an argument as philosophers use this term is

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9 What is an Argument?

What is an argument.

This is an introductory textbook in logic and critical thinking. Both logic and critical thinking centrally involve the analysis and assessment of arguments. “Argument” is a word that has multiple distinct meanings, so it is important to be clear from the start about the sense of the word that is relevant to the study of logic. In one sense of the word, an argument is a heated exchange of differing views as in the following:

Sally: Abortion is morally wrong and those who think otherwise are seeking to justify murder!

Bob: Abortion is not morally wrong and those who think so are right-wing bigots who are seeking to impose their narrow-minded views on all the rest of us!

Sally and Bob are having an argument in this exchange. That is, they are each expressing conflicting views in a heated manner. However, that is not the sense of “argument” with which logic is concerned. Logic concerns a different sense of the word “argument.” An argument, in this sense, is a reason for thinking that a statement, claim or idea is true . For example:

Sally: Abortion is morally wrong because it is wrong to take the life of an innocent human being, and a fetus is an innocent human being.

In this example Sally has given an argument against the moral permissibility of abortion. That is, she has given us a reason for thinking that abortion is morally wrong. The conclusion of the argument is the first four words, “abortion is morally wrong.” But whereas in the first example Sally was simply asserting that abortion is wrong (and then trying to put down those who support it), in this example she is offering a reason for why abortion is wrong.

We can (and should) be more precise about our definition of an argument. But before we can do that, we need to introduce some further terminology that we will use in our definition. As I’ve already noted, the conclusion of Sally’s argument is that abortion is morally wrong. But the reason for thinking the conclusion is true is what we call the premise . So we have two parts of an argument: the premise and the conclusion. Typically, a conclusion will be supported by two or more premises. Both premises and conclusions are statements. A statement is a type of sentence that can be true or false and corresponds to the grammatical category of a “declarative sentence.” For example, the sentence,

The Nile is a river in northeastern Africa

is a statement. Why? Because it makes sense to inquire whether it is true or false. (In this case, it happens to be true.) But a sentence is still a statement even if it is false. For example, the sentence,

The Yangtze is a river in Japan

is still a statement; it is just a false statement (the Yangtze River is in China). In contrast, none of the following sentences are statements:

Please help yourself to more casserole

Don’t tell your mother about the surprise

Do you like Vietnamese pho?

The reason that none of these sentences are statements is that it doesn’t make sense to ask whether those sentences are true or false (rather, they are requests or commands, and questions, respectively).

So, to reiterate: all arguments are composed of premises and conclusions, which are both types of statements. The premises of the argument provide a reason for thinking that the conclusion is true. And arguments typically involve more than one premise.

A Brief Introduction to Philosophy Copyright © 2021 by Southern Alberta Institution of Technology (SAIT) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Arguments and Philosophical Reasoning

Lesson Plan

Materials needed

• Chalkboard or whiteboard
• Computer and projector or equipment to watch short video clips from the web

Introduction This lesson can be used at any time in a philosophy course, for a meeting of a philosophy club or discussion group, or for a workshop. Because it introduces students or participants to the method of how philosophers approach philosophical questions, it is especially appropriate as a first lesson or experience. It is intended to get students or participants to recognize that philosophical reasoning takes place in the form of argumentation. This lesson, however, stops short of providing tools for evaluating philosophical arguments. Therefore, if you are using this as the first lesson in a class or for a first meeting of a philosophy club or interest group, it would be natural to follow it up with some lessons on critical thinking or logic to provide a more complete foundation in philosophical reasoning. In turn, those lessons could be followed by explorations of philosophical content, in which you would use the method of philosophical reasoning to address specific philosophical questions or topics.

Am I Your Teacher? (10 minutes)

• Begin by writing “I am the teacher of this class” (or whatever would be most appropriate for your setting) at the bottom of the board with a line drawn above it. Ask the students or participants to show by raising hands how many of them think this statement is true. Presumably, all of them will. If so, ask them why they think this. As they give reasons, write the reasons on the board above the line. Once there are a large number of reasons on the board, ask them what everything written on the board together is called. The purpose is to illustrate that an argument is being made.

I told you that I am the teacher.

I am standing at the front of the class.

I am leading this exercise.

I am the only adult in the room.

____________________________

I am the teacher of this class

• Ask the students or participants why they think you had them do this as the first exercise when exploring philosophy. Lead a brief discussion. A few points to try to develop during the discussion include:
• What you have written on the board is an example of an argument
• Arguments are the way we think and reason—when we’re reasoning something out, what we’re doing is forming a series of arguments in our heads
• Philosophy is essentially a process of thinking systematically about difficult and interesting questions, and a primary component of philosophy centers on making and evaluating arguments.

  What Is an Argument? (10 minutes)

• Begin this activity by showing the Monty Python clip, “ The Argument Clinic .”
• After showing the clip, ask:

What are the two different concepts of “argument” presented in the skit?

The two concepts are:

• Mere contradiction or a dispute (Yes it is… No it isn’t… Yes it is… No it isn’t…)
• (Proposed by the customer) “A collected series of statements to establish a definite proposition.”

When we talk about arguments as used by philosophers, we are talking about an argument in the latter sense. Again, doing philosophy is essentially a process of making and evaluating arguments.

Parts of an Argument (10 minutes)

• Return to the “I am the teacher of this class” argument. You’ll use it as an example to illustrate and help explore what arguments are and how they work.
• In a group discussion, explore the parts of an argument. As you do so, it will be helpful to develop the following points and to introduce the following terms:

Ask what parts constitute an argument. What are its basic building blocks? Arguments are composed of sentences. In fact, they are made up of a particular type of sentence, known as a proposition.

Proposition : A declarative sentence that has a truth value. In other words, a proposition is a sentence that can be either true or false. To be precise, propositions express facts about the world that can either be true or false. Examples include “Today is Monday” and “It’s raining outside.”

Question: Are there kinds of sentences that are not propositions? Answer: Yes. Questions, commands, exclamations, etc., are all types of sentences that are not propositions because they lack a truth value. Examples include “Go open the door,” and “What is today’s date?”

Typically, most of the propositions in an argument state facts or provide information which support the claim being made. These propositions are known as premises.

Premise : A proposition serving as a reason for a conclusion.

The claim being made is known as the conclusion of the argument.

Conclusion : A proposition that is supported or entailed by a set of premises.

Arguments always have one conclusion, but the number of premises can vary quite a bit. The “I am the teacher of this class” argument has several premises.

Question: Can there be an argument with only one premise? Answer: Yes. For example, “Bill is an unmarried male. Therefore, Bill is a bachelor.”

Question: Can there be an argument with no premises? Answer: Yes. For example, consider an argument with no premises and the following conclusion: “It is either Monday in Tokyo or it is not Monday in Tokyo.”

It’s worth noting that adding premises doesn’t necessarily add support for a conclusion. For example, the argument above with no premises is in fact a compelling argument, since it always has to either be Monday or not be Monday in Tokyo.

• Now we can say what an argument is in a more precise way:

Argument : An argument is a set (a collection) of propositions in which one proposition, known as the conclusion, is claimed to derive support from the other propositions, known as premises.

• To summarize:
• Arguments are the way we think and reason—when we’ve reasoning something out, what we are really doing is forming a series of arguments in our heads.
• Though “argument” can also mean a dispute in common use, that’s not the sense in which we mean it when doing philosophy.
• Arguments consist of a conclusion and (almost always) some premises.
• The conclusion is what the argument is meant to support as being true; it’s the claim being made.
• The premises provide support for the conclusion.
• There can be any number of premises, from 0 to an infinite number (but having more premises doesn’t necessarily mean there is more support for the conclusion!).
• The premises and conclusion are propositional statements; that is, they are sentences that express facts (propositions) about the world that may be true or false.

Argument Dissection (10 minutes)

The “I am the teacher of this class” argument is in normal form. That’s just a fancy way of saying that the premises have been collected together in a list with the conclusion following them. Often, we separate the conclusion from the premises by drawing a line between them (or by putting in the symbol \, which means “therefore,” before the conclusion) to make it very clear which proposition is the conclusion. Usually arguments written in English prose are not so simply presented. The conclusion may be stated first, or for stylistic reasons it might not be at either the beginning or the end of the prose. Converting an argument from English prose into normal form allows us to clearly pick out the premises and conclusion.

How can we identify the premises and the conclusion of an argument in ordinary prose? It can take some judgment, but we are usually guided by indicator words. The propositions in arguments are often accompanied by words that indicate whether that proposition is a premise or a conclusion.

As a group, brainstorm words or phrases that might indicate that the proposition they introduce is a premise or a conclusion. The following lists provide some of the most common premise and conclusion indicators.

Premise Indicators: since, because, for, in that, as, given that, for the reason that, may be inferred from, owing to, inasmuch as

Conclusion Indicators: therefore, consequently, thus, hence, it follows that, for this reason, we may infer, we may conclude, entails that, implies that

With that background in hand, the next activity will help everyone see that arguments are in fact all around us and help them to identify more easily the structure of those arguments, which is an important first step in evaluating whether we should be convinced by the argument.

• Hand out to each student or participant a couple of arguments you have found in editorials, blogs, philosophy texts, or wherever. Ask them to re-write the arguments in normal form, identifying the premises and the conclusions.
• When done, ask everyone to pair up. Each person should show his or her partner the original arguments and the rewritten arguments in normal form. Each pair should then discuss whether or not the premises and conclusions were correctly identified. Float throughout the room and answer questions.

