.
Example 2: If any kind of gun control laws are enacted, citizens will not be allowed to have any guns at all.
Analysis: While passing new gun control laws may result in new restrictions, it is highly unlikely the consequences would be so extreme; gun control is a complex issue and each law that may be passed would have different outcomes. Words such as “all,” “always,” “never,” “everyone,” “at all” are problematic because they cannot be supported with evidence. Consider making less sweeping and more modest conclusions.
Suggestions for Avoiding Generalizations
Replace “absolute” expressions with more “softening” expressions.
Replace words like “all” or “everyone” with “most people.” Instead of “no one” use “few people.”
Replace “always” with “typically” or “usually” or “often.”
Replace “never” with “rarely” or “infrequently” or the “to be verb” + “unlikely.”
Replace “will” with “may or might or could” or use the “to be verb” + “likely.”
Example 1 revised: Luis could consider going to a technical school. This education track is more likely to lead to financial success.
Example 2 revised: If extensive gun control laws are enacted, some citizens may feel their constitutional rights are being limited.
#2 Loaded Words
Explanation: Some words contain positive or negative connotations, which may elicit a positive or negative emotional response. Try to avoid them in academic writing when making an argument because your arguments should be based on reason (facts and evidence), not emotions. In fact, using these types of words may cause your reader to react against you as the writer, rather than being convincing as you hoped. Therefore they can make your argument actually weaker rather than stronger.
Example 1: It is widely accepted by reasonable people that free-trade has a positive effect on living standards, although some people ignorantly disagree with this.
Analysis: The words “reasonable” (positive) and “ignorantly” (negative) may bias the readers about the two groups without giving any evidence to support this bias.
Example 2: This decision is outrageous and has seriously jeopardized the financial futures for the majority of innocent citizens.
Analysis: The words “outrageous,” “seriously,” and “innocent” appeal to readers’ emotions in order to persuade them more easily. However, the most persuasive arguments in academic writing will be supported with evidence instead of drawing on emotions.
Suggestions for Avoiding Loaded Words
Choose appropriate vocabulary.
Omit adjectives and adverbs, especially if they carry emotion, value, or judgment.
Replace/add softeners like, “potentially” or modals like “might” or “may.”
Example 1 revised: It is widely accepted by many people that free-trade may have a positive effect on living standards, although some people may disagree with this.
Example 2 revised: This decision has potentially serious consequences for the financial futures for the majority of citizens.
#3 Inappropriate authority figures
Explanation: Using famous names may or may not help you prove your point. However, be sure to use the name logically and in relation to their own area of authority.
Example 1: Albert Einstein , one of the fathers of atomic energy, was a vegetarian and believed that animals deserved to be treated fairly. In short, animal testing should be banned.
Analysis: While Einstein is widely considered one of the great minds of the 20th century, he was a physicist , not an expert in animal welfare or ethics.
Example 2: Nuclear power is claimed to be safe because there is very little chance for an accident to happen, but little chance does not have the same meaning as safety. Riccio (2013), a news reporter for the Wisconsin State Journal, holds a strong opinion against the use of nuclear energy and constructions of nuclear power plants because he believes that the safety features do not meet the latest standards.
Analysis: In order to provide strong evidence to support the claim regarding the safety features of nuclear power plants, expert opinion is needed ; the profession of a reporter does not provide sufficient expertise to validate the claim.
Suggestions for Avoiding Inappropriate Authority Figures
Replace inappropriate authority figures with credible experts.
Read through your sources and look for examples of experts. Pay attention to their credentials. (See examples below.)
Find new sources written by or citing legitimate experts in the field.
Google the authority figure you wish to use to determine if they are an expert in the field. Use the Library Databases to locate a substantive or scholarly article related to your topic. Cite the author of one of these articles or use an indirect citation to cite an expert mentioned in the article.
Example 1 revised: Kitty Block, president and CEO of the Humane Society of the U.S. , emphasizes the need for researchers to work with international governments and agencies to follow new guidelines to protect animals and minimize their use in animal testing.
Example 2 revised: Edwin Lyman, senior scientist of the Global Security Program, points out that while the U.S. has severe-accident management programs, these plans are not evaluated by the Nuclear Regulatory Commission, and therefore may be subject to accidents or sabotage.
#4 Either/Or Arguments
Explanation: When you argue a point, be careful not to limit the choices to only two or three. This needs to be qualified.
Example 1: Studying abroad either increases job opportunities or causes students to become depressed.
Analysis: This statement implies that only two things may happen, whereas in reality these are two among many possible outcomes.
Example 2: People can continue to spend countless amounts of tax dollars fighting the use of a relatively safe drug, or they can make a change, legalize marijuana, and actually see a tax and revenue benefit for our state. (owl.excels ior.edu)
Analysis: Most issues are very complex and hardly ever either/or, i.e. they rarely have only two opposing ways of looking at them or two possible outcomes. Instead, use language that acknowledges the complexity of the issue.
Suggestions for Avoiding Either/Or Arguments
Offer more than one or two choices, options, or outcomes.
If relevant for your essay focus, offer more than one or two choices, options, or outcomes.
Acknowledge that multiple outcomes or perspectives exist.
Example 1 revised: Studying abroad may have a wide spectrum of outcomes , both positive and negative, from increasing job opportunities to leading to financial debt and depression.
Example 2 revised: There are a number of solutions for mitigating the illegal sale of marijuana, including legalizing the use of the drug in a wider range of contexts, increasing education about the drug and its use, and creating legal businesses for the sale, among other business related solutions.
#5 Slippery Slope
Explanation: When you argue that a chain reaction will take place, i.e. say that one problem may lead to a greater problem, which in turn leads to a greater problem, often ending in serious consequences. This way of arguing exaggerates and distorts the effects of the original choice. If the series of events is extremely improbable, your arguments will not be taken seriously.
Example 1: Animal experimentation reduces society’s respect for life. If people don’t respect life, they are likely to be more and more tolerant of violent acts like war and murder. Soon society will become a battlefield in which everyone constantly fears for their lives.
Analysis: This statement implies that allowing animal testing shows a moral problem which can lead to completely different, greater outcomes: war, death, the end of the world! Clearly an exaggeration.
Example 2: If stricter gun control laws are enacted, the right of citizens to own guns may be greatly restricted, which may limit their ability to defend themselves against terrorist attacks. When that happens, the number of terrorist attacks in this country may increase. Therefore, gun control laws may result in higher probability of widespread terrorism. (owl.excelsior.edu)
Analysis: The issue of gun control is exaggerated to lead into a very different issue. Check your arguments to make sure any chains of consequences are reasonable and still within the scope of your focused topic. (writingcenter.unc.edu)
Suggestions for Avoiding Slippery Slope
Think through the chain of events.
Carefully think about the chain of events and know when to stop to make sure these events are still within the narrowed focus of your essay.
Example 1 revised: If animal experimentation is not limited, an increasing number of animals will likely continue to be hurt or killed as a result of these experiments.
Example 2 revised: With stricter gun laws, the number of citizens who are able to obtain firearms may be reduced, which could lead to fewer deaths involving guns.
As you read your own work, imagine you are reading the draft for the first time. Look carefully for any instances of faulty logic and then use the tips above to eliminate the logical fallacies in your writing.
Adapted from Great Essays by Folse, Muchmore-Vokoun, & Soloman
Argument is a central concept for philosophy. Philosophers rely heavily on arguments to justify claims, and these practices have been motivating reflections on what arguments and argumentation are for millennia. Moreover, argumentative practices are also pervasive elsewhere; they permeate scientific inquiry, legal procedures, education, and political institutions. The study of argumentation is an inter-disciplinary field of inquiry, involving philosophers, language theorists, legal scholars, cognitive scientists, computer scientists, and political scientists, among many others. This entry provides an overview of the literature on argumentation drawing primarily on philosophical sources, but also engaging extensively with relevant sources from other disciplines.
1. Terminological Clarifications
2.1 deduction, 2.2 induction, 2.3 abduction, 2.4 analogy, 2.5 fallacies, 3.1 adversarial and cooperative argumentation, 3.2 argumentation as an epistemic practice, 3.3 consensus-oriented argumentation, 3.4 argumentation and conflict management, 3.5 conclusion, 4.1 argumentation theory, 4.2 artificial intelligence and computer science, 4.3 cognitive science and psychology, 4.4 language and communication, 4.5 argumentation in specific social practices, 5.1 argumentative injustice and virtuous argumentation, 5.2 emotions and argumentation, 5.3 cross-cultural perspectives on argumentation, 5.4 argumentation and the internet, 6. conclusion, references for the main text, references for the historical supplement, other internet resources, related entries.
An argument can be defined as a complex symbolic structure where some parts, known as the premises, offer support to another part, the conclusion. Alternatively, an argument can be viewed as a complex speech act consisting of one or more acts of premising (which assert propositions in favor of the conclusion), an act of concluding, and a stated or implicit marker (“hence”, “therefore”) that indicates that the conclusion follows from the premises (Hitchcock 2007). [ 1 ] The relation of support between premises and conclusion can be cashed out in different ways: the premises may guarantee the truth of the conclusion, or make its truth more probable; the premises may imply the conclusion; the premises may make the conclusion more acceptable (or assertible).
For theoretical purposes, arguments may be considered as freestanding entities, abstracted from their contexts of use in actual human activities. But depending on one’s explanatory goals, there is also much to be gained from considering arguments as they in fact occur in human communicative practices. The term generally used for instances of exchange of arguments is argumentation . In what follows, the convention of using “argument” to refer to structures of premises and conclusion, and “argumentation” to refer to human practices and activities where arguments occur as communicative actions will be adopted.
Argumentation can be defined as the communicative activity of producing and exchanging reasons in order to support claims or defend/challenge positions, especially in situations of doubt or disagreement (Lewiński & Mohammed 2016). It is arguably best conceived as a kind of dialogue , even if one can also “argue” with oneself, in long speeches or in writing (in articles or books) for an intended but silent audience, or in groups rather than in dyads (Lewiński & Aakhus 2014). But argumentation is a special kind of dialogue: indeed, most of the dialogues we engage in are not instances of argumentation, for example when asking someone if they know what time it is, or when someone shares details about their vacation. Argumentation only occurs when, upon making a claim, someone receives a request for further support for the claim in the form of reasons, or estimates herself that further justification is required (Jackson & Jacobs 1980; Jackson, 2019). In such cases, dialogues of “giving and asking for reasons” ensue (Brandom, 1994; Bermejo Luque 2011). Since most of what we know we learn from others, argumentation seems to be an important mechanism to filter the information we receive, instead of accepting what others tell us uncritically (Sperber, Clément, et al. 2010).