Evaluating Arguments (10 minutes)

This is a fun activity to help everyone start thinking about how to evaluate whether we should be convinced by an argument. Begin this activity by showing the Monty Python clip, “ She’s a Witch! ”

Begin a discussion about whether people are convinced by the argument provided in the video clip. Try to focus the discussion on whether the premises provide good reasons for believing that the conclusion is correct. Note that until the characters in the video clip actually use the scale, they don’t know whether some of the facts asserted in the premises are true. That’s often the case in exploring philosophical questions. What’s important is the logical relationship between the premises and the conclusion. Hypothetically, if the premises were all to turn out to be true, would they then make it likely that the conclusion would also be true? By asking that question, we can evaluate the reasoning in an argument. Philosophers often focus the most on this step. If the reasoning in an argument is good, then we can go on to ask whether the premises are in fact true. Often that requires empirical investigation (and so may require the aid of scientists or other specialists). If both are the case—the reasoning is good and the premises are true—only then should we assent to the conclusion.

After a few minutes, pause the discussion. Ask the students to write a paragraph defending why they are or are not convinced by the argument in the video clip. Remind everyone that the paragraph should, of course, take the form of an argument!

If this lesson is being used for a one-time event, you can ask some volunteers to read their paragraphs and then resume a discussion about what they learned. If you are using this lesson as part of a class or a series of meetings, you can always ask the students or participants to write the paragraph at home and bring it with them to the next meeting. You can then discuss their paragraphs and what they learned from the exercise. If you are teaching a formal course, you can have the students turn in their paragraphs as an assignment.

Follow-Up and Conclusions

If this lesson is part of a course or a long sequence of meetings, it would be worthwhile to follow up with another lesson or two on how to properly evaluate arguments. How that is done will depend on how formal or informal you want to be in thinking about logic, and also how long you want to spend on an introductory philosophical reasoning unit.

Supplemental Materials

There are a number of excellent textbooks and resources on arguments, critical thinking, and logic. For example, reading the first two chapters of the following logic textbook would prepare you thoroughly for leading this lesson:

Hurley, Patrick. A Concise Introduction to Logic  (Twelfth ed.). Stamford: Cengage Learning, 2015.

(As an aside, reading the third and fourth chapters of the Hurley text would prepare you well for a potential follow-up lesson on distinguishing deductive from non-deductive arguments and evaluating arguments.)

A supplementary text with a more informal discussion of arguments is the following:

Weston, Anthony. A Rulebook for Arguments (4th ed.). Indianapolis: Hackett Publications, 2009.

The following brief magazine article was written by the authors of this lesson and, in a fun way, explores how philosophers investigate philosophical questions:

Gluck, S. and Rodriguez, C. “The Philosopher’s Toolbox,” Imagine 17.4 (2010): 20-21.

( Available online here )

This lesson plan, created by Stuart Gluck and Carlos Rodriguez, is part of a series of lesson plans in Philosophy in Education: Questioning and Dialogue in Schools , by Jana Mohr Lone and Michael D. Burroughs (Rowman & Littlefield, 2016) .

If you would like to change or adapt any of PLATO's work for public use, please feel free to contact us for permission at [email protected] .

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I. Definition

An argument is a series of statements with the goal of persuading someone of something. When they’re successful, arguments start with a specific point of view, something that the reader doubts ; by the end of the argument, the reader has been convinced and no longer doubts this view. In order to argue well, you have to put yourself in the reader’s position and imagine what doubts they might have about your claim.

Argument is not the same as fighting!

From watching political debates and sports analysis on TV, you might get the impression that arguments are hostile and aggressive, more intended to defeat the opponent than to persuade anyone. But this isn’t necessarily true. In fact, the best arguments come from a place of sympathy and friendship — when friends have differing points of view, they may explain the reasoning behind their view as a way of building understanding. Often this takes the form of a friendly argument or debate .

In fact, learning to argue well is one of the most important skills you can develop — in your personal and professional relationships, a certain amount of conflict and disagreement is inevitable. If you don’t know how to argue with reason and logic, then all you’re left with is fighting . An argument is all about coming to an agreement (or, if agreement is not possible, at least understanding the reasons why it’s impossible). Fighting, on the other hand, is all about expressing emotions like anger and hurt, without caring about the other person’s point of view. Argument, if you know how to do it right, can resolve differences; fighting usually just makes them worse.

II. Types of Argument

There are three basic types of argument: deductive, inductive, and mixed . They are based on three different types of inference (see next section for more on what an inference is). If you find this confusing, visit our article on Inferences for more detail.

• Deductive arguments are built from deductive inferences
• Inductive arguments are built from inductive inferences
• Mixed arguments are built from both types of inference

So what’s the difference between deductive and inductive inferences?

Deductive inferences have to be true. You start from a basic statement or “premise,” and as long as that premise is true there is no logical way for the conclusion to be false.

• If x=y, then we can deductively infer that y=x. There’s no way for that not to be true!
• If Socrates is a man and all men are mortal, then Socrates must be mortal as well.

You could always question the premises of a deductive argument (for example, you might say that Socrates is a god, not a man, and therefore question whether he’s mortal), but if you accept the premises you have no logical choice but to accept the conclusion.

Inductive inferences don’t have to be true, but probably are.

For the whole history of human experience the sun has risen in the east and set in the west; therefore, the sun will do the same thing tomorrow.

This is almost certainly true! Most people would readily accept this line of argument. However, notice that it’s a matter of probability, not a matter of logical certainty like a deductive argument. After all, it’s possible that aliens could come and destroy the sun, meaning it wouldn’t rise or set ever again. That’s extremely unlikely, but not logically impossible.

So, in strict logical terms, deductive arguments seem stronger than inductive ones. However, inductive arguments have one crucial advantage: they usually matter more. In our day-to-day life, almost all of our decisions are based on inductive inferences:

• It usually takes me an hour to get to work, so if I leave at 8:00 I’ll probably get there by 9
• Yesterday I got sick after eating Wendy’s, so I won’t go there for lunch today
• My best friend advised me not to skip class, and her advice is usually good, so I’ll follow it

These inferences are all inductive — they’re all based on reasonable probability, not absolute logical certainty.

Deductive arguments, on the other hand, are based on absolute certainty, but their conclusions are often trivial:

• y=x, so therefore x=y . But who cares? These are just different ways of writing the same equation. The first statement might be very important: y=x might be the key to solving an important algebra problem. But the deductive argument doesn’t provide any new information on top of what we already started with.
• I am a human, and all humans are primates, so therefore I am a primate . Again, does this really matter? The statement “all humans are primates” is certainly interesting in its own right, but does “I am a primate” really add anything new on top of it?

III. Argument vs. Claim vs. Inference

In short, an argument is made up of claims connected by inferences . Each individual step in the argument is a separate claim. There’s a main claim , or “thesis,” which is supported by supporting claims . As we saw in section1, the supporting claims are intended to respond to doubts about the main claim.

Inferences are usually not stated out loud; they are invisible connectors between the claims in the argument.

Think about a cover letter . A cover letter is your chance to persuade someone that they ought to hire you — it’s a kind of argument that people in nearly every line of work have to master. A cover letter might work like this (the underlined portions would be stated explicitly (claims), whereas the italic parts are just implied/anticipated (inferences)):

Thesis: You should hire me.

Expected doubt : We need someone with statistics skills, which most people don’t have

Supporting claim: I studied statistics in college.

( Hidden Inference: when people study something in college they gain skills in that subject)

Expected doubt : OK, but studying something in college doesn’t mean you can apply it

Supporting claim: I also did a market-research internship during the summer

(Hidden Inference: real-world internships teach people to apply their knowledge )

And so on. In the cover letter, each paragraph covers out one of the supporting claims, providing further support and detail. In the end, if you’ve correctly anticipated your reader’s doubts, you will persuade them that you are the best person for the job!

IV. Quotations About Argument

“I find I am much prouder of the victory I obtain over myself, when, in the very ardor of dispute, I make myself submit to my adversary’s force of reason, than I am pleased with the victory I obtain over him through his weakness.” (Michel de Montaigne)

The French essayist Montaigne had a talent for argument, and understood the importance of listening to the other person’s point of view rather than just trying to defeat it. In fact, this quote is a pretty apt summary of the difference between argument and fighting — when you argue, you always remain open to the possibility that you will be the one persuaded in the end, rather than just hanging on to your side no matter what.

“There can be no progress without head-on confrontation.” (Christopher Hitchens)

Another master of the art of argument, journalist Christopher Hitchens was an outspoken proponent of various controversial views, from politics and religion to science and literature. In all of these areas he emphasized the importance of arguments and logic, not because he was an inherently contentious man (though that may have been true — opinions differ), but mainly because he believed that the clash of ideas would lead to new, better ideas.

V. The History and Importance of Argument

Arguments are probably as old as language itself. In fact, it’s possible that language originated as a way for pre-human primates to influence one another’s behavior without resorting to violence. Imagine you’re a homo ergaster on the African savannah: you want one of your group-mates to help you search for berries, but she’s more interested in grooming. Wouldn’t it be helpful if you could reason with her and persuade her to spend her energy in a different direction? It’s possible that language evolved as, among other things, a tool for persuasion.

However it started, argument is an extremely widespread human behavior. Different cultures have different ways of going about it — different ideas, for example, of what counts as polite argument, or what sorts of topics are appropriate to argue about in a given setting. But all human beings, across the globe, use language to make claims, express doubts, and respond to those doubts.

While some rulers try to suppress argument, others historically have welcomed it. For example, the Mughal Emperor Akbar was a Muslim who ruled India from 1556-1605. He knew that his people followed many different religions and philosophies, and built temples and schools for the specific purpose of staging reasonable, enlightening arguments among all faiths and points of view. His hope was that, through argument, people of different religions would learn from each other and that eventually a new religion would emerge, combining the best insights from each tradition.