The study of arguments and argumentation is also closely connected to the study of reasoning , understood as the process of reaching conclusions on the basis of careful, reflective consideration of the available information, i.e., by an examination of reasons . According to a widespread view, reasoning and argumentation are related (as both concern reasons) but fundamentally different phenomena: reasoning would belong to the mental realm of thinking—an individual inferring new information from the available information by means of careful consideration of reasons—whereas argumentation would belong to the public realm of the exchange of reasons, expressed in language or other symbolic media and intended for an audience. However, a number of authors have argued for a different view, namely that reasoning and argumentation are in fact two sides of the same coin, and that what is known as reasoning is by and large the internalization of practices of argumentation (MacKenzie 1989; Mercier & Sperber 2017; Mercier 2018). For the purposes of this entry, we can assume a close connection between reasoning and argumentation so that relevant research on reasoning can be suitably included in the discussions to come.
2. Types of Arguments
Arguments come in many kinds. In some of them, the truth of the premises is supposed to guarantee the truth of the conclusion, and these are known as deductive arguments. In others, the truth of the premises should make the truth of the conclusion more likely while not ensuring complete certainty; two well-known classes of such arguments are inductive and abductive arguments (a distinction introduced by Peirce, see entry on C.S. Peirce ). Unlike deduction, induction and abduction are thought to be ampliative: the conclusion goes beyond what is (logically) contained in the premises. Moreover, a type of argument that features prominently across different philosophical traditions, and yet does not fit neatly into any of the categories so far discussed, are analogical arguments. In this section, these four kinds of arguments are presented. The section closes with a discussion of fallacious arguments, that is, arguments that seem legitimate and “good”, but in fact are not. [ 2 ]
Valid deductive arguments are those where the truth of the premises necessitates the truth of the conclusion: the conclusion cannot but be true if the premises are true. Arguments having this property are said to be deductively valid . A valid argument whose premises are also true is said to be sound . Examples of valid deductive arguments are the familiar syllogisms, such as:
All humans are living beings. All living beings are mortal. Therefore, all humans are mortal.
In a deductively valid argument, the conclusion will be true in all situations where the premises are true, with no exceptions. A slightly more technical gloss of this idea goes as follows: in all possible worlds where the premises hold, the conclusion will also hold. This means that, if I know the premises of a deductively valid argument to be true of a given situation, then I can conclude with absolute certainty that the conclusion is also true of that situation. An important property typically associated with deductive arguments (but with exceptions, such as in relevant logic), and which differentiates them from inductive and abductive arguments, is the property of monotonicity : if premises A and B deductively imply conclusion C , then the addition of any arbitrary premise D will not invalidate the argument. In other words, if the argument “ A and B ; therefore C ” is deductively valid, then the argument “ A , B and D ; therefore C ” is equally deductively valid.
Deductive arguments are the objects of study of familiar logical systems such as (classical) propositional and predicate logic, as well as of subclassical systems such as intuitionistic and relevant logics (although in relevant logic the property of monotonicity does not hold, as it may lead to violations of criteria of relevance between premises and conclusion—see entry on relevance logic ). In each of these systems, the relation of logical consequence in question satisfies the property of necessary truth-preservation (see entry on logical consequence ). This is not surprising, as these systems were originally designed to capture arguments of a very specific kind, namely mathematical arguments (proofs), in the pioneering work of Frege, Russell, Hilbert, Gentzen, and others. Following a paradigm established in ancient Greek mathematics and famously captured in Euclid’s Elements , argumentative steps in mathematical proofs (in this tradition at least) must have the property of necessary truth preservation (Netz 1999). This paradigm remained influential for millennia, and still codifies what can be described as the “classical” conception of mathematical proof (Dutilh Novaes 2020a), even if practices of proof are ultimately also quite diverse. (In fact, there is much more to argumentation in mathematics than just deductive argumentation [Aberdein & Dove 2013].)
However, a number of philosophers have argued that deductive validity and necessary truth preservation in fact come apart. Some have reached this conclusion motivated by the familiar logical paradoxes such as the Liar or Curry’s paradox (Beall 2009; Field 2008; see entries on the Liar paradox and on Curry’s paradox ). Others have defended the idea that there are such things as contingent logical truths (Kaplan 1989; Nelson & Zalta 2012), which thus challenge the idea of necessary truth preservation. It has also been suggested that what is preserved in the transition from premises to conclusions in deductive arguments is in fact warrant or assertibility rather than truth (Restall 2004). Yet others, such as proponents of preservationist approaches to paraconsistent logic, posit that what is preserved by the deductive consequence relation is the coherence, or incoherence, of a set of premises (Schotch, Brown, & Jennings 2009; see entry on paraconsistent logic ). Nevertheless, it is fair to say that the view that deductive validity is to be understood primarily in terms of necessary truth preservation is still the received view.
Relatedly, there are a number of pressing philosophical issues pertaining to the justification of deduction, such as the exact nature of the necessity involved in deduction (metaphysical, logical, linguistic, epistemic; Shapiro 2005), and the possibility of offering a non-circular foundation for deduction (Dummett 1978). Furthermore, it is often remarked that the fact that a deductive argument is not ampliative may entail that it cannot be informative, which in turn would mean that its usefulness is quite limited; this problem has been described as “the scandal of deduction” (Sequoiah-Grayson 2008).
Be that as it may, deductive arguments have occupied a special place in philosophy and the sciences, ever since Aristotle presented the first fully-fledged theory of deductive argumentation and reasoning in the Prior Analytics (and the corresponding theory of scientific demonstration in the Posterior Analytics ; see Historical Supplement ). The fascination for deductive arguments is understandable, given their allure of certainty and indubitability. The more geometrico (a phrase introduced by Spinoza to describe the argumentative structure of his Ethics as following “a geometrical style”—see entry on Spinoza ) has been influential in many fields other than mathematics. However, the focus on deductive arguments at the expense of other types of arguments has arguably skewed investigations on argument and argumentation too much in one specific direction (see (Bermejo-Luque 2020) for a critique of deductivism in the study of argumentation).
In recent decades, the view that everyday reasoning and argumentation by and large do not follow the canons of deductive argumentation has been gaining traction. In psychology of reasoning, Oaksford and Chater were the first to argue already in the 1980s that human reasoning “in the wild” is essentially probabilistic, following the basic canons of Bayesian probabilities (Oaksford & Chater 2018; Elqayam 2018; see section 5.3 below). Computer scientists and artificial intelligence researchers have also developed a strong interest in non-monotonic reasoning and argumentation (Reiter 1980), recognizing that, outside specific scientific contexts, human reasoning tends to be deeply defeasible (Pollock 1987; see entries on non-monotonic logic and defeasible reasoning ). Thus seen, deductive argumentation might be considered as the exception rather than the rule in human argumentative practices taken as a whole (Dutilh Novaes 2020a). But there are others, especially philosophers, who still maintain that the use of deductive reasoning and argumentation is widespread and extends beyond niches of specialists (Shapiro 2014; Williamson 2018).
Inductive arguments are arguments where observations about past instances and regularities lead to conclusions about future instances and general principles. For example, the observation that the sun has risen in the east every single day until now leads to the conclusion that it will rise in the east tomorrow, and to the general principle “the sun always rises in the east”. Generally speaking, inductive arguments are based on statistical frequencies, which then lead to generalizations beyond the sample of cases initially under consideration: from the observed to the unobserved. In a good, i.e., cogent , inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion. In contrast with a deductively valid argument, in an inductive argument the degree of support will never be maximal, as there is always the possibility of the conclusion being false given the truth of the premises. A gloss in terms of possible worlds might be that, while in a deductively valid argument the conclusion will hold in all possible worlds where the premises hold, in a good inductive argument the conclusion will hold in a significant proportion of the possible worlds where the premises hold. The proportion of such worlds may give a measure of the strength of support of the premises for the conclusion (see entry on inductive logic ).
Inductive arguments have been recognized and used in science and elsewhere for millennia. The concept of induction ( epagoge in Greek) was understood by Aristotle as a progression from particulars to a universal, and figured prominently both in his conception of the scientific method and in dialectical practices (see entry on Aristotle’s logic, section 3.1 ). However, a deductivist conception of the scientific method remained overall more influential in Aristotelian traditions, inspired by the theory of scientific demonstration of the Posterior Analytics . It is only with the so-called “scientific revolution” of the early modern period that experiments and observation of individual cases became one of the pillars of scientific methodology, a transition that is strongly associated with the figure of Francis Bacon (1561–1626; see entry on Francis Bacon ).
Inductive inferences/arguments are ubiquitous both in science and in everyday life, and for the most part quite reliable. The functioning of the world around us seems to display a fair amount of statistical regularity, and this is referred to as the “Uniformity Principle” in the literature on the problem of induction (to be discussed shortly). Moreover, it has been argued that generalizing from previously observed frequencies is the most basic principle of human cognition (Clark 2016).
However, it has long been recognized that inductive inferences/arguments are not unproblematic. Hume famously offered the first influential formulation of what became known as “the problem of induction” in his Treatise of Human Nature (see entries on David Hume and on the problem of induction ; Howson 2000). Hume raises the question of what grounds the correctness of inductive inferences/arguments, and posits that there must be an argument establishing the validity of the Uniformity Principle for inductive inferences to be truly justified. He goes on to argue that this argument cannot be deductive, as it is not inconceivable that the course of nature may change. But it cannot be probable either, as probable arguments already presuppose the validity of the Uniformity Principle; circularity would ensue. Since these are the only two options, he concludes that the Uniformity Principle cannot be established by rational argument, and hence that induction cannot be justified.
A more recent influential critique of inductive arguments is the one offered in (Harman 1965). Harman argues that either enumerative induction is not always warranted, or it is always warranted but constitutes an uninteresting special case of the more general category of inference to the best explanation (see next section). The upshot is that, for Harman, induction should not be considered a warranted form of inference in its own right.
Given the centrality of induction for scientific practice, there have been numerous attempts to respond to the critics of induction, with various degrees of success. Among those, an influential recent response to the problem of induction is Norton’s material theory of induction (Norton 2003). But the problem has not prevented scientists and laypeople alike from continuing to use induction widely. More recently, the use of statistical frequencies for social categories to draw conclusions about specific individuals has become a matter of contention, both at the individual level (see entry on implicit bias ) and at the institutional level (e.g., the use of predictive algorithms for law enforcement [Jorgensen Bolinger 2021]). These debates can be seen as reoccurrences of Hume’s problem of induction, now in the domain of social rather than of natural phenomena.