In Europe, a short time later, this sort of argument fueled the Scientific Revolution and later the Enlightenment. Drawing on the ideas of non-European thinkers in places like India, China, and the Middle East, Europeans developed a method of argument and experimentation that we call science. They also began to consider new forms of government based on arguments and persuasion rather than royal decrees and birthright — thinkers like Benjamin Franklin, Jean-Jacques Rousseau, and Thomas Jefferson conceived of a government founded on constant argument, both in the public square and in institutions like Congress .

VI. Argument in Popular Culture

Sports shows provide great examples of both arguments and fighting. They usually start with a controversial thesis like “Aaron Rodgers is a better quarterback than Carson Palmer.” Then the two hosts will argue back and forth over whether the thesis is true or false. Sometimes, they will listen to each other, anticipate the doubts of the other side, and respond to them rationally; other times, they just shout over each other and never make any progress towards persuasion, in which case it’s an example of fighting rather than argument.

“Ladies and gentlemen of the jury, this is Chewbacca. Chewbacca is a Wookiee from the planet Kashyyyk. But Chewbacca lives on the planet Endor….If Chewbacca lives on Endor you must acquit!” (Johnnie Cochran, South Park )

This line from South Park is a spoof of the real Johnnie Cochran, the lawyer in the O.J. Simpson trial, but it’s also an example of a (terrible) deductive argument. The argument is structured like this:

• If Chewbacca lives on Endor, you must acquit (find my client not guilty)
• Chewbacca lives on Endor
• Therefore, you must acquit

Statement #1 is clearly an absurd premise, but if it were true then this deductive argument would have the force of absolute logical certainty. That’s the problem with deductive reasoning : if the premises are accurate, it’s air-tight; but often they are not.

a. Deductive inferences

b. Responses to doubt

c. Inductive inferences

a. Inference

c. Fighting

a. Mixed argument

b. Supporting claim

c. Deductive reasoning

d. Inductive reasoning

a. The Enlightenment in Europe

b. The Mughal period in India

c. Medieval Islam

d. All human societies

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Supplement to Argument and Argumentation

Historical supplement: argumentation in the history of philosophy.

Arguments and argumentation figure prominently in most (if not all) influential philosophical traditions. This Supplement presents argumentation as discussed in five prominent traditions from the past: ancient Greek, classical Indian, classical Chinese, medieval Latin, and medieval Islamicate philosophy. The goal is not to present an exhaustive historical account of these developments, but rather to offer a sample of reflections on argumentation in five noteworthy philosophical traditions.

2.2 Islamicate

1. ancient traditions.

Argumentative practices in ancient Greece constitute one of the main historical examples of a well-developed argumentative tradition (Dutilh Novaes 2020: ch. 5). The relevant sociopolitical background is that of Athenian democracy (508 to 322 BCE), where citizens could participate in decisions pertaining to governance of the city (M. Hansen 1977–81 [1991]). The three main political bodies were the assembly, the boule, and the courts of law; in all three, decisions were reached on the basis of extensive debates. Thus, being a persuasive orator was of paramount importance for a citizen, both to obtain votes in the assembly and to argue for a legal case in court.

In this setting, those who could train citizens to become skilled orators had something immensely valuable to offer. Many of the well-known thinkers of this period were exactly that: itinerant professional teachers who became collectively known as the Sophists (Notomi 2014; see entry on the Sophists ). But with the end of the so-called golden age of Athenian democracy and the disastrous results of the Peloponnesian Wars (431–404 BCE) for Athens, this mode of discursive engagement came to be criticized as a sign of the failure of democracy as a political system. Plato famously (and somewhat unfairly) offers harsh criticism of the Sophists in his dialogues (e.g., the Gorgias , the Republic ; see entry on Plato ): according to Plato, they only aim at shallow persuasion rather than at the truth (Irani 2017).

Plato promotes a different style of argumentative discourse: instead of the long speeches of the rhetoricians, and following his teacher Socrates (see entry on Socrates ), he favors dialogical interactions where speakers take turns in quick succession, in what became known as dialectical encounters . Dialectic seems to have predated Socrates and Plato, as the Eleatic philosophers (Parmenides, Zeno) were apparently already practitioners of this kind of discourse (Castelnérac & Marion 2009; see entry on Zeno of Elea ). But Plato was arguably the first to reflect and theorize on these different styles of argumentation.

What does a dialectical encounter look like, concretely? There are a number of detailed reconstructions of the basic features of this practice in the literature (Castelnérac & Marion 2009; Fink 2012). Aristotle’s Topics and its “ninth chapter”, the Sophistical Refutations , may be read as the (presumably) first regimentation/systematization of these practices, thus providing support for a general description thereof:

First of all there are the agents: the questioner and the answerer. There may also have been an audience ( Sophistical Refutations 16 175a20–30). The questioner has two main jobs: first, to extract a thesis, the “starting point” for the debate from the answerer; second, to try to force the answerer to admit the contradictory of that starting point, by getting the answerer to agree to certain premises. Alternatively, the questioner can try to reduce the thesis to absurdity. In either case, the questioner aims to refute the answerer. Crucially, the starting point should be something that can be affirmed or denied ( Topics 8.2. 158a14–22). For example, “what is knowledge?” would not be allowed as a starting point, as the answerer cannot reply “yes” or “no”. The answerer, on the other hand, has only one task, which is to remain un-refuted within a fixed time ( Topics 8.10. 161a1–15). If the answerer is refuted, then the answer should make clear that it is not their fault, but is due solely to the starting point ( Topics 8.4. 159a18–22) (Duncombe & Dutilh Novaes 2016: 3).

A key component of dialectic is the concept of refutation , or elenchus in Greek: questioner aims at refutation, answerer tries to avoid being refuted. Readers of Plato will recall the numerous instances where Socrates, by means of questions, elicits various discursive commitments from his interlocutors, only to show that, taken together, these commitments are incoherent. The interlocutor is thus refuted , and must revise their previous discursive commitments so as to restore coherence. But beyond these basic details, there is much discussion in the literature on how best to understand the concept of elenchus (Wolfsdorf 2013).

Practices of dialectic provided the background for the emergence of the first fully-fledged logical system in history, Aristotle’s syllogistic, as described in the Prior Analytics (Dutilh Novaes 2020: ch. 6; see entry on Aristotle’s logic ). Syllogistic differs from dialectic more generally in that it views as valid only arguments having the property of necessary truth-preservation (i.e., deductive arguments), whereas dialectic also allows for inductive and analogical arguments (as attested by the wide range of arguments used in Plato’s dialogues). But Aristotle remained equally interested in dialectic more generally, as attested by his manuals on how to argue well in dialectical encounters, the Topics and the Sophistical Refutations , and by the extensive discussions on dialectic even in the Prior Analytics . A key concept introduced by Aristotle in the Sophistical Refutations is that of fallacies , i.e., arguments that appear correct but are ultimately incorrect, thus leading to faulty conclusions (see entry on fallacies ). For millennia (and to this day), the identification and study of fallacies remained one of the main instruments to study argumentation.

Plato and Aristotle were not the only Greek thinkers interested in dialectic (see entry on the dialectical school ). Later authors continued to discuss the concept of dialectic, even if it acquired different meanings for different authors and traditions (see entry on ancient logic ). The Stoics are particularly worth mentioning, as they are credited with developing the first fully-fledged propositional logic, where the validity of arguments is analyzed by means of schemata where numbers take the place of propositions (whereas in Aristotle’s syllogistic, letters take the place of terms). Modus Ponens, for example, was formulated by the Stoics as:

If the 1 st , then the 2 nd . But the 1 st , therefore the 2 nd

(See entry on ancient logic .) In sum, a concern with rational discourse and argumentation was a constant element in ancient Greek philosophy, from the early stages with pre-Socratic thinkers all the way until late antiquity.

The classical Indian tradition shares with the ancient Greek tradition the pervasiveness of debating practices. In fact, it might seem that Indian thinkers relished engaging in lively debates even more than their Greek peers, as attested by their sophisticated reflections on argumentation (both for instruction and practice, and as theoretical investigations; Matilal 1998: chs 2 and 3; Solomon 1976). As is well known, classical Indian philosophy is extremely diverse, branching into a plethora of schools. These essentially fall within two groups: Brahmanical schools, which accepted the validity of the Vedic sacred texts (such as Nyāya and Yoga), and schools that rejected the authority of the Vedas (such as Buddhism and Jainism). There was much disagreement among these different schools, thus generating ample opportunity for lively discussions.

While the emergence of sustained debating practices in ancient Greece was greatly influenced by the political background, in India debating practices emerged as a response to different circumstances, in particular to address metaphysical, epistemological and religious issues (see entry on epistemology in classical Indian philosophy ). The historical record suggests that kings and rulers encouraged and patronized such debates between sages, thus providing an institutional, social embedding quite different from the background for intellectual endeavors in ancient Greece. On the whole, while the Greeks were primarily interested in moral and political issues, Indian thinkers mainly focused on ontological, epistemological, medical, and religious questions such as the distinction of the soul from the body, the purpose of life, the different sources of knowledge, and the existence of the after-life (Matilal 1998; though these discussions also had moral implications).

The popularity of debates dates back to the early stages in the history of Indian thought (as early as 1700 BCE), but the first theories of argumentation only appeared around the time of the Buddha and other religious reformers (6 th century BCE). By the third and second centuries BCE, monks and Brahmans were required to have training in the art of debating. Debating manuals were written within the different sectarian schools (Matilal 1998), containing accounts of highly regimented debating practices displaying the same level of sophistication (if not beyond) as Greek dialectic (see entry on logic in classical Indian philosophy ). The Indian authors distinguished between friendly, honest debates, where presumably the common goal was the search for truth, from competitive ones where the goal was mere victory. In the influential Nyāya-sūtra manual, attributed to Akṣapāda Gautama and widely available by 150 CE (exact dates of composition are uncertain), the former were called vāda , while the latter were called jalpa and vitaṇḍā (Nicholson 2010). These manuals contained instructions on how to perform at honest debates as well as discussions of clever argumentative tricks that may be used by disputatious opponents in competitive debates, so as to help the novice to identify and rebut these tricks (Prets 2001). In particular, Indian philosophers also developed sophisticated theories of fallacies (Phillips 2017) that served purposes similar to Aristotle’s Sophistical Refutations (Ganeri 2001).

Indian philosophical discussions also tend to have a strong epistemological focus, with a concern for the nature of evidence and discussions on the means of knowledge, pramāṇa s (see entry on epistemology in classical Indian philosophy ). The Nyāya-sūtra , for example, can be read as offering a formulation of acceptable and sound methods for philosophical discourse and inquiry. Inference ( anumāna ) was viewed by the Nyāya philosophers (as well as by other schools of thought) as one of the pramāṇa s, one of the means of knowledge. But Indian thinkers saw no contradiction between dialectical and epistemological approaches; as is clear in particular in the works of the influential fifth–sixth century CE Buddhist thinker Dignāga, inference—the cognitive process taking one from the known to the unknown—and argument—a device of persuasion—are but two sides of a single coin (see entry on logic in classical Indian philosophy, section 4 ).

There is much discussion among scholars on whether earlier Indian thinkers did or did not draw a sharp distinction between (what we now call) deductive and inductive reasoning (Siderits 2003), and between monotonic and non-monotonic reasoning (Taber 2004). Inferential knowledge was typically viewed as the product of repeated observations of individual cases, and many authors from the earlier period seemed to view these inferences as sufficiently reliable; an exception were some skeptical thinkers, who emphasized precisely the fact that these inferences were not necessarily truth-preserving (Matilal 1998; Siderits 2003). By contrast, later authors, in particular Dignāga, explicitly recognized arguments having the property of necessary truth-preservation as comprising a special class of arguments. Indeed, over the centuries theories and practices of argumentation in the Indian tradition continued to evolve, thus offering much valuable material for those interested in the history of theories of argumentation.

Chinese intellectuals were also deeply interested in argumentation (C. Hansen 1983), a practice described as biàn or biàn shuō in classical Chinese texts. In particular, the thinkers associated with the “School of Names” were especially keen on disputations, including idle contests of wits (at least according to their critics). Indeed, some of these thinkers have been described as the “Chinese sophists”, given the (at least superficial) similarities with the Greek sophists (see entry on the School of Names ). Moreover, Chinese thinkers also dealt with contexts of “mass persuasion”, that is persuasion of large groups of people (even if they were not fellow citizens like in Greece), such as groups of followers of different masters.

Biàn is in fact a more general concept, its core meaning pertaining to drawing distinctions,

as a verb referring to the act of distinguishing or discriminating things from each other and as a noun referring to distinctions. (Fraser 2013: 4)

But for these classical Chinese thinkers, a debate or argument is in fact an activity primarily aimed at drawing distinctions , hence the secondary meaning the term acquired as referring to disputation and argument. Essentially, the question in a disputation is usually whether a given name is suitably applied to a given object (or event), as revealed by a passage from the Mohist Dialectics (A74, as cited in the entry on Mohist canons (note 25) ):

Canon: Biàn is contending over converses. Winning in biàn is fitting the thing. Explanation: One calls it “ox”, the other calls it “non-ox”. This is contending over converses. These do not jointly fit the object. If they do not jointly fit, it must be that one does not fit.

While this may seem like an idle discussion, Chinese thinkers took the rectification of names to be of paramount importance. If speakers do not use names and terms uniformly, chaos and anarchy will ensue. In particular, they will not be able to follow commands as intended by their superiors, as these thinkers emphasized the action-guiding over the descriptive functions of language (see entry on the School of Names, supplement “Disputation in context” ).

While intellectuals of all main traditions in the classical period discussed (and presumably engaged in) biàn , there are three main (interrelated) accounts of argumentation in classical Chinese thought: that of the early Mohists in their rebuttal of fatalism, that of the later Mohist dialectic, and that of Xúnzǐ (a prominent thinker in the Confucian tradition; Fraser 2013). And yet, while they contain sophisticated analyses of proper and improper uses of language in disputations, they remain fundamentally different from the theories of argumentation found in Aristotle’s texts, for example, in particular in that there is no explicit articulation of inferential rules and principles—even if implicitly they seem to endorse certain principles, such as the principle of non-contradiction when stating that something cannot both be called “ox” and “non-ox” (see passage quoted above). The key concept in the Chinese context is that of analogy:

inference is thus understood as the act of distinguishing something as a certain kind of thing on the basis of having distinguished it as similar to a relevant “model” or “standard”. (Fraser 2013: 4)

As noted above, analogical reasoning is also widely present in the Greek tradition, but in the latter it coexists with other modes of reasoning, including deductive reasoning. In this respect, we may say that the property of necessary truth-preservation did not stand out for the Chinese thinkers, who were primarily concerned with language-world relations rather than with relations between sentences (as part of a more general pragmatic intellectual orientation). So here again we have an argumentative tradition tailored to the needs of its practitioners in their own sociocultural circumstances.

2. Medieval Traditions

The Latin medieval intellectual tradition is commonly thought to span from Boethius in the sixth century up to the fifteenth century and beyond. The common denominators were the use of Latin as lingua franca and its (institutional as well as intellectual) proximity with Christianity. A focus on debating and argumentation is a crucial feature of this tradition, in particular as crystalized in what is known as scholastic disputation . Scholastic disputation is a formalized, rigorous procedure for debate, based on fairly strict rules, which became one of the main approaches for intellectual inquiry in medieval Europe (Novikoff 2013). Inspired by ancient Greek argumentation methods, it was then further developed in the monasteries of the early Middle Ages. It reached its pinnacle from the twelfth century onwards, especially with the birth and growth of universities, where it became one of the main teaching methods (see entry on literary forms of medieval philosophy ). The influence of disputations went well beyond universities, expanding towards multiple spheres of cultural life.

Schematically, such disputations may be described thus:

[A disputation] is a regular form of teaching, apprenticeship and research, presided over by a master, characterized by a dialectical method which consists of bringing forward and examining arguments based on reason and authority which oppose one another on a given theoretical or practical problem and which are furnished by participants, and where the master must come to a doctrinal solution by an act of determination which confirms him in his function as master. (Bazán, Wippel, Fransen, & Jacquart 1985: 40; as quoted in the entry on literary forms of medieval philosophy )

In other words, a disputation starts with a statement, and then goes on to examine arguments in favor and against the statement. A disputation is essentially a dialogical practice in that it features two (possibly fictive) parties disagreeing on a given statement and producing arguments to defend their respective positions, even if both roles can be played by one and the same person. The goal may simply be that of convincing an interlocutor and/or the audience, but the implication is typically that something deeper is achieved, namely coming closer to the truth by examining the question from many different angles (Angelelli 1970).

Medieval intellectuals engaged in “live” disputations, both privately, between a master and a pupil, and as grand public events attended by the university community at large (Novikoff 2013). Moreover, the general structure is used extensively in some of the most prominent writings by these authors (some of them are in fact written-up versions of disputations actually having taken place, known as reportatio ). For example, Aquinas’ Summa Theologica —possibly the most influential work from the scholastic tradition—follows the structure of a disputation, with arguments for and against specific claims being examined (see entry on Thomas Aquinas ). Indeed, disputation became one of the chief methods for intellectual inquiry in general, and medieval treatises on philosophical topics typically contain a fair amount of disputational vocabulary. The widespread presence of disputation and related genres has been described as “the institutionalization of conflict” in scholasticism (see entry on literary forms of medieval philosophy ).

Logical textbooks were expected to provide the required training to excel in the art of disputation, with chapters on fallacies, consequence, the logical structure and meaning of propositions, obligationes (a special kind of disputation) etc., all of which are directly relevant for the art of disputation (see entries on medieval theories of consequence , properties of terms , and obligationes ). In fact, to a great extent Latin medieval authors did not differentiate between “ logica ” and “ dialectica ”, as attested by the fact that a number of influential logical textbooks—Abelard’s De Dialectica , Buridan’s Summulae de dialectica —bore the term “ dialectica ” in their titles. As late as in the sixteenth century, the Spanish scholastic author Domingo de Soto still defined dialectic/logic as “the art or science of disputing” (Ashworth 2011).

But elsewhere, Renaissance authors such as Lorenzo Valla (Nauta 2009; see entry on Lorenzo Valla ) were harsh critics of the genre of scholastic disputation. These authors deplored the lack of applicability of scholastic logic; Valla for example saw syllogisms as an artificial type of reasoning, useless for orators on account of being too far removed from natural ways of speaking and arguing. They condemned the cumbersome, artificial and overly technical Latin of scholastic authors, and defended a return to the classical Latin of Cicero and Vergil. Many Renaissance authors did not belong to the university system, where scholasticism was still the norm in the fifteenth century; instead, many were civil servants, and were thus involved in politics, administration, and civic life in general. As such, they were much more interested in rhetoric and persuasion than in logic and demonstration (Dutilh Novaes 2017).