An abductive argument is one where, from the observation of a few relevant facts, a conclusion is drawn as to what could possibly explain the occurrence of these facts (see entry on abduction ). Abduction is widely thought to be ubiquitous both in science and in everyday life, as well as in other specific domains such as the law, medical diagnosis, and explainable artificial intelligence (Josephson & Josephson 1994). Indeed, a good example of abduction is the closing argument by a prosecutor in a court of law who, after summarizing the available evidence, concludes that the most plausible explanation for it is that the defendant must have committed the crime they are accused of.
Like induction, and unlike deduction, abduction is not necessarily truth-preserving: in the example above, it is still possible that the defendant is not guilty after all, and that some other, unexpected phenomena caused the evidence to emerge. But abduction is significantly different from induction in that it does not only concern the generalization of prior observation for prediction (though it may also involve statistical data): rather, abduction is often backward-looking in that it seeks to explain something that has already happened. The key notion is that of bringing together apparently independent phenomena or events as explanatorily and/or causally connected to each other, something that is absent from a purely inductive argument that only appeals to observed frequencies. Cognitively, abduction taps into the well-known human tendency to seek (causal) explanations for phenomena (Keil 2006).
As noted, deduction and induction have been recognized as important classes of arguments for millennia; the concept of abduction is by comparison a latecomer. It is important to notice though that explanatory arguments as such are not latecomers; indeed, Aristotle’s very conception of scientific demonstration is based on the concept of explaining causes (see entry on Aristotle ). What is recent is the conceptualization of abduction as a special class of arguments, and the term itself. The term was introduced by Peirce as a third class of inferences distinct from deduction and induction: for Peirce, abduction is understood as the process of forming explanatory hypotheses, thus leading to new ideas and concepts (whereas for him deduction and induction could not lead to new ideas or theories; see the entry on Peirce ). Thus seen, abduction pertains to contexts of discovery , in which case it is not clear that it corresponds to instances of arguments, properly speaking. In its modern meaning, however, abduction pertains to contexts of justification , and thus to speak of abductive arguments becomes appropriate. An abductive argument is now typically understood as an inference to the best explanation (Lipton 1971 [2003]), although some authors contend that there are good reasons to distinguish the two concepts (Campos 2011).
While the main ideas behind abduction may seem simple enough, cashing out more precisely how exactly abduction works is a complex matter (see entry on abduction ). Moreover, it is not clear that abductive arguments are always or even generally reliable and cogent. Humans seem to have a tendency to overshoot in their quest for causal explanations, and often look for simplicity where there is none to be found (Lombrozo 2007; but see Sober 2015 on the significance of parsimony in scientific reasoning). There are also a number of philosophical worries pertaining to the justification of abduction, especially in scientific contexts; one influential critique of abduction/inference to the best explanation is the one articulated by van Fraassen (Fraassen 1989). A frequent concern pertains to the connection between explanatory superiority and truth: are we entitled to conclude that the conclusion of an abductive argument is true solely on the basis of it being a good (or even the best) explanation for the phenomena in question? It seems that no amount of philosophical a priori theorizing will provide justification for the leap from explanatory superiority to truth. Instead, defenders of abduction tend to offer empirical arguments showing that abduction tends to be a reliable rule of inference. In this sense, abduction and induction are comparable: they are widely used, grounded in very basic human cognitive tendencies, but they give rise to a number of difficult philosophical problems.
Arguments by analogy are based on the idea that, if two things are similar, what is true of one of them is likely to be true of the other as well (see entry on analogy and analogical reasoning ). Analogical arguments are widely used across different domains of human activity, for example in legal contexts (see entry on precedent and analogy in legal reasoning ). As an example, take an argument for the wrongness of farming non-human animals for food consumption: if an alien species farmed humans for food, that would be wrong; so, by analogy, it is wrong for us humans to farm non-human animals for food. The general idea is captured in the following schema (adapted from the entry on analogy and analogical reasoning ; S is the source domain and T the target domain of the analogy):
S is similar to T in certain (known) respects.
S has some further feature Q .
Therefore, T also has the feature Q , or some feature Q * similar to Q .
The first premise establishes the analogy between two situations, objects, phenomena etc. The second premise states that the source domain has a given property. The conclusion is then that the target domain also has this property, or a suitable counterpart thereof. While informative, this schema does not differentiate between good and bad analogical arguments, and so does not offer much by way of explaining what grounds (good) analogical arguments. Indeed, contentious cases usually pertain to premise 1, and in particular to whether S and T are sufficiently similar in a way that is relevant for having or not having feature Q .
Analogical arguments are widely present in all known philosophical traditions, including three major ancient traditions: Greek, Chinese, and Indian (see Historical Supplement ). Analogies abound in ancient Greek philosophical texts, for example in Plato’s dialogues. In the Gorgias , for instance, the knack of rhetoric is compared to pastry-baking—seductive but ultimately unhealthy—whereas philosophy would correspond to medicine—potentially painful and unpleasant but good for the soul/body (Irani 2017). Aristotle discussed analogy extensively in the Prior Analytics and in the Topics (see section 3.2 of the entry on analogy and analogical reasoning ). In ancient Chinese philosophy, analogy occupies a very prominent position; indeed, it is perhaps the main form of argumentation for Chinese thinkers. Mohist thinkers were particularly interested in analogical arguments (see entries on logic and language in early Chinese philosophy , Mohism and the Mohist canons ). In the Latin medieval tradition too analogy received sustained attention, in particular in the domains of logic, theology and metaphysics (see entry on medieval theories of analogy ).
Analogical arguments continue to occupy a central position in philosophical discussions, and a number of the most prominent philosophical arguments of the last decades are analogical arguments, e.g., Jarvis Thomson’s violinist argument purportedly showing the permissibility of abortion (Thomson 1971), and Searle’s Chinese Room argument purportedly showing that computers cannot display real understanding (see entry on the Chinese Room argument ). (Notice that these two arguments are often described as thought experiments [see entry on thought experiments ], but thought experiments are often based on analogical principles when seeking to make a point that transcends the thought experiment as such.) The Achilles’ heel of analogical arguments can be illustrated by these two examples: both arguments have been criticized on the grounds that the purported similarity between the source and the target domains is not sufficient to extrapolate the property of the source domain (the permissibility of disconnecting from the violinist; the absence of understanding in the Chinese room) to the target domain (abortion; digital computers and artificial intelligence).
In sum, while analogical arguments in general perhaps confer a lesser degree of conviction than the other three kinds of arguments discussed, they are widely used both in professional circles and in everyday life. They have rightly attracted a fair amount of attention from scholars in different disciplines, and remain an important object of study (see entry on analogy and analogical reasoning ).
One of the most extensively studied types of arguments throughout the centuries are, perhaps surprisingly, arguments that appear legitimate but are not, known as fallacious arguments . From early on, the investigation of such arguments occupied a prominent position in Aristotelian logical traditions, inspired in particular by his book Sophistical Refutations (see Historical Supplement ). The thought is that, to argue well, it is not sufficient to be able to produce and recognize good arguments; it is equally (or perhaps even more) important to be able to recognize bad arguments by others, and to avoid producing bad arguments oneself. This is particularly true of the tricky cases, namely arguments that appear legitimate but are not, i.e., fallacies.
Some well-know types of fallacies include (see entry on fallacies for a more extensive discussion):
The fallacy of equivocation, which occurs when an arguer exploits the ambiguity of a term or phrase which has occurred at least twice in an argument to draw an unwarranted conclusion.
The fallacy of begging the question, when one of the premises and the conclusion of an argument are the same proposition, but differently formulated.
The fallacy of appeal to authority, when a claim is supported by reference to an authority instead of offering reasons to support it.
The ad hominem fallacy, which involves bringing negative aspects of an arguer, or their situation, to argue against the view they are advancing.
The fallacy of faulty analogy, when an analogy is used as an argument but there is not sufficient relevant similarity between the source domain and the target domain (as discussed above).
Beyond their (presumed?) usefulness in teaching argumentative skills, the literature on fallacies raises a number of important philosophical discussions, such as: What determines when an argument is fallacious or rather a legitimate argument? (See section 4.3 below on Bayesian accounts of fallacies) What causes certain arguments to be fallacious? Is the focus on fallacies a useful approach to arguments at all? (Massey 1981) Despite the occasional criticism, the concept of fallacies remains central in the study of arguments and argumentation.
3. Types of Argumentation
Just as there are different types of arguments, there are different types of argumentative situations, depending on the communicative goals of the persons involved and background conditions. Argumentation may occur when people are trying to reach consensus in a situation of dissent, but it may also occur when scientists discuss their findings with each other (to name but two examples). Specific rules of argumentative engagement may vary depending on these different types of argumentation.
A related point extensively discussed in the recent literature pertains to the function(s) of argumentation. [ 3 ] What’s the point of arguing? While it is often recognized that argumentation may have multiple functions, different authors tend to emphasize specific functions for argumentation at the expense of others. This section offers an overview of discussions on types of argumentation and its functions, demonstrating that argumentation is a multifaceted phenomenon that has different applications in different circumstances.
A question that has received much attention in the literature of the past decades pertains to whether the activity of argumentation is primarily adversarial or primarily cooperative. This question in fact corresponds to two sub-questions: the descriptive question of whether instances of argumentation are on the whole primarily adversarial or cooperative; and the normative question of whether argumentation should be (primarily) adversarial or cooperative. A number of authors have answered “adversarial” to the descriptive question and “cooperative” to the normative question, thus identifying a discrepancy between practices and normative ideals that must be remedied (or so they claim; Cohen 1995).
A case in point: recently, a number of far-right Internet personalities have advocated the idea that argumentation can be used to overpower one’s opponents, as described in the book The Art of the Argument: Western Civilization’s Last Stand (2017) by the white supremacist S. Molyneux. Such aggressive practices reflect a vision of argumentation as a kind of competition or battle, where the goal is to “score points” and “beat the opponent”. Authors who have criticized (overly) adversarial practices of argumentation include (Moulton 1983; Gilbert 1994; Rooney 2012; Hundleby 2013; Bailin & Battersby 2016). Many (but not all) of these authors formulated their criticism specifically from a feminist perspective (see entry on feminist perspectives on argumentation ).
Feminist critiques of adversarial argumentation challenge ideals of argumentation as a form of competition, where masculine-coded values of aggression and violence prevail (Kidd 2020). For these authors, such ideals encourage argumentative performances where excessive use of forcefulness is on display. Instances of aggressive argumentation in turn have a number of problematic consequences: epistemic consequences—the pursuit of truth is not best served by adversarial argumentation—as well as moral/ethical/political consequences—these practices exclude a number of people from participating in argumentative encounters, namely those for whom displays of aggression do not constitute socially acceptable behavior (women and other socially disadvantaged groups in particular). These authors defend alternative conceptions of argumentation as a cooperative, nurturing activity (Gilbert 1994; Bailin & Battersby 2016), which are traditionally feminine-coded values. Crucially, they view adversarial conceptions of argumentation as optional , maintaining that the alternatives are equally legitimate and that cooperative conceptions should be adopted and cultivated.