The demise of scholasticism was a gradual process, and for centuries the logic taught at universities was still based on general Aristotelian theories such as syllogistic. But as a whole, logic and argumentation became less prominent topics of discussion for thinkers in the early modern period (Dutilh Novaes 2020: ch. 7). One exception is the so-called Port Royal Logic (1662), which presented itself explicitly as a manual on the art of thinking, but which contains extensive discussions on modes of arguing as well (see entry on Port Royal logic ).

With the advent of Islam in the seventh century, a new cultural and intellectual tradition was initiated; alongside the novelty of Islam, it drew significantly from earlier sources such as ancient Greek philosophy and also Persian and Arabic sources (among others). (The term “Islamicate” is used to refer to what pertains to regions in which Muslims are culturally dominant, but not specifically to the religion of Islam as such.) The primary language of learning in this tradition was Arabic, but significant texts were also written in Persian, Turkish and Hebrew (among other languages).

In this tradition, the term jadal was generally used to refer to argumentative practices and accompanying theories; it is commonly translated as “dialectic” or “disputation theory” (Young 2017; Miller 2020). Islamicate theories of argumentation come in many kinds, emerging within specific fields of inquiry such as theology and later jurisprudence, but also as domain-independent reflections on how to reason and argue well, in particular but not exclusively in connection with logic and ancient Greek sources such as Aristotle (see entry on Arabic and Islamic philosophy of language and logic ).

The advent of the Abbasid Caliphate (750–1258) marked the beginning of systematic efforts to translate a wide range of ancient Greek texts, in particular texts by Aristotle and his commentators, under the protection and sponsorship of these rulers. The translation movement culminated around 830 in the circle of al-Kindî in Baghdad, and inaugurated the intellectual tradition of falsafa (an alliteration for the Greek word “ philosophia ”), which, at least initially, was viewed as a competitor for the “local” traditions of kalam (rational theology) and fiqh (Islamic jurisprudence) (Miller 2020; see entries on Greek sources in Arabic and Islamic philosophy and on Arabic and Islamic natural philosophy and natural science ). The latter also offered accounts of reasoning and argumentation (in their specific domains), but until the eleventh century there was little cross-pollination between them and Greek-inspired logic and philosophy.

The earliest fully-fledged theories of jadal emerged in theological contexts, around the turn of the ninth to the tenth century (Miller 2020: ch. 2). For these theologians, jadal is a method for attaining truth, used by God in disputing with the Jews, and taught by God to his prophet. The focus is thus predominantly epistemological, but jadal is said to explicitly involve at least two people (thus being different from solitary speculation) who exchange questions and answers. The ultimate goal is to defend and prove the truth of Islam in contexts of religious disputes. The authors in this tradition wrote detailed treatises that included discussions of rules of conduct during debates, objections and counter-objections, and signs of defeat. The theological tradition of jadal then provided the substratum for the development of dialectical theories of jurisprudence (Miller 2020: ch. 4).

Within falsafa , argumentation was initially studied from the perspective of the Aristotelian Organon . By the early tenth century, a group of self-declared Peripatetics in Baghdad presented themselves as the defenders of Aristotelian orthodoxy. The most famous member of this group was al-Farabi, who composed a series of commentaries on the books of the Organon , including an influential commentary on Aristotle’s Topics , which was known as the Book of Dialectic ( Kitāb al-Jadal ; (DiPasquale 2019; see entries on al-Farabi and al-Farabi’s philosophy of logic and language ). At this stage, unsurprisingly, these thinkers were predominantly interested in the key topics of Aristotle’s logical canon such as syllogistic, dialectic, and demonstration, and developed detailed theories on argumentation (Miller 2020: ch. 3).

All this was to change thanks to the larger-than-life figure of Ibn Sina (Avicenna; ca. 970–1037; see entry on Ibn Sina ). Ibn Sina reoriented the Aristotelian conception of logic as closely connected with dialectic and argumentation towards a more epistemological, mentalistic approach (see entry on Ibn Sina’s logic ). Ibn Sina went on to become the most influential thinker in the Islamicate tradition in subsequent centuries, and this meant that the study of logic, referred to as mantiq , became by and large divorced from jadal .

In later periods, the “foreign” theories of the falsafa tradition were finally (partially) incorporated into the original traditions in jurisprudence, law and theology, in particular with the rise of the madrasa system starting in the late eleventh century (El-Rouayheb 2016; madrasas were official institutions of learning, functionally similar to European universities). In the madrasas, the Arabic scholastic method became consolidated and widely disseminated (see entry on Arabic and Islamic philosophy of language and logic ). But theories of disputation tended to be studied as an independent discipline, called “the science of disputation” ( 'ilm al-munazara ) or “the rules of discussion” ( ādāb al-baḥth ), whereas logic ( mantiq ) remained focused on epistemological concerns. As described by Miller (2020: 103),

ādāb al-baḥth emerged as an independent intellectual discipline and literary genre by adopting concepts from Aristotelian logic and philosophy as well as rules formulated in the context of both juridical and theological dialectics. (The earliest works in the ādāb al-baḥth tradition date to the first half of the 14 th century)

Thus, over the centuries, authors and thinkers in the Islamic World produced sophisticated theories of argumentation, and this from different angles, in particular theology, law, and philosophy.

Copyright © 2021 by Catarina Dutilh Novaes < cdutilhnovaes @ gmail . com >

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James Pryor, "What Is an Argument?

An argument is not the same thing as a quarrel. The goal of an argument is not to attack your opponent, or to impress your audience. The goal of an argument is to offer good reasons in support of your conclusion , reasons that all parties to your dispute can accept.

Nor is an argument just the denial of what the other person says. Even if what your opponent says is wrong and you know it to be wrong, to resolve your dispute you have to produce arguments. And you haven't yet produced an argument against your opponent until you offer some reasons that show him to be wrong.

Here's a sample argument. The premises are in red.

• No one can receive an NYU degree unless he or she has paid tuition to NYU.
• Shoeless Joe Jackson received an NYU degree.
• So, Shoeless Joe Jackson paid tuition to NYU.

In this argument, it is clear what the premises are, and what the conclusion is. Sometimes it will take skill to identify the conclusion and the premises of an argument. You will often have to extract premises and conclusions from more complex and lengthy passages of prose. When you do this, it is helpful to look out for certain key words that serve as indicators or flags for premises or conclusions.

Some common premise-flags are the words because , since , given that , and for . These words usually come right before a premise. Here are some examples:

Your car needs a major overhaul, for the carburetor is shot.

My Given that euthanasia is a common medical practice, the state legislatures ought to legalize it and set up some kind of regulations to prevent abuse.

Because euthanasia is murder, it is always morally wrong.

We must engage in affirmative action, because America is still a racist society.

Since abortion is a hotly contested issue in this country, nobody should force his opinion about it on anyone else.

Some common conclusion-flags are the words thus , therefore , hence , it follows that , so , and consequently . These words usually come right before a conclusion. Here are some examples:

You need either a new transmission, or a new carburetor, or an entirely new car; so you had better start saving your pennies.

Affirmative action violates the rights of white males to a fair shake; hence it is unjust.

It is always wrong to kill a human being, and a fetus is undoubtedly a human being. It follows that abortion is always wrong.

A woman's right to control what happens to her body always takes precedence over the rights of a fetus. Consequently , abortion is always morally permissible.

Euthanasia involves choosing to die rather than to struggle on. Thus , euthanasia is a form of giving up, and it is therefore cowardly and despicable.

Authors do not always state all the premises of their arguments. Sometimes they just take certain premises for granted. It will take skill to identify these hidden or unspoken premises. We will discuss this more later.

Whether an argument convinces us depends wholly on whether we believe its premises, and whether its conclusion seems to us to follow from those premises. So when we're evaluating an argument, there are two questions to ask:

• Are its premises true and worthy of our belief?
• Does its conclusion really follow from the premises?

These are completely independent issues. Whether or not an argument's premises are true is one question; and whether or not its conclusion follows from its premises is another, wholly separate question.

If we don't accept the premises of an argument, we don't have to accept its conclusion, no matter how clearly the conclusion follows from the premises. Also, if the argument's conclusion doesn't follow from its premises, then we don't have to accept its conclusion in that case, either, even if the premises are obviously true.

So bad arguments come in two kinds. Some are bad because their premises are false; others are bad because their conclusions do not follow from their premises. (Some arguments are bad in both ways.)

If we recognize that an argument is bad, then it loses its power to convince us. That doesn't mean that a bad argument gives us reason to reject its conclusion. The bad argument's conclusion might after all be true; it's just that the bad argument gives us no reason to believe that the conclusion is true.

Let's consider our sample argument again:

In this argument, the conclusion does in fact follow from the premises, but at least one of the premises is false. It's not true that one has to pay tuition in order to receive an NYU degree. (NYU gives out a number of honorary degrees every year to people who were never NYU students, and never paid tuition.) Probably the other premise is false, too: as far as I know, Shoeless Joe Jackson did not ever receive an NYU degree. So this argument does not, by itself, establish that Shoeless Joe Jackson paid tuition to NYU.

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2 Evaluating Arguments

Nathan Smith

One particularly relevant application of logic is assessing the relative strength of philosophical claims. While the topics covered by philosophers are fascinating, it is often difficult to determine which positions on these topics are the right ones. Many students are led to think that philosophy is just a matter of opinion. After all, who could claim to know the final answer to philosophical questions?

It’s not likely that anyone will ever know the final answer to deep philosophical questions. Yet there are clearly better and worse answers; and philosophy can help us distinguish them. This chapter will give you some tools to begin to distinguish which positions on philosophical topics are well-founded and which are not. When a person makes a claim about a philosophical subject, you should ask, “What are the arguments to support that claim?” Once you have identified an argument, you can use these tools to assess whether it’s a good or bad one, whether the evidence and reasoning really support the claim or not.

In broad terms, there are two features of arguments that make them good: (1) the structure of the argument and (2) the truth of the evidence provided by the argument. Logic deals more directly with the structure of arguments. When we examine the logic of arguments, we are interested in whether the arguments have the right architecture, whether the evidence provided is the right sort of evidence to support the conclusion drawn. However, once we try to evaluate the truth of the conclusion, we need to know whether the evidence is true. We’ll look at both of these considerations in what follows.

Inference and Implication: Why Conclusions Follow from Premises

An argument is a connected series of propositions, some of which are called premises and at least one of which is a conclusion. The premises provide the reasons or evidence that supports the conclusion. From the point of view of the reader, an argument is meant to persuade the reader that, once the premises are accepted as true, the conclusion follows from them. If the reader accepts the premises, then she ought to accept the conclusion. The act of reasoning that connects the premises to the conclusion is called an inference . A good argument supports a rational inference to the conclusion, a bad argument supports no rational inference to the conclusion. [1]

Consider the following example:

• All human beings are mortal.
• Socrates is a human being.
• [latex]/ \therefore[/latex] Socrates is mortal.

This argument asserts that Socrates is mortal. It does so by appealing to the fact that Socrates is a human being, together with the idea that all human beings are mortal. There is clearly a strong connection between the premises and conclusion. Imagine a reader who accepts both premises but denies the conclusion. This person would have to believe that Socrates is a human being and that all human beings are mortal, but still deny that Socrates is mortal. How could such a person maintain that belief? It just doesn’t seem rational to believe the premises but deny the conclusion!

Now consider the following argument:

• I saw a black cat today.
• My knee is aching.
• [latex]/ \therefore[/latex] It is going to rain.

Suppose that it does, in fact, rain and the person who advances this argument believes that it is going to rain. Is that person justified in their belief that it will rain? Not based on the argument presented here! In this argument, there is a very weak connection between the premises and the conclusion. So, even if the conclusion turns out to be true, there is no reason why a reader ought to accept the conclusion given these premises (there may be other reasons for thinking it is going to rain that are not provided here, of course). The point is that these premises do not provide the right sort of evidence to justify the conclusion.

So far, I have described the connection between premises and conclusion in terms of the psychological demand placed on a reader of the argument. However, we can describe this connection from another perspective. We can say that the premises of an argument logically imply a conclusion. Either way of speaking is correct. What they assert is that good arguments present a strong connection between the truth of the premises and the truth of the conclusion. In the next few sections, we will examine three different types of logical connection, each with its own rules for evaluation. Sometimes logical implication is guaranteed (as in the case of deductive arguments ), sometimes the logical connection only ensures the conclusion is probable (as with inductive and abductive arguments ).

Deductive Arguments

Deductive arguments are the most common type of argument in philosophy, and for good reason. Deductive arguments attempt to demonstrate that the conclusion follows necessarily from the premises. As long as the premises of a good deductive argument are true, the conclusion is true as a matter of logic. This means that if I know the premises are true, I know with one-hundred percent certainty that the conclusion is also true! This may be hard to believe; after all, how can we be absolutely certain about anything? But notice what I am saying: I am not saying that we know the conclusion is true with one-hundred percent certainty. I am saying that we can be one-hundred percent certain the conclusion is true, on the condition that the premises are true. If one of the premises is false, then the conclusion is not guaranteed.

Here are two examples of good deductive arguments. They are both valid and have true premises. A valid argument is an argument whose premises guarantee the truth of the conclusion. That is, if the premises are true, then it is impossible for the conclusion to be false. A valid deductive argument whose premises are all true is called a sound argument .

• If it rained outside, then the streets will be wet.
• It rained outside.
• [latex]/ \therefore[/latex] The streets are wet.
•  Either the world ended on December 12, 2012 or it continues today.
• The world did not end on December 12, 2012.
• [latex]/ \therefore[/latex] The world continues today.

Hopefully, you can see that these arguments present a close connection between the premises and conclusion. It seems impossible to deny the conclusion while accepting that the premises are all true. This is what makes them valid deductive arguments. To show what happens when similar arguments employ false premises, consider the following examples:

•  If Russia wins the 2018 FIFA World Cup, then Russia is the reigning FIFA world champion [in 2019].
• Russia won the 2018 FIFA World Cup.
• [latex]/ \therefore[/latex] Russia is the reigning FIFA world champion [in 2019].
• Either snow is cold or snow is dry.
• Snow is not cold.
• [latex]/ \therefore[/latex] Snow is dry.

You may recognize that these arguments have the same structure as the previous two arguments. That is, each expresses the same connection between the premises and conclusion, and they are all deductively valid. However, these latter two arguments have at least one false premise and this false premise is the reason why these otherwise valid arguments reach a false conclusion. In the case of these arguments, the structure is good, but the evidence is bad.

Deductive arguments are either valid or invalid because of the form or structure of the argument. They are sound or unsound based on the form, plus the content. You might become familiar with some of the common forms of arguments (many of them have names) and once you do, you will be able to tell when a deductive argument is invalid.

Now let’s look at some invalid deductive arguments. These are arguments that have the wrong structure or form. Perhaps you have heard a playful argument like the following:

• Grass is green.
• Money is green.
• [latex]/ \therefore[/latex] Grass is money.

Here is another example of the same argument:

• All tigers are felines.
• All lions are felines.
• [latex]/ \therefore[/latex] All tigers are lions.

These arguments are examples of the fallacy of the undistributed middle term . The name is not important, but you may recognize what is going on here. The two types of objects in each conclusion are each a member of some third type, but they are not members of each other. So, the premises are all true, but the conclusions are false. If you encounter an argument with this structure, you will know that it is invalid.

But what do you do if you cannot immediately recognize when an argument is invalid? Philosophers look for counterexamples. A counterexample is a scenario in which the premises of the argument are true while the conclusion is clearly false. This automatically shows that it is possible for the argument’s premises to be true and the conclusion false. So, a counterexample demonstrates that the argument is invalid. After all, validity requires that if the premises are all true, the conclusion cannot possibly be false. Consider the following argument, which is an example of a fallacy called affirming the consequent :

• The streets are wet.
• [latex]/ \therefore[/latex] It rained outside.

Can you imagine a scenario where the premises are true, but the conclusion is false?

What if a water main broke and flooded the streets? Then the streets would be wet, but it may not have rained. It would still remain true that if it had rained, the streets would be wet, but in this scenario even if it didn’t rain, the streets would still be wet. So, the scenario where a water main breaks demonstrates this argument is invalid.

The counterexample method can also be applied to arguments where there is no clear scenario that makes the premises true and the conclusion false, but we will have to apply it a little differently. In these cases, we need to imagine another argument that has exactly the same structure as the argument in question but uses propositions that more easily produce a counterexample. Suppose I made the following argument:

• Most people who live near the coast know how to swim.
• Mary lives near the coast.
• [latex]/ \therefore[/latex] Mary knows how to swim.

I don’t know if Mary knows how to swim, but I do know that this argument does not provide sufficient reasons for us to know that Mary knows how to swim. I can demonstrate this by imagining another argument with the same structure as this argument, but the premises of this argument are clearly true while its conclusion is false:

• Most months in the calendar year have at least 30 days.
• February is a month in the calendar year.
• [latex]/ \therefore[/latex] February has at least 30 days.

To review, deductive arguments purport to lead to a conclusion that must be true if all the premises are true. But there are many ways a deductive argument can go wrong. In order to evaluate a deductive argument, we must answer the following questions:

• Are the premises true? If the premises are not true, then even if the argument is valid, the conclusion is not guaranteed to be true.
• Is the form of the argument a valid form? Does this argument have the exact same structure as one of the invalid arguments noted in this chapter or elsewhere in this book? [2]
• Can you come up with a counterexample for the argument? If you can imagine a case in which the premises are true but the conclusion is false, then you have demonstrated that the argument is invalid.

Inductive Arguments

Almost all of the formal logic taught to philosophy students is deductive. This is because we have a very well-established formal system, called first-order logic, that explains deductive validity. [3] Conversely, most of the inferences we make on a daily basis are inductive or abductive. The problem is that the logic governing inductive and abductive inferences is significantly more complex and more difficult to formalize than deductive inferences.

The chief difference between deductive arguments and inductive or abductive arguments is that while the former arguments aim to guarantee the truth of the conclusion, the latter arguments only aim to ensure that the conclusion is more probable . Even the conclusions of the best inductive and abductive arguments may still turn out to be false. Consequently, we do not refer to these arguments as valid or invalid. Instead, arguments with good inductive and abductive inferences are strong ; bad ones are weak . Similarly, strong inductive or abductive arguments with true premises are called cogent .

Here’s a table to help you remember these distinctions:

Inductive inferences typically involve an appeal to past experience in order to infer some further claim directly related to that experience. In its classic formulation, inductive inferences move from observed instances to unobserved instances, reasoning that what is not yet observed will resemble what has been observed before. Generalizations, statistical inferences, and forecasts about the future are all examples of inductive inference. [4] A classic example is the following:

• The Sun rose today.
• The Sun rose yesterday.
• The Sun has risen every day of human history.
• [latex]/ \therefore[/latex] The Sun will rise tomorrow.

You might wonder why this conclusion is merely probable. Is there anything more certain than the fact that the Sun will rise tomorrow? Well, not much. But at some point in the future, the Sun, like all other stars, will die out and its light will become so faint that there will be no sunrise on the Earth. More radically, imagine an asteroid disrupting the Earth’s rotation so that it fails to spin in coordination with our 24-hour clocks—in this case, the Sun would also fail to rise tomorrow. Finally, any inference about the future must always contain a degree of uncertainty because we cannot be certain that the future will resemble the past. So, even though the inference is very strong, it does not provide us with one-hundred percent certainty.