By contrast, others have argued that adversariality, when suitably understood, can be seen as an integral and in fact desirable component of argumentation (Govier 1999; Aikin 2011; Casey 2020; but notice that these authors each develop different accounts of adversariality in argumentation). Such authors answer “adversarial” both to the descriptive and to the normative questions stated above. One overall theme is the need to draw a distinction between (excessive) aggressiveness and adversariality as such. Govier, for example, distinguishes between ancillary (negative) adversariality and minimal adversariality (Govier 1999). The thought is that, while the feminist critique of excessive aggression in argumentation is well taken, adversariality conceived and practiced in different ways need not have the detrimental consequences of more extreme versions of belligerent argumentation. Moreover, for these authors, adversariality in argumentation is simply not optional: it is an intrinsic feature of argumentative practices, but these practices also require a background of cooperation and agreement regarding, e.g., the accepted rules of inference.
But ultimately, the presumed opposition between adversarial and cooperative conceptions of argumentation may well be merely apparent. It may be argued for example that actual argumentative encounters ought to be adversarial or cooperative to different degrees, as different types of argumentation are required for different situations (Dutilh Novaes forthcoming). Indeed, perhaps we should not look for a one-fits-all model of how argumentation ought to be conducted across different contexts and situation, given the diversity of uses of argumentation.
We speak of argumentation as an epistemic practice when we take its primary purpose to be that of improving our beliefs and increasing knowledge, or of fostering understanding. To engage in argumentation can be a way to acquire more accurate beliefs: by examining critically reasons for and against a given position, we would be able to weed out weaker, poorly justified beliefs (likely to be false) and end up with stronger, suitably justified beliefs (likely to be true). From this perspective, the goal of engaging in argumentation is to learn , i.e., to improve one’s epistemic position (as opposed to argumentation “to win” (Fisher & Keil 2016)). Indeed, argumentation is often said to be truth-conducive (Betz 2013).
The idea that argumentation can be an epistemically beneficial process is as old as philosophy itself. In every major historical philosophical tradition, argumentation is viewed as an essential component of philosophical reflection precisely because it may be used to aim at the truth (indeed this is the core of Plato’s critique of the Sophists and their excessive focus on persuasion at the expense of truth (Irani 2017; see Historical Supplement ). Recent proponents of an epistemological approach to argumentation include (Goldman 2004; Lumer 2005; Biro & Siegel 2006). Alvin Goldman captures this general idea in the following terms:
Norms of good argumentation are substantially dedicated to the promotion of truthful speech and the exposure of falsehood, whether intentional or unintentional. […] Norms of good argumentation are part of a practice to encourage the exchange of truths through sincere, non-negligent, and mutually corrective speech. (Goldman 1994: 30)
Of course, it is at least in theory possible to engage in argumentation with oneself along these lines, solitarily weighing the pros and cons of a position. But a number of philosophers, most notably John Stuart Mill, maintain that interpersonal argumentative situations, involving people who truly disagree with each other, work best to realize the epistemic potential of argumentation to improve our beliefs (a point he developed in On Liberty (1859; see entry on John Stuart Mill ). When our ideas are challenged by engagement with those who disagree with us, we are forced to consider our own beliefs more thoroughly and critically. The result is that the remaining beliefs, those that have survived critical challenge, will be better grounded than those we held before such encounters. Dissenters thus force us to stay epistemically alert instead of becoming too comfortable with existing, entrenched beliefs. On this conception, arguers cooperate with each other precisely by being adversarial, i.e., by adopting a critical stance towards the positions one disagrees with.
The view that argumentation aims at epistemic improvement is in many senses appealing, but it is doubtful that it reflects the actual outcomes of argumentation in many real-life situations. Indeed, it seems that, more often than not, we are not Millians when arguing: we do not tend to engage with dissenting opinions with an open mind. Indeed, there is quite some evidence suggesting that arguments are in fact not a very efficient means to change minds in most real-life situations (Gordon-Smith 2019). People typically do not like to change their minds about firmly entrenched beliefs, and so when confronted with arguments or evidence that contradict these beliefs, they tend to either look away or to discredit the source of the argument as unreliable (Dutilh Novaes 2020c)—a phenomenon also known as “confirmation bias” (Nickerson 1998).
In particular, arguments that threaten our core beliefs and our sense of belonging to a group (e.g., political beliefs) typically trigger all kinds of motivated reasoning (Taber & Lodge 2006; Kahan 2017) whereby one outright rejects those arguments without properly engaging with their content. Relatedly, when choosing among a vast supply of options, people tend to gravitate towards content and sources that confirm their existing opinions, thus giving rise to so-called “echo chambers” and “epistemic bubbles” (Nguyen 2020). Furthermore, some arguments can be deceptively convincing in that they look valid but are not (Tindale 2007; see entry on fallacies ). Because most of us are arguably not very good at spotting fallacious arguments, especially if they are arguments that lend support to the beliefs we already hold, engaging in argumentation may in fact decrease the accuracy of our beliefs by persuading us of false conclusions with incorrect arguments (Fantl 2018).
In sum, despite the optimism of Mill and many others, it seems that engaging in argumentation will not automatically improve our beliefs (even if this may occur in some circumstances). [ 4 ] However, it may still be argued that an epistemological approach to argumentation can serve the purpose of providing a normative ideal for argumentative practices, even if it is not always a descriptively accurate account of these practices in the messy real world. Moreover, at least some concrete instances of argumentation, in particular argumentation in science (see section 4.5 below) seem to offer successful examples of epistemic-oriented argumentative practices.
Another important strand in the literature on argumentation are theories that view consensus as the primary goal of argumentative processes: to eliminate or resolve a difference of (expressed) opinion. The tradition of pragma-dialectics is a prominent recent exponent of this strand (Eemeren & Grootendorst 2004). These consensus-oriented approaches are motivated by the social complexity of human life, and the attribution of a role of social coordination to argumentation. Because humans are social animals who must often cooperate with other humans to successfully accomplish certain tasks, they must have mechanisms to align their beliefs and intentions, and subsequently their actions (Tomasello 2014). The thought is that argumentation would be a particularly suitable mechanism for such alignment, as an exchange of reasons would make it more likely that differences of opinion would decrease (Norman 2016). This may happen precisely because argumentation would be a good way to track truths and avoid falsehoods, as discussed in the previous section; by being involved in the same epistemic process of exchanging reasons, the participants in an argumentative situation would all come to converge towards the truth, and thus the upshot would be that they also come to agree with each other. However, consensus-oriented views need not presuppose that argumentation is truth-conducive: the ultimate goal of such instances of argumentation is that of social coordination, and for this tracking truth is not a requirement (Patterson 2011).
In particular, the very notion of deliberative democracy is viewed as resting crucially on argumentative practices that aim for consensus (Fishkin 2016; see entry on democracy ). (For present purposes, “deliberation” and “argumentation” can be treated as roughly synonymous). In a deliberative democracy, for a decision to be legitimate, it must be preceded by authentic public deliberation—a discussion of the pros and cons of the different options—not merely the aggregation of preferences that occurs in voting. Moreover, in democratic deliberation, when full consensus does not emerge, the parties involved may opt for a compromise solution, e.g., a coalition-based political system.
A prominent theorist of deliberative democracy thus understood is Jürgen Habermas, whose “discourse theory of law and democracy” relies heavily on practices of political justification and argumentation taking place in what he calls “the public sphere” (Habermas 1992 [1996]; 1981 [1984]; see entry on Habermas ). He starts from the idea that politics allows for the collective organization of people’s lives, including the common rules they will live by. Political argumentation is a form of communicative practice, so general assumptions for communicative practices in general apply. However, additional assumptions apply as well (Olson 2011 [2014]). In particular, deliberating participants must accept that anyone can participate in these discursive practices (democratic deliberation should be inclusive), and that anyone can introduce and challenge claims that are made in the public sphere (democratic deliberation should be free). They must also see one another as having equal status, at least for the purposes of deliberation (democratic deliberation should be equal). In turn, critics of Habermas’s account view it as unrealistic, as it presupposes an ideal situation where all citizens are treated equally and engage in public debates in good faith (Mouffe 1999; Geuss 2019).
More generally, it seems that it is only under quite specific conditions that argumentation reliably leads to consensus (as also suggested by formal modeling of argumentative situations (Betz 2013; Olsson 2013; Mäs & Flache 2013)). Consensus-oriented argumentation seems to work well in cooperative contexts, but not so much in situations of conflict (Dutilh Novaes forthcoming). In particular, the discussing parties must already have a significant amount of background agreement—especially agreement on what counts as a legitimate argument or compelling evidence—for argumentation and deliberation to lead to consensus. Especially in situations of deep disagreement (Fogelin 1985), it seems that the potential of argumentation to lead to consensus is quite limited. Instead, in many real-life situations, argumentation often leads to the opposite result; people disagree with each other even more after engaging in argumentation (Sunstein 2002). This is the well-documented phenomenon of group polarization , which occurs when an initial position or tendency of individual members of a group becomes more extreme after group discussion (Isenberg 1986).
In fact, it may be argued that argumentation will often create or exacerbate conflict and adversariality, rather than leading to the resolution of differences of opinions. Furthermore, a focus on consensus may end up reinforcing and perpetuating existing unequal power relations in a society.
In an unjust society, what purports to be a cooperative exchange of reasons really perpetuates patterns of oppression. (Goodwin 2007: 77)
This general point has been made by a number of political thinkers (e.g., Young 2000), who have highlighted the exclusionary implications of consensus-oriented political deliberation. The upshot is that consensus may not only be an unrealistic goal for argumentation; it may not even be a desirable goal for argumentation in a number of situations (e.g., when there is great power imbalance). Despite these concerns, the view that the primary goal of argumentation is to aim for consensus remains influential in the literature.
Finally, a number of authors have attributed to argumentation the potential to manage (pre-existing) conflict. In a sense, the consensus-oriented view of argumentation just discussed is a special case of conflict management argumentation, based on the assumption that the best way to manage conflict and disagreement is to aim for consensus and thus eliminate conflict. But conflict can be managed in different ways, not all of them leading to consensus; indeed, some authors maintain that argumentation may help mitigate conflict even when the explicit aim is not that of reaching consensus. Importantly, authors who identify conflict management (or variations thereof) as a function for argumentation differ in their overall appreciation of the value of argumentation: some take it to be at best futile and at worst destructive, [ 5 ] while others attribute a more positive role to argumentation in conflict management.
To this category also belong the conceptualizations of argumentation-as-war discussed (and criticized) by a number of authors (Cohen 1995; Bailin & Battersby 2016); in such cases, conflict is not so much managed but rather enacted (and possibly exacerbated) by means of argumentation. Thus seen, the function of argumentation would not be fundamentally different from the function of organized competitive activities such as sports or even war (with suitable rules of engagement; Aikin 2011).
When conflict emerges, people have various options: they may choose not to engage and instead prefer to flee; they may go into full-blown fighting mode, which may include physical aggression; or they may opt for approaches somewhere in between the fight-or-flee extremes of the spectrum. Argumentation can be plausibly classified as an intermediary response:
[A]rgument literally is a form of pacifism—we are using words instead of swords to settle our disputes. With argument, we settle our disputes in ways that are most respectful of those who disagree—we do not buy them off, we do not threaten them, and we do not beat them into submission. Instead, we give them reasons that bear on the truth or falsity of their beliefs. However adversarial argument may be, it isn’t bombing. […] argument is a pacifistic replacement for truly violent solutions to disagreements…. (Aikin 2011: 256)
This is not to say that argumentation will always or even typically be the best approach to handle conflict and disagreement; the point is rather that argumentation at least has the potential to do so, provided that the background conditions are suitable and that provisions to mitigate escalation are in place (Aikin 2011). Versions of this view can be found in the work of proponents of agonistic conceptions of democracy and political deliberation (Wenman 2013; see entry on feminist political philosophy ). For agonist thinkers, conflict and strife are inevitable features of human lives, and so cannot be eliminated; but they can be managed. One of them is Chantal Mouffe (Mouffe 2000), for whom democratic practices, including argumentation/deliberation, can serve to contain hostility and transform it into more constructive forms of contest. However, it is far from obvious that argumentation by itself will suffice to manage conflict; typically, other kinds of intervention must be involved (Young 2000), as the risk of argumentation being used to exercise power rather than as a tool to manage conflict always looms large (van Laar & Krabbe 2019).
From these observations on different types of argumentation, a pluralistic picture emerges: argumentation, understood as the exchange of reasons to justify claims, seems to have different applications in different situations. However, it is not clear that some of the goals often attributed to argumentation such as epistemic improvement and reaching consensus can in fact be reliably achieved in many real life situations. Does this mean that argumentation is useless and futile? Not necessarily, but it may mean that engaging in argumentation will not always be the optimal response in a number of contexts.
4. Argumentation Across Fields of Inquiry and Social Practices
Argumentation is practiced and studied in many fields of inquiry; philosophers interested in argumentation have much to benefit from engaging with these bodies of research as well.
To understand the emergence of argumentation theory as a specific field of research in the twentieth century, a brief discussion of preceding events is necessary. In the nineteenth century, a number of textbooks aiming to improve everyday reasoning via public education emphasized logical and rhetorical concerns, such as those by Richard Whately (see entry on fallacies ). As noted in section 3.2 , John Stuart Mill also had a keen interest in argumentation and its role in public discourse (Mill 1859), as well as an interest in logic and reasoning (see entries on Mill and on fallacies ). But with the advent of mathematical logic in the final decades of the nineteenth century, logic and the study of ordinary, everyday argumentation came apart, as logicians such as Frege, Hilbert, Russell etc. were primarily interested in mathematical reasoning and argumentation. As a result, their logical systems are not particularly suitable to study everyday argumentation, as this is simply not what they were designed to do. [ 6 ]
Nevertheless, in the twentieth century a number of authors took inspiration from developments in formal logic and expanded the use of logical tools to the analysis of ordinary argumentation. A pioneer in this tradition is Susan Stebbing, who wrote what can be seen as the first textbook in analytic philosophy, and then went on to write a number of books aimed at a general audience addressing everyday and public discourse from a philosophical/logical perspective (see entry on Susan Stebbing ). Her 1939 book Thinking to Some Purpose , which can be considered as one of the first textbooks in critical thinking, was widely read at the time, but did not become particularly influential for the development of argumentation theory in the decades to follow.
By contrast, Stephen Toulmin’s 1958 book The Uses of Argument has been tremendously influential in a wide range of fields, including critical thinking education, rhetoric, speech communication, and computer science (perhaps even more so than in Toulmin’s own original field, philosophy). Toulmin’s aim was to criticize the assumption (widely held by Anglo-American philosophers at the time) that any significant argument can be formulated in purely formal, deductive terms, using the formal logical systems that had emerged in the preceding decades (see (Eemeren, Garssen, et al. 2014: ch. 4). While this critique was met with much hostility among fellow philosophers, it eventually gave rise to an alternative way of approaching argumentation, which is often described as “informal logic” (see entry on informal logic ). This approach seeks to engage and analyze instances of argumentation in everyday life; it recognizes that, while useful, the tools of deductive logic alone do not suffice to investigate argumentation in all its complexity and pragmatic import. In a similar vein, Charles Hamblin’s 1970 book Fallacies reinvigorated the study of fallacies in the context of argumentation by re-emphasizing (following Aristotle) the importance of a dialectical-dialogical background when reflecting on fallacies in argumentation (see entry on fallacies ).
Around the same time as Toulmin, Chaïm Perelman and Lucie Olbrechts-Tyteca were developing an approach to argumentation that emphasized its persuasive component. To this end, they turned to classical theories of rhetoric, and adapted them to give rise to what they described as the “New Rhetoric”. Their book Traité de l’argumentation: La nouvelle rhétorique was published in 1958 in French, and translated into English in 1969. Its key idea:
since argumentation aims at securing the adherence of those to whom it is addressed, it is, in its entirety, relative to the audience to be influenced. (Perelman & Olbrechts-Tyteca 1958 [1969: 19])
They introduced the influential distinction between universal and particular audiences: while every argument is directed at a specific individual or group, the concept of a universal audience serves as a normative ideal encapsulating shared standards of agreement on what counts as legitimate argumentation (see Eemeren, Garssen, et al. 2014: ch. 5).
The work of these pioneers provided the foundations for subsequent research in argumentation theory. One approach that became influential in the following decades is the pragma-dialectics tradition developed by Frans van Eemeren and Rob Grootendorst (Eemeren & Grootendorst 1984, 2004). They also founded the journal Argumentation , one of the flagship journals in argumentation theory. Pragma-dialectics was developed to study argumentation as a discourse activity, a complex speech act that occurs as part of interactional linguistic activities with specific communicative goals (“pragma” refers to the functional perspective of goals, and “dialectic” to the interactive component). For these authors, argumentative discourse is primarily directed at the reasonable resolution of a difference of opinion. Pragma-dialectics has a descriptive as well as a normative component, thus offering tools both for the analysis of concrete instances of argumentation and for the evaluation of argumentation correctness and success (see Eemeren, Garssen, et al. 2014: ch. 10).
Another leading author in argumentation theory is Douglas Walton, who pioneered the argument schemes approach to argumentation that borrows tools from formal logic but expands them so as to treat a wider range of arguments than those covered by traditional logical systems (Walton, Reed, & Macagno 2008). Walton also formulated an influential account of argumentation in dialogue in collaboration with Erik Krabbe (Walton & Krabbe 1995). Ralph Johnson and Anthony Blair further helped to consolidate the field of argumentation theory and informal logic by founding the Centre for Research in Reasoning, Argumentation, and Rhetoric in Windsor (Ontario, Canada), and by initiating the journal Informal Logic . Their textbook Logical Self-Defense (Johnson & Blair 1977) has also been particularly influential.
The study of argumentation within computer science and artificial intelligence is a thriving field of research, with dedicated journals such as Argument and Computation and regular conference series such as COMMA (International Conference on Computational Models of Argument; see Rahwan & Simari 2009 and Eemeren, Garssen, et al. 2014: ch. 11 for overviews).
The historical roots of argumentation research in artificial intelligence can be traced back to work on non-monotonic logics (see entry on non-monotonic logics ) and defeasible reasoning (see entry on defeasible reasoning ). Since then, three main different perspectives have emerged (Eemeren, Garssen, et al. 2014: ch. 11): the theoretical systems perspective, where the focus is on theoretical and formal models of argumentation (following the tradition of philosophical and formal logic); the artificial systems perspective, where the aim is to build computer programs that model or support argumentative tasks, for instance, in online dialogue games or in expert systems; the natural systems perspective, which investigates argumentation in its natural form with the help of computational tools (e.g., argumentation mining [Peldszus & Stede 2013; Habernal & Gurevych 2017], where computational methods are used to identify argumentative structures in large corpora of texts).
An influential approach in this research tradition is that of abstract argumentation frameworks , initiated by the pioneering work of Dung (1995). Before that, argumentation in AI was studied mostly under the inspiration of concepts coming from informal logic such as argumentation schemes, context, stages of dialogues and argument moves. By contrast, the key notion in the framework proposed by Dung is that of argument attack , understood as an abstract formal relation roughly intended to capture the idea that it is possible to challenge an argument by means of another argument (assertions are understood as a special case of arguments with zero premises). Arguments can then be represented in networks of attacks and defenses: an argument A can attack an argument B , and B in turn may attack further arguments C and D (the connection with the notion of defeaters is a natural one, which Dung also addresses).
Besides abstract argumentation, three other important lines of research in AI are: the (internal) structure of arguments; argumentation in multi-agent systems; applications to specific tasks and domains (Rahwan & Siwari 2009). The structural approach investigates formally features such as argument strength/force (e.g., a conclusive argument is stronger than a defeasible argument), argument schemes (Bex, Prakken, Reed, & Walton 2003) etc. Argumentation in multi-agent systems is a thriving subfield with its own dedicated conference series (ArgMAS), based on the recognition that argumentation is a particularly suitable vehicle to facilitate interaction in the artificial environments studied by AI researchers working on multi-agent systems (see a special issue of the journal Argument & Computation [Atkinson, Cerutti, et al. 2016]). Finally, computational approaches in argumentation have also thrived with respect to specific domains and applications, such as legal argumentation (Prakken & Sartor 2015). Recently, as a reaction to the machine-learning paradigm, the idea of explainable AI has gotten traction, and the concept of argumentation is thought to play a fundamental role for explainable AI (Sklar & Azhar 2018).
Argumentation is also an important topic of investigation within cognitive science and psychology. Researchers in these fields are predominantly interested in the descriptive question of how people in fact engage in argumentation, rather than in the normative question of how they ought to do it (although some of them have also drawn normative conclusions, e.g., Hahn & Oaksford 2006; Hahn & Hornikx, 2016). Controlled experiments are one of the ways in which the descriptive question can be investigated.