Consider the following, very similar inference, from the perspective of a chicken:

• When the farmer came to the coop yesterday, he brought us food.
• When the farmer came to the coop the day before, he brought us food.
• Every day that I can remember, the farmer has come to the coop to bring us food.
• [latex]/ \therefore[/latex] When the farmer comes today, he will bring food.

From a chicken’s perspective, this inference looks equally as strong as the previous one. But this chicken will be surprised on that fateful day when the farmer comes to the coop with a hatchet to butcher her! From the chicken’s perspective, the inference may appear strong, but from the farmer’s perspective, it’s fatally flawed. The chicken’s inference shares some similarities with the following example:

• A recent poll of over 5,000 people in the USA found that 85% of them are members of the National Rifle Association.
• The poll found that 98% of respondents were strongly or very strongly opposed to any firearms regulation.
• [latex]/ \therefore[/latex] Support of gun rights is very strong in the USA.

While the conclusion of this argument may be true and certainly appears to be supported by the premises, there is a key weakness that undermines the argument. You may suspect that these polling numbers present unusually high support for guns, even in the USA. [5] So, you may suspect that something is wrong with the data. But if I tell you that this poll was taken outside of a gun show, then you should realize that data may be correct, but the sample is clearly flawed. This reveals something important about inductive inferences. Inductive inferences depend on whether the sample set of experiences from which the conclusion is inferred are representative of the whole population described in the conclusion. In the cases of the chicken and gun rights, we are provided with a sample of experiences that are not representative of the populations in the conclusion. If we want to generalize about chicken farmer behavior, we need to sample the range of behaviors a farmer engages in. One chicken may not have enough data points to make a generalization about farmer behavior. Similarly, if we want to make a claim about the gun control preferences in the USA, we need to have a sample that represents all Americans, not just those who attend gun shows. The sample of experiences in a strong inductive argument must be representative of the conclusion that is drawn from it.

To review, strong inductive inferences lead to conclusions that are made more likely by the premises, but not guaranteed to be true. They are typically used to make generalizations, infer statistical probabilities, and make forecasts about the future. To evaluate an inductive inference, you should use the following guidelines:

• Are the premises true? Just like deductive arguments, inductive arguments require true premises to infer that the conclusion is likely to be true.
• Are the examples cited in the premises a large enough sample? The larger the sample, the greater the likelihood it is representative of the population as a whole, and thus the more likely inductive inferences made on the basis of it will be strong.

Abductive Arguments

Abductive arguments produce conclusions that attempt to explain the phenomena found in the premises. From a commonsense point of view, we can think of abductive inferences as “reading between the lines,” “using context clues,” or “putting two and two together.” We typically use these phrases to describe an inference to an explanation that is not explicitly provided. This is why abductive arguments are often called an “inference to the best explanation.” From a scientific perspective, abduction is a critical part of hypothesis formation. Whereas the classic “scientific method” teaches that science is deductive and that the purpose of experimentation is to test a hypothesis (by confirming or disconfirming the hypothesis), it is not always clear how scientists arrive at a hypothesis. Abduction provides an explanation for how scientists generate likely hypotheses for experimental testing.

Even though Sherlock Holmes is famous for declaring, in the course of his investigations, “Deduction, my dear Watson,” he probably should have said “Abduction”! Consider the following inference:

• The victim’s body has multiple stab wounds on its right side.
• There was evidence of a struggle between the murderer and the victim.
• [latex]/ \therefore[/latex] The murderer was left-handed.

You should recognize that the conclusion is not guaranteed by the premises, and so it is not a deductive argument. Additionally, the argument is not inductive, because the conclusion isn’t simply an extension from past experiences. This argument attempts to provide the best explanation for the evidence in the premises. In a struggle, two people are most likely to be standing face to face. Also, the killer probably attacked with his or her dominant hand. It would be unnatural for a right-handed person to stab with their left hand or to stab a person facing them on that person’s right side. So, the fact that the murderer is left-handed provides the most likely explanation for the stab wounds.

You use these sorts of inferences regularly. For instance, suppose that when you come home from work, you notice that the door to your apartment is unlocked and various items from the refrigerator are out on the counter. You might infer that your roommate is home. Of course, this explanation is not guaranteed to be true. For instance, you may have forgotten to lock the door and put away your food in your haste to get out the door. Abductive inferences attempt to reason to the most likely conclusion, not one that is guaranteed to be true.

What makes an abductive inference strong or weak? Good explanations ought to take account of all the available evidence. If the conclusion leaves some evidence unexplained, then it is probably not a strong argument. Additionally, extraordinary claims require extraordinary evidence. If an explanation requires belief in some entirely novel or supernatural entity, or generally requires us to revise deeply held beliefs, then we ought to demand that the evidence for this explanation is very solid. Finally, when assessing alternative explanations, we should heed the advice of “Ockham’s Razor.” William of Ockham argued that given any two explanations, the simpler one is more likely to be true. In other words, we should be skeptical of explanations that require complex mechanics, extensive caveats and exceptions, or an extremely precise set of circumstances, in order to be true. [6]

Consider the following arguments with identical premises:

•  There have been hundreds of stories about strange objects in the night sky.
• There is some video evidence of these strange objects.
• Some people have recalled encounters with extraterrestrial life forms.
• There are no peer-reviewed scientific accounts of extraterrestrial life forms visiting earth.
• [latex]/ \therefore[/latex] There must be a vast conspiracy denying the existence of aliens.
• There have been hundreds of stories about strange objects in the night sky.
• [latex]/ \therefore[/latex] The stories, videos, and recollections are probably the result of confusion, confabulation or exaggeration, or are outright falsifications.

Which is the more likely explanation?

To review, abductive inferences assert a conclusion that the premises do not guarantee, but which aims to provide the most likely explanation for the phenomena detailed in the premises. To assess the strength of an abductive inference, use the following guidelines:

• Is all the relevant evidence provided? If critical pieces of information are missing, then it may not be possible to know what the right explanation is.
• Does the conclusion explain all of the evidence provided? If the conclusion fails to account for some of the evidence, then it may not be the best explanation.
• Extraordinary claims require extraordinary evidence! If the conclusion asserts something novel, surprising, or contrary to standard explanations, then the evidence should be equally compelling.
• Use Ockham’s Razor; recognize that the simpler of two explanations is likely the correct one.

Exercise One

For each argument decide whether it is deductive, inductive or abductive. If it contains more than one type of inference, indicate which.

• Every human being has a heart,
• If something has a heart, then it has a liver
• [latex]/ \therefore[/latex] Every human being has a liver

Answer: This is a deductive argument because it is attempting to show that it’s impossible for the conclusion to be false if the premises are true.

• Chickens from my farm have gone missing,
• My farm is in the British countryside,
• [latex]/ \therefore[/latex] There are foxes killing my chickens
• All flamingos are pink birds,
• All flamingos are fire breathing creatures,
• [latex]/ \therefore[/latex] Some pink birds are fire breathing creatures
• Every Friday so far this year the cafeteria has served fish and chips,
• If the cafeteria’s serving fish and chips and I want fish and chips then I should bring in £4,
• If the cafeteria isn’t serving fish and chips then I shouldn’t bring in £4,
• I always want fish and chips,
• [latex]/ \therefore[/latex] I should bring in £4 next Friday
• If Bob Dylan or Italo Calvino were awarded the Nobel Prize in Literature, then the choices made by the Swedish Academy would be respectable,
• The choices made by the Swedish Academy are not respectable,
• [latex]/ \therefore[/latex] Neither Bob Dylan nor Italo Calvino have been awarded the Nobel Prize in Literature
• In all the games that the Boston Red Sox have played so far this season they have been better than their opposition,
• If a team plays better than their opposition in every game then they win the World Series
• [latex]/ \therefore[/latex] The Boston Red Sox will win the league
• There are lights on in the front room and there are noises coming from upstairs,
• If there are noises coming from upstairs then Emma is in the house,
• [latex]/ \therefore[/latex] Emma is in the house

Exercise Two

Give examples of arguments that have each of the following properties:

• Valid, and has at least one false premise and a false conclusion
• Valid, and has at least one false premise and a true conclusion
• Invalid, and has at least one false premise and a false conclusion
• Invalid, and has at least one false premise and a true conclusion
• Invalid, and has true premises and a true conclusion
• Invalid, and has true premises and a false conclusion
• Strong, but invalid [Hint: Think about inductive arguments.]
• This does not mean that bad arguments cannot be psychologically persuasive. In fact, people are often persuaded by bad arguments. However, a good philosophical assessment of an argument ought to rely purely on the rationality of its inferences. ↵
• Chapters 3 and 4 of this Introduction address types of fallacies. Fallacies are just systematic mistakes made within arguments. You can learn more examples of invalid argument forms in these chapters. ↵
• Chapter 3 introduces formal logic. ↵
• You may notice that the inference from the previous section about Mary being able to swim could be rephrased as a kind of inductive argument. If it is true that most people who live near the coast can swim and Mary lives near the coast, then it follows that Mary probably can swim. This demonstrates an important difference between deductive and inductive arguments. ↵
• See, for instance, recent Gallup polling: 2019. “Guns.” http://news.gallup.com/poll/1645/guns.aspx. ↵
• While Ockham’s Razor is a good rule of thumb in evaluating explanations, there is considerable debate among philosophers of science about whether simplicity it is a feature of good scientific explanations or not. ↵

A psychological act that links premises to a conclusion in an argument.