Systematic research specifically on argumentation within cognitive science and psychology has significantly increased over the last 10 years. Before that, there had been extensive research on reasoning conceived as an individual, internal process, much of which had been conducted using task materials such as syllogistic arguments (Dutilh Novaes 2020b). But due to what may be described as an individualist bias in cognitive science and psychology (Mercier 2018), these researchers did not draw explicit connections between their findings and the public acts of “giving and asking for reasons”. It is only somewhat recently that argumentation began to receive sustained attention from these researchers. The investigations of Hugo Mercier and colleagues (Mercier & Sperber 2017; Mercier 2018) and of Ulrike Hahn and colleagues (Hahn & Oaksford 2007; Hornikx & Hahn 2012; Collins & Hahn 2018) have been particularly influential. (See also Paglieri, Bonelli, & Felletti 2016, an edited volume containing a representative overview of research on the psychology of argumentation.) Another interesting line of research has been the study of the development of reasoning and argumentative skills in young children (Köymen, Mammen, & Tomasello 2016; Köymen & Tomasello 2020).
Mercier and Sperber defend an interactionist account of reasoning, according to which the primary function of reasoning is for social interactions, where reasons are exchanged and receivers of reasons decide whether they find them convincing—in other words, for argumentation (Mercier & Sperber 2017). They review a wealth of evidence suggesting that reasoning is rather flawed when it comes to drawing conclusions from premises in order to expand one’s knowledge. From this they conclude, on the basis of evolutionary arguments, that the function of reasoning must be a different one, indeed one that responds to features of human sociality and the need to exercise epistemic vigilance when receiving information from others. This account has inaugurated a rich research program which they have been pursuing with colleagues for over a decade now, and which has delivered some interesting results—for example, that we seem to be better at evaluating the quality of arguments proposed by others than at formulating high-quality arguments ourselves (Mercier 2018).
In the context of the Bayesian (see entry on Bayes’ theorem ) approach to reasoning that was first developed by Mike Oaksford and Nick Chater in the 1980s (Oaksford & Chater 2018), Hahn and colleagues have extended the Bayesian framework to the investigation of argumentation. They claim that Bayesian probabilities offer an accurate descriptive model of how people evaluate the strength of arguments (Hahn & Oaksford 2007) as well as a solid perspective to address normative questions pertaining to argument strength (Hahn & Oaksford 2006; Hahn & Hornikx 2016). The Bayesian approach allows for the formulation of probabilistic measures of argument strength, showing that many so-called “fallacies” may nevertheless be good arguments in the sense that they considerably raise the probability of the conclusion. For example, deductively invalid argument schemes (such as affirming the consequent (AC) and denying the antecedent (DA)) can also provide considerable support for a conclusion, depending on the contents in question. The extent to which this is the case depends primarily on the specific informational context, captured by the prior probability distribution, not on the structure of the argument. This means that some instances of, say, AC, may offer support to a conclusion while others may fail to do so (Eva & Hartmann 2018). Thus seen, Bayesian argumentation represents a significantly different approach to argumentation from those inspired by logic (e.g., argument schemes), but they are not necessarily incompatible; they may well be complementary perspectives (see also [Zenker 2013]).
Argumentation is primarily (though not exclusively) a linguistic phenomenon. Accordingly, argumentation is extensively studied in fields dedicated to the study of language, such as rhetoric, linguistics, discourse analysis, communication, and pragmatics, among others (see Eemeren, Garssen, et al. 2014: chs 8 and 9). Researchers in these areas develop general theoretical models of argumentation and investigate concrete instances of argumentation in specific domains on the basis of linguistic corpora, discourse analysis, and other methods used in the language sciences (see the edited volume Oswald, Herman, & Jacquin [2018] for a sample of the different lines of research). Overall, research on argumentation within the language sciences tends to focus primarily on concrete occurrences of arguments in a variety of domains, adopting a largely descriptive rather than normative perspective (though some of these researchers also tackle normative considerations).
Some of these analyses approach arguments and argumentation primarily as text or self-contained speeches, while others emphasize the interpersonal, communicative nature of “face-to-face” argumentation (see Eemeren, Garssen, et al. 2014: section 8.9). One prominent approach in this tradition is due to communication scholars Sally Jackson and Scott Jacobs. They have drawn on speech act theory and conversation analysis to investigate argumentation as a disagreement-relevant expansion of speech acts that, through mutually recognized reasons, allows us to manage disagreements despite the challenges they pose for communication and coordination of activities (Jackson & Jacobs 1980; Jackson 2019). Moreover, they perceive institutionalized practices of argumentation and concrete “argumentation designs”—such as for example randomized controlled trials in medicine—as interventions aimed at improving methods of disagreement management through argumentation.
Another communication scholar, Dale Hample, has further argued for the importance of approaching argumentation as an essentially interpersonal communicative activity (Hample 2006, 2018). This perspective allows for the consideration of a broader range of factors, not only the arguments themselves but also (and primarily) the people involved in those processes: their motivations, psychological processes, and emotions. It also allows for the formulation of questions pertaining to individual as well as cultural differences in argumentative styles (see section 5.3 below).
Another illuminating perspective views argumentative practices as inherently tied to broader socio-cultural contexts (Amossy 2009). The Journal of Argumentation in Context was founded in 2012 precisely to promote a contextual approach to argumentation. Once argumentation is no longer only considered in abstraction from concrete instances taking place in real-life situations, it becomes imperative to recognize that argumentation does not take place in a vacuum; typically, argumentative practices are embedded in other kinds of practices and institutions, against the background of specific socio-cultural, political structures. The method of discourse analysis is particularly suitable for a broader perspective on argumentation, as shown by the work of Ruth Amossy (2002) and Marianne Doury (2009), among others.
Argumentation is crucial in a number of specific organized social practices, in particular in politics, science, law, and education. The relevant argumentative practices are studied in each of the corresponding knowledge domains; indeed, while some general principles may govern argumentative practices across the board, some may be specific to particular applications and domains.
As already mentioned, argumentation is typically viewed as an essential component of political democratic practices, and as such it is of great interest to political scientists and political theorists (Habermas 1992 [1996]; Young 2000; Landemore 2013; Fishkin 2016; see entry on democracy ). (The term typically used in this context is “deliberation” instead of “argumentation”, but these can be viewed as roughly synonymous for our purposes.) General theories of argumentation such as pragma-dialectic and the Toulmin model can be applied to political argumentation with illuminating results (Wodak 2016; Mohammed 2016). More generally, political discourse seems to have a strong argumentative component, in particular if argumentation is understood more broadly as not only pertaining to rational discourse ( logos ) but as also including what rhetoricians refer to as pathos and ethos (Zarefsky 2014; Amossy 2018). But critics of argumentation and deliberation in political contexts also point out the limitations of the classical deliberative model (Sanders 1997; Talisse 2019).
Moreover, scientific communities seem to offer good examples of (largely) well-functioning argumentative practices. These are disciplined systems of collective epistemic activity, with tacit but widely endorsed norms for argumentative engagement for each domain (which does not mean that there are not disagreements on these very norms). The case of mathematics has already been mentioned above: practices of mathematical proof are quite naturally understood as argumentative practices (Dutilh Novaes 2020a). Furthermore, when a scientist presents a new scientific claim, it must be backed by arguments and evidence that her peers are likely to find convincing, as they follow from the application of widely agreed-upon scientific methods (Longino 1990; Weinstein 1990; Rehg 2008; see entry on the social dimensions of scientific knowledge ). Other scientists will in turn critically examine the evidence and arguments provided, and will voice objections or concerns if they find aspects of the theory to be insufficiently convincing. Thus seen, science may be viewed as a “game of giving and asking for reasons” (Zamora Bonilla 2006). Certain features of scientific argumentation seem to ensure its success: scientists see other scientists as prima facie peers, and so (typically at least) place a fair amount of trust in other scientists by default; science is based on the principle of “organized skepticism” (a term introduced by the pioneer sociologist of science Robert Merton [Merton, 1942]), which means that asking for further reasons should not be perceived as a personal attack. These are arguably aspects that distinguish argumentation in science from argumentation in other domains in virtue of these institutional factors (Mercier & Heintz 2014). But ultimately, scientists are part of society as a whole, and thus the question of how scientific and political argumentation intersect becomes particularly relevant (Kitcher 2001).
Another area where argumentation is essential is the law, which also corresponds to disciplined systems of collective activity with rules and principles for what counts as acceptable arguments and evidence. legal reasoning ).--> In litigation (in particular in adversarial justice systems), there are typically two sides disagreeing on what is lawful or just, and the basic idea is that each side will present its strongest arguments; it is the comparison between the two sets of arguments that should lead to the best judgment (Walton 2002). Legal reasoning and argumentation have been extensively studied within jurisprudence for decades, in particular since Ronald Dworkin’s (1977) and Neil MacCormick’s (1978) responses to HLA Hart’s highly influential The Concept of Law (1961). A number of other views and approaches have been developed, in particular from the perspectives of natural law theory, legal positivism, common law, and rhetoric (see Feteris 2017 for an overview). Overall, legal argumentation is characterized by extensive uses of analogies (Lamond 2014), abduction (Askeland 2020), and defeasible/non-monotonic reasoning (Bex & Verheij 2013). An interesting question is whether argumentation in law is fundamentally different from argumentation in other domains, or whether it follows the same overall canons and norms but applied to legal topics (Raz 2001).
Finally, the development of argumentative skills is arguably a fundamental aspect of (formal) education (Muller Mirza & Perret-Clermont 2009). Ideally, when presented with arguments, a learner should not simply accept what is being said at face value, but should instead reflect on the reasons offered and come to her own conclusions. Argumentation thus fosters independent, critical thinking, which is viewed as an important goal for education (Siegel 1995; see entry on critical thinking ). A number of education theorists and developmental psychologists have empirically investigated the effects of emphasizing argumentative skills in educational settings, with encouraging results (Kuhn & Crowell 2011). There has been in particular much emphasis on argumentation specifically in science education, based on the assumption that argumentation is a key component of scientific practice (as noted above); the thought is that this feature of scientific practice should be reflected in science education (Driver, Newton, & Osborne 2000; Erduran & Jiménez-Aleixandre 2007).
5. Further Topics
Argumentation is a multi-faceted phenomenon, and the literature on arguments and argumentation is massive and varied. This entry can only scratch the surface of the richness of this material, and many interesting, relevant topics must be left out for reasons of space. In this final section, a selection of topics that are likely to attract considerable interest in future research are discussed.
In recent years, the concept of epistemic injustice has received much attention among philosophers (Fricker 2007; McKinnon 2016). Epistemic injustice occurs when a person is unfairly treated qua knower on the basis of prejudices pertaining to social categories such as gender, race, class, ability etc. (see entry on feminist epistemology and philosophy of science ). One of the main categories of epistemic injustice discussed in the literature pertains to testimony and is known as testimonial injustice : this occurs when a testifier is not given a degree of credibility commensurate to their actual expertise on the relevant topic, as a result of prejudice. (Whether credibility excess is also a form of testimonial injustice is a moot point in the literature [Medina 2011].)
Since argumentation can be viewed as an important mechanism for sharing knowledge and information, i.e., as having significant epistemic import (Goldman 2004), the question arises whether there might be instances of epistemic injustice pertaining specifically to argumentation, which may be described as argumentative injustice , and which would be notably different from other recognized forms of epistemic injustice such as testimonial injustice. Bondy (Bondy 2010) presented a first articulation of the notion of argumentative injustice, modeled after Fricker’s notion of epistemic injustice and relying on a broadly epistemological conception of argumentation. However, Bondy’s analysis does not take into account some of the structural elements that have become central to the analysis of epistemic injustice since Fricker’s influential work, so it seems further discussion of epistemic injustice in argumentation is still needed. For example, in situations of disagreement, epistemic injustice can give rise to further obstacles to rational argumentation, leading to deep disagreement (Lagewaard 2021).
Moreover, as often noted by critics of adversarial approaches, argumentation can also be used as an instrument of domination and oppression used to overpower and denigrate an interlocutor (Nozick 1981), especially an interlocutor of “lower” status in the context in question (Moulton 1983; see entry on feminist approaches to argumentation ). From this perspective, it is clear that argumentation may also be used to reinforce and exacerbate injustice, inequalities and power differentials (Goodwin 2007). Given this possibility, and in response to the perennial risk of excessive aggressiveness in argumentative situations, a normative account of how argumentation ought to be conducted so as to avoid these problematic outcomes seem to be required.
One such approach is virtue argumentation theory . Drawing on virtue ethics and virtue epistemology (see entries on virtue ethics and virtue epistemology ), virtue argumentation theory seeks to theorize how to argue well in terms of the dispositions and character of arguers rather than, for example, in terms of properties of arguments considered in abstraction from arguers (Aberdein & Cohen 2016). Some of the argumentative virtues identified in the literature are: willingness to listen to others (Cohen 2019), willingness to take a novel viewpoint seriously (Kwong 2016), humility (Kidd 2016), and open-mindedness (Tanesini 2020).
By the same token, defective argumentation is conceptualized not (only) in terms of structural properties of arguments (e.g., fallacious argument patterns), but in terms of the vices displayed by arguers such as arrogance and narrow-mindedness, among others (Aberdein 2016). Virtue argumentation theory now constitutes a vibrant research program, as attested by a special issue of Topoi dedicated to the topic (see [Aberdein & Cohen 2016] for its Introduction). It allows for a reconceptualization of classical themes within argumentation theory while also promising to provide concrete recommendations on how to argue better. Whether it can fully counter the risk of epistemic injustice and oppressive uses of argumentation is however debatable, at least as long as broader structural factors related to power dynamics are not sufficiently taken into account (Kukla 2014).
On some idealized construals, argumentation is conceived as a purely rational, emotionless endeavor. But the strong connection between argumentative activities and emotional responses has also long been recognized (in particular in rhetorical analyses of argumentation), and more recently has become the object of extensive research (Walton 1992; Gilbert 2004; Hample 2006: ch. 5). Importantly, the recognition of a role for emotions in argumentation does not entail a complete rejection of the “rationality” of argumentation; rather, it is based on the rejection of a strict dichotomy between reason and emotion (see entry on emotion ), and on a more encompassing conception of argumentation as a multi-layered human activity.
Rather than dispassionate exchanges of reasons, instances of argumentation typically start against the background of existing emotional relations, and give rise to further affective responses—often, though not necessarily, negative responses of aggression and hostility. Indeed, it has been noted that, by itself, argumentation can give rise to conflict and friction where there was none to be found prior to the argumentative engagement (Aikin 2011). This occurs in particular because critical engagement and requests for reasons are at odds with default norms of credulity in most mundane dialogical interactions, thus creating a perception of antagonism. But argumentation may also give rise to positive affective responses if the focus is on coalescence and cooperation rather than on hostility (Gilbert 1997).
The descriptive claim that instances of argumentation are typically emotionally charged is not particularly controversial, though it deserves to be further investigated; the details of affective responses during instances of argumentation and how to deal with them are non-trivial (Krabbe & van Laar 2015). What is potentially more controversial is the normative claim that instances of argumentation may or should be emotionally charged, i.e., that emotions may or ought to be involved in argumentative processes, even if it may be necessary to regulate them in such situations rather than giving them free rein (González, Gómez, & Lemos 2019). The significance of emotions for persuasion has been recognized for millennia (see entry on Aristotle’s rhetoric ), but more recently it has become clear that emotions also have a fundamental role to play for choices of what to focus on and what to care about (Sinhababu 2017). This general point seems to apply to instances of argumentation as well. For example, Howes and Hundleby (Howes & Hundleby 2018) argue that, contrary to what is often thought, anger can in fact make a positive contribution to argumentative encounters. Indeed, anger may have an important epistemological role in such encounters by drawing attention to relevant premises and information that may otherwise go unnoticed. (They recognize that anger may also derail argumentation when the encounter becomes a full-on confrontation.)
In sum, the study of the role of emotions for argumentation, both descriptively and normatively speaking, has attracted the interest of a number of scholars, traditionally in connection with rhetoric and more recently also from the perspective of argumentation as interpersonal communication (Hample 2006). And yet, much work remains to be done on the significance of emotions for argumentation, in particular given that the view that argumentation should be a purely rational, dispassionate endeavor remains widely (even if tacitly) endorsed.
Once we adopt the perspective of argumentation as a communicative practice, the question of the influence of cultural factors on argumentative practices naturally arises. Is there significant variability in how people engage in argumentation depending on their sociocultural backgrounds? Or is argumentation largely the same phenomenon across different cultures? Actually, we may even ask ourselves whether argumentation in fact occurs in all human cultures, or whether it is the product of specific, contingent background conditions, thus not being a human universal. For comparison: it had long been assumed that practices of counting were present in all human cultures, even if with different degrees of complexity. But in recent decades it has been shown that some cultures do not engage systematically in practices of counting and basic arithmetic at all, such as the Pirahã in the Amazon (Gordon 2004; see entry on culture and cognitive science ). By analogy, it seems that the purported universality of argumentative practices should not be taken for granted, but rather be treated as a legitimate empirical question. (Incidentally, there is some anecdotal evidence that the Pirahã themselves engage in argumentative exchanges [Everett 2008], but to date their argumentative skills have not been investigated systematically, as is the case with their numerical skills.)
Of course, how widespread argumentative practices will be also depends on how the concept of “argumentative practices” is defined and operationalized in the first place. If it is narrowly defined as corresponding to regimented practices of reason-giving requiring clear markers and explicit criteria for what counts as premises, conclusions and relations of support between them, then argumentation may well be restricted to cultures and subcultures where such practices have been explicitly codified. By contrast, if argumentation is defined more loosely, then a wider range of communicative practices will be considered as instances of argumentation, and thus presumably more cultures will be found to engage in (what is thus viewed as) argumentation. This means that the spread of argumentative practices across cultures is not only an empirical question; it also requires significant conceptual input to be addressed.
But if (as appears to be the case) argumentation is not a strictly WEIRD phenomenon, restricted to Western, Educated, Industrialized, Rich, and Democratic societies (Henrich, Heine, & Norenzayan 2010), then the issue of cross-cultural variability in argumentative practices gives rise to a host of research questions, again both at the descriptive and at the normative level. Indeed, even if at the descriptive level considerable variability in argumentative practices is identified, the normative question of whether there should be universally valid canons for argumentation, or instead specific norms for specific contexts, remains pressing. At the descriptive level, a number of researchers have investigated argumentative practices in different WEIRD as well as non-WEIRD cultures, also addressing questions of cultural variability (Hornikx & Hoeken 2007; Hornikx & de Best 2011).
A foundational work in this context is Edwin Hutchins’ 1980 book Culture and Inference , a study of the Trobriand Islanders’ system of land tenure in Papua New Guinea (Hutchins 1980). While presented as a study of inference and reasoning among the Trobriand Islanders, what Hutchins in fact investigated were instances of legal argumentation in land courts by means of ethnographic observation and interviews with litigants. This led to the formulation of a set of twelve basic propositions codifying knowledge about land tenure, as well as transfer formulas governing how this knowledge can be applied to new disputes. Hutchins’ analysis showed that the Trobriand Islanders had a sophisticated argumentation system to resolve issues pertaining to land tenure, in many senses resembling argumentation and reasoning in so-called WEIRD societies in that it seemed to recognize as valid simple logical structures such as modus ponens and modus tollens .
More recently, Hugo Mercier and colleagues have been conducting studies in countries such as Japan (Mercier, Deguchi, Van der Henst, & Yama 2016) and Guatemala (Castelain, Girotto, Jamet, & Mercier 2016). While recognizing the significance and interest of cultural differences (Mercier 2013), Mercier maintains that argumentation is a human universal, as argumentative capacities and tendencies are a result of natural selection, genetically encoded in human cognition (Mercier 2011; Mercier & Sperber 2017). He takes the results of the cross-cultural studies conducted so far as confirming the universality of argumentation, even considering cultural differences (Mercier 2018).
Another scholar who has been carrying out an extensive research program on cultural differences in argumentation is communication theorist Dale Hample. With different sets of colleagues, he has conducted studies by means of surveys where participants (typically, university undergraduates) self-report on their argumentative practices in countries such as China, Japan, Turkey, Chile, the Netherlands, Portugal, the United States (among others; Hample 2018: ch. 7). His results overall show a number of similarities, which may be partially explained by the specific demographic (university students) from which participants are usually recruited. But interesting differences have also been identified, for example different levels of willingness to engage in argumentative encounters.
In a recent book (Tindale 2021), philosopher Chris Tindale adopts an anthropological perspective to investigate how argumentative practices emerge from the experiences of peoples with diverse backgrounds. He emphasizes the argumentative roles of place, orality, myth, narrative, and audience, also assessing the impacts of colonialism on the study of argumentation. Tindale reviews a wealth of anthropological and ethnographic studies on argumentative practices in different cultures, thus providing what is to date perhaps the most comprehensive study on argumentation from an anthropological perspective.
On the whole, the study of differences and commonalities in argumentative practices across cultures is an established line of research on argumentation, but arguably much work remains to be done to investigate these complex phenomena more thoroughly.
So far we have not yet considered the question of the different media through which argumentation can take place. Naturally, argumentation can unfold orally in face-to-face encounters—discussions in parliament, political debates, in a court of law—as well as in writing—in scientific articles, on the Internet, in newspaper editorials. Moreover, it can happen synchronically, with real-time exchanges of reasons, or asynchronically. While it is reasonable to expect that there will be some commonalities across these different media and environments, it is also plausible that specific features of different environments may significantly influence how argumentation is conducted: different environments present different kinds of affordances for arguers (Halpern & Gibbs 2013; Weger & Aakhus 2003; see entry on embodied cognition for the concept of affordance). Indeed, if the Internet represents a fundamentally novel cognitive ecology (Smart, Heersmink, & Clowes 2017), then it will likely give rise to different forms of argumentative engagement (Lewiński 2010). Whether these new forms will represent progress (according to some suitable metric) is however a moot point.
In the early days of the Internet in the 1990s, there was much hope that online spaces would finally realize the Habermasian ideal of a public sphere for political deliberation (Hindman 2009). The Internet was supposed to act as the great equalizer in the worldwide marketplace of ideas, finally attaining the Millian ideal of free exchange of ideas (Mill 1859). Online, everyone’s voice would have an equal chance of being heard, everyone could contribute to the conversation, and everyone could simultaneously be a journalist, news consumer, engaged citizen, advocate, and activist.
A few decades later, these hopes have not really materialized. It is probably true that most people now argue more —in social media, blogs, chat rooms, discussion boards etc.—but it is much less obvious that they argue better . Indeed, rather than enhancing democratic ideals, some have gone as far as claiming that instead, the Internet is “killing democracy” (Bartlett 2018). There is very little oversight when it comes to the spreading of propaganda and disinformation online (Benkler, Faris, & Roberts 2018), which means that citizens are often being fed faulty information and arguments. Moreover, it seems that online environments may lead to increased polarization when polemic topics are being discussed (Yardi & Boyd 2010), and to “intellectual arrogance” (Lynch 2019). Some have argued that online discussions lead to more overly emotional engagement when compared to other forms of debate (Kramer, Guillory, & Hancock 2014). But not everyone is convinced that the Internet has only made things worse when it comes to argumentation, or in any case that it cannot be suitably redesigned so as to foster rather than destroy democratic ideals and deliberation (Sunstein 2017).
Be that as it may, the Internet is here to stay, and online argumentation is a pervasive phenomenon that argumentation theorists have been studying and will continue to study for years to come. In fact, if anything, online argumentation is now more often investigated empirically than other forms of argumentation, among other reasons thanks to the development of argument mining techniques (see section 4.2 above) which greatly facilitate the study of large corpora of textual material such as those produced by online discussions. Beyond the very numerous specific case studies available in the literature, there have been also attempts to reflect on the phenomenon of online argumentation in general, for example in journal special issues dedicated to argumentation in digital media such as in Argumentation and Advocacy (Volume 47(2), 2010) and Philosophy & Technology (Volume 30(2), 2017). However, a systematic analysis of online argumentation and how it differs from other forms of argumentation remains to be produced.
Argument and argumentation are multifaceted phenomena that have attracted the interest of philosophers as well as scholars in other fields for millennia, and continue to be studied extensively in various domains. This entry presents an overview of the main strands in these discussions, while acknowledging the impossibility of fully doing justice to the enormous literature on the topic. But the literature references below should at least provide a useful starting point for the interested reader.
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abduction | analogy: medieval theories of | analogy and analogical reasoning | Aristotle | Aristotle, General Topics: logic | Aristotle, General Topics: rhetoric | Bacon, Francis | Bayes’ Theorem | bias, implicit | Chinese Philosophy: logic and language in Early Chinese Philosophy | Chinese Philosophy: Mohism | Chinese Philosophy: Mohist Canons | Chinese room argument | cognition: embodied | critical thinking | Curry’s paradox | democracy | emotion | epistemology: virtue | ethics: virtue | fallacies | feminist philosophy, interventions: epistemology and philosophy of science | feminist philosophy, interventions: political philosophy | feminist philosophy, topics: perspectives on argumentation | Habermas, Jürgen | Hume, David | induction: problem of | legal reasoning: precedent and analogy in | liar paradox | logic: inductive | logic: informal | logic: non-monotonic | logic: paraconsistent | logic: relevance | logical consequence | Peirce, Charles Sanders | reasoning: defeasible | scientific knowledge: social dimensions of | Spinoza, Baruch | Stebbing, Susan | thought experiments
Acknowledgments
Thanks to Merel Talbi, Elias Anttila, César dos Santos, Hein Duijf, Silvia Ivani, Caglar Dede, Colin Rittberg, Marcin Lewiński, Andrew Aberdein, Malcolm Keating, Maksymillian Del Mar, and an anonymous referee for suggestions and/or comments on earlier drafts. This research was supported by H2020 European Research Council [771074-SEA].
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The author's logic may look like this: Premise 1: Projects funded by taxpayer dollars should benefit a majority of the public. Premise 2: The proposed stadium construction benefits very few members of the public. Conclusion: Therefore, the stadium construction should not be funded by taxpayer dollars.
Logic studies valid forms of inference like modus ponens.. Logic is the study of correct reasoning.It includes both formal and informal logic.Formal logic is the study of deductively valid inferences or logical truths.It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. . Informal logic is associated with informal ...
The most famous logical sequence, called the syllogism, was developed by the Greek philosopher Aristotle. His most famous syllogism is: Premise 1: All men are mortal. Premise 2: Socrates is a man. Conclusion: Therefore, Socrates is mortal. In this sequence, premise 2 is tested against premise 1 to reach the logical conclusion.
Logic, therefore, is essential to the practice of philosophy. But logic is not merely a tool for evaluating philosophical arguments; it has altered the course of the ongoing philosophical conversation. As logicians developed formal systems to model the structure of an ever-wider range of discursive practices, philosophers have been able to ...
The logic in a sentence~~ • Tenses and language usage The tenses and language usage need to be consistent. Unless it's a paraphrase, a quote normally has its own tense. Other than that, your expressions and explanations should use the same tense throughout the essay. If you refer to an item/a place/an idea, be consistent on the name;
Key Takeaways: Logic. Logic—shows how ideas fit together by using reason.; Formal Logic—a formal and rigorous study of logic, such as in math and philosophy.; Informal Logic—the application of logic to arguments of all types: in scholarship, in business, and in life. Informal logic is what this part of the chapter covers. Deductive Argument—guarantees a true conclusion based on the ...
1.1 Introduction. Hermione Granger got it right when, facing the potion-master's test in Harry Potter, she said: "This isn't magic - it's logic - a puzzle. A lot of the greatest wizards haven't got an ounce of logic; they'd be stuck here forever." In the real world, we are better off. We use Logic in just about everything we do.
logic. philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics and other disciplines. The term logic comes from the Greek word logos. The variety of senses that logos possesses may suggest the difficulties to be encountered in ...
For the purposes of this course, logic means "reasoning based on thought and evidence." In practical terms, logic is the ability to analyze and evaluate persuasive or argument writing for effectiveness. By extension, it also means that you can learn to use logic in your own argumentative writing. Like any other new skill, you are likely to ...
29580. Noah Levin. Golden West College NGE Far Press. What is thinking? It may seem strange to begin a logic textbook with this question. 'Thinking' is perhaps the most intimate and personal thing that people do.
Elements. Logical theory begins with the notion of an argument, which is defined as one or more statements, called "premises," offered as evidence, or reason to believe, that a further statement, called the "conclusion," is true. In plain terms, an argument is reasoning offered in support of a conclusion.
This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a ...
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion. [2] [3] It can be defined as "selecting and interpreting information from a given context, making connections, and verifying and drawing conclusions based on ...
Aristotle: Logic. Aristotelian logic, after a great and early triumph, consolidated its position of influence to rule over the philosophical world throughout the Middle Ages up until the 19 th Century. All that changed in a hurry when modern logicians embraced a new kind of mathematical logic and pushed out what they regarded as the antiquated and clunky method of syllogisms.
The basic structure of an essay always consists of an introduction, a body, and a conclusion. But for many students, the most difficult part of structuring an essay is deciding how to organize information within the body. This article provides useful templates and tips to help you outline your essay, make decisions about your structure, and ...
An essay is a focused piece of writing designed to inform or persuade. There are many different types of essay, but they are often defined in four categories: argumentative, expository, narrative, and descriptive essays. Argumentative and expository essays are focused on conveying information and making clear points, while narrative and ...
Both logic and ontology are important areas of philosophy covering large, diverse, and active research projects. These two areas overlap from time to time and problems or questions arise that concern both. This survey article is intended to discuss some of these areas of overlap. In particular, there is no single philosophical problem of the ...
is known as the philosophy of logic or the theory of truth and meaning. The Prior Analytics has to do with a theory of correct inferences, including some observations on modal logic. The Posterior Analytics suggests a study of scien tific methods. The Topics may be seen as a treatment of the art of thinking.
Rhetoric, the last part of the trivium, is the study of the rules of persuasion, as well as their written and spoken use. Logic fits in between these two, and is the study of the structure of thought and how thought is expressed in words. Modern logic, on the other hand, is largely mathematical. A course in modern logic (and I have taught it ...
Logical Fallacies. Logical fallacies are errors in reasoning based on faulty logic. Good writers want to convince readers to agree with their arguments—their reasons and conclusions. If your arguments are not logical, readers won't be convinced. Logic can help prove your point and disprove your opponent's point—and perhaps change a ...
Argument is a central concept for philosophy. Philosophers rely heavily on arguments to justify claims, and these practices have been motivating reflections on what arguments and argumentation are for millennia. Moreover, argumentative practices are also pervasive elsewhere; they permeate scientific inquiry, legal procedures, education, and ...
Bertrand Russell: Metaphysics. Metaphysics is not a school or tradition but rather a sub-discipline within philosophy, as are ethics, logic and epistemology.Like many philosophical terms, "metaphysics" can be understood in a variety of ways, so any discussion of Bertrand Russell's metaphysics must select from among the various possible ways of understanding the notion, for example, as ...
Using Logic Apps you can streamline and provide schema in the trigger, which would be automatically imported as a function definition. Consumption Logic Apps: Currently supported consumption workflows. Request trigger: Function calling requires a REST-based API. Logic Apps with a request trigger provides a REST endpoint.