One proposition P logically implies another Q if whenever P is true, Q is also true. Arguments in which the premises logically imply the conclusion are known as valid arguments.

An argument that aims to be valid.

An argument that moves from observed instances of a certain phenomenon to unobserved instances of the same phenomenon.

An argument that attempts to provide the best explanation possible of certain other phenomena as its conclusion. Also known as inference to the best explanation .

An argument in which it is impossible for the premises to be true and the conclusion false.

A valid argument with actually true premises . Thus, if an argument is sound, its conclusion must be true.

A counterexample is a scenario in which the premises of the argument are true while the conclusion is false. If an argument has a counterexample, it is not valid.

An inductive or abductive argument in which the premises make the conclusion likely to be true.

An inductive or abductive argument in which the premises fail to make the conclusion likely to be true.

A strong inductive or abductive argument with true premises. If an argument is cogent, then its conclusion is likely to be true.

Evaluating Arguments Copyright © 2020 by Nathan Smith is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Philosophical Terms and Methods Philosophical Arguments

What is an argument, an argument’s structure, different flavors of argument, valid arguments, implicit or hidden premises, sound arguments, persuasive arguments, begging the question, conclusive or not.

Philosophy has a lot to do with arguments . It’s about giving arguments and it’s about evaluating or critically examining other people’s arguments to determine how good they are, and sometimes objecting to or resisting those arguments, or defending them against other people’s objections.

A philosophical argument is not the same thing as a quarrel ; it (ideally and usually) won’t involve screaming abuse, making threats, or throwing things. The goal of an argument is not to attack your opponent, or to impress your audience. Its goal is to offer good reasons in support of your conclusion , reasons that all parties to your dispute can accept.

Neither is an argument just the denial of what the other person says. Even if what your opponent says is wrong and you know it to be wrong, to resolve your dispute you have to produce arguments. And you haven’t produced an argument against your opponent until you offer some reasons that show him to be wrong.

Fundamentally, an argument is some reason (or several reasons) offered in support of a conclusion.

An important thing to remember is that even if a given argument is bad, its conclusion might still be true ! So just because we criticize or object to some argument, does not mean that we’ve thereby refuted its conclusion. We’re just saying that argument doesn’t give good reasons for the conclusion. There may be other, better arguments that do. It may even be a conclusion that we ourselves want to accept.

When you’re arguing, you’ll usually take certain theses for granted (these are the premises of your argument) and attempt to show that if one accepts those premises, then one ought also to accept the argument’s conclusion.

Here’s a sample argument. The premises are in red.

• No one can receive a UNC degree unless he or she has paid tuition to UNC.
• The famous baseball player Shoeless Joe Jackson received a UNC degree.
• So, Shoeless Joe Jackson paid tuition to UNC.

In this argument, it’s clear what the premises are, and what the conclusion is. Sometimes it will take skill to identify the conclusion and the premises of an argument. The conclusion won’t always come last; sometimes it may instead be announced first. Rarely, it might even occur in the middle.

Sometimes an argument will have several conclusions — some of them will be intermediate steps on the way to the argument’s main conclusion. Or there may be a main conclusion that the argument is primarily trying to establish, and then several further consequences the author claims follows from that main conclusion.

You will often have to extract an argument’s premises and conclusion(s) from more complex and lengthy passages of prose. When you do this, it is helpful to look out for certain key words that serve as indicators or flags for premises or conclusions.

Some common premise-flags are the words because , since , given that , and for . These words usually come right before a premise. Here are some examples:

Your car needs a major overhaul, for the carburetor is shot. Given that euthanasia is a common medical practice, the state legislatures ought to legalize it and set up some kind of regulations to prevent abuse. Because euthanasia is murder, it is always morally wrong. We must engage in affirmative action, because America is still a racist society. Since abortion is a hotly contested issue in this country, nobody should force his opinion about it on anyone else.

Some common conclusion-flags are the words thus , therefore , hence , it follows that , so , and consequently . These words usually come right before a conclusion. Here are some examples:

You need either a new transmission, or a new carburetor, or an entirely new car; so you had better start saving your pennies. Affirmative action violates the rights of white males to a fair shake; hence it is unjust. It is always wrong to kill a human being, and a fetus is undoubtedly a human being. It follows that abortion is always wrong. A woman’s right to control what happens to her body always takes precedence over the rights of a fetus. Consequently , abortion is always morally permissible. Euthanasia involves choosing to die rather than to struggle on. Thus , euthanasia is a form of giving up, and it is therefore cowardly and despicable.

As we said, the premises are what the author takes for granted and relies on, in order to establish something else. Sometimes they will be observations about specific facts; other times they may be general principles. We’ll discuss what it takes for an author to be entitled to their premises below .

Authors don’t always state all the premises of their arguments. Sometimes they rely on certain premises implicitly . It will take skill to identify these hidden or unspoken premises. We’ll discuss this more below , too.

Arguments come in different flavors.

The most important category for our discussion will be deductive or demonstrative arguments . As philosophers use these labels, this means arguments structured so that if their premises are true, their conclusion also has to be true. Mathematical proofs are good examples of this. Most of the arguments philosophers concern themselves with are also — or purport to be — arguments of this flavor.

Ordinarily, we talk about Sherlock Holmes “deducing” certain things, but most of his reasoning doesn’t count as “deductive” in that philosopher’s sense. Neither are most of the arguments we employ in everyday life deductive arguments. They aren’t attempts to prove a thesis conclusively. Instead, they just cite evidence, and provide reasoning, that tries to make their conclusion plausible , or reasonable to believe , or show that it’s probably true . Such arguments can still sometimes be good — in the sense that a reasonable person may find them persuasive or compelling.

Some examples include: concluding that it won’t snow on June 1st this year, because it hasn’t snowed on June 1st for any of the last 100 years; concluding that your friend is jealous because that’s the best explanation you can come up with of his behavior; and so on.

Philosophers have different labels and ways of categorizing these non-deductive arguments. You may see the labels “inductive,” and/or “ampliative,” and/or “inference to the best explanation,” or others. It’s controversial and difficult to know what qualities make such arguments good. Fortunately, we don’t need to concern ourselves with those questions. These non-deductive arguments won’t play a large role our (or in many other) introductory philosophy courses. We’ll mostly work with deductive arguments.

What Makes a Deductive Argument Good?

Whether a deductive argument should convince us depends wholly on whether we accept its premises, and whether its conclusion follows from those premises. So when we’re evaluating such an argument, there are two kinds of question to ask:

• Are its premises true and worth accepting?
• Does its conclusion really follow from the premises?

These are completely independent issues. Whether or not to accept an argument’s premises is one question; and whether or not its conclusion follows from its premises is another, wholly separate question.

If we don’t accept the premises of an argument, we don’t have to accept its conclusion, no matter how clearly the conclusion follows from the premises. Also, if the argument’s conclusion doesn’t follow from its premises, then we don’t have to accept its conclusion in that case, either, even if the premises are obviously true.

So bad arguments come in two kinds. Some are bad because their premises are false; others are bad because their conclusions do not follow from their premises. (Some arguments are bad in both ways.)

Let’s consider our sample argument again:

• Shoeless Joe Jackson received a UNC degree.

In this argument, the conclusion does in fact follow from the premises, but at least one of the premises is false. It’s not true that one has to pay tuition in order to receive a UNC degree. (For example, UNC sometimes gives out honorary degrees to people who were never UNC students, and never paid tuition.) Probably the other premise is false, too: as far as I know, Shoeless Joe Jackson did not ever receive a UNC degree.

So this argument does not, by itself, establish that Shoeless Joe Jackson paid tuition to UNC.

If we recognize that an argument is bad, it should lose its power to convince us. As we mentioned before, that doesn’t mean that an argument’s being bad gives us reason to reject its conclusion. The bad argument’s conclusion might after all be true; it’s just that the bad argument gives us no reason to believe the conclusion is true.

Philosophers use some special terminology to describe the qualities that make a deductive argument good.

We call an argument deductively valid (or, for short, just “valid”) when it has the right kind of structure, so that its conclusion logically follows from, or “is implied or entailed by,” its premises.

Terminology : The Philosophical Glossary warns about being careful to only call inferences and arguments “valid”:

In philosophical discussions, usually only inferences or arguments can be valid… Not points, objections, beliefs, questions, or worries…

For points and beliefs and statements, what you probably want to say is that they’re true (or false). Or that they’re justified or well-supported (or undefended or controversial).

In our courses, don’t call a statement “valid”… Don’t call an inference or an argument “true.”

The Glossary also has tips about when to say “imply/entail” and when to say “infer.”

Validity is a property of an argument’s form. It doesn’t matter what the premises and the conclusion actually say. It just matters whether the argument has the right structure. So, in particular, a valid argument need not have true premises, nor need it have a true conclusion. The following is a valid argument:

• All cats are reptiles.
• Bugs Bunny is a cat.
• So Bugs Bunny is a reptile.

Neither of the premises of this argument is true. Nor is the conclusion. But the premises are of such a form that if they were both true, then the conclusion would also have to be true. Hence the argument is valid.

To tell whether an argument is valid, figure out what the form of the argument is, and then try to think of some other argument of that same form and having true premises but a false conclusion. If you succeed, then every argument of that form must be invalid. A valid form of argument can never lead you from true premises to a false conclusion.

For instance, consider the argument:

• If Socrates was a philosopher, then he wasn’t a historian.
• Socrates wasn’t a historian.
• So Socrates was a philosopher.

This argument is of the form If P then Q. Q. So P. (If you like, you could say the form is: If P then not-Q. Not-Q. So P. For present purposes, it doesn’t matter.) The conclusion of the argument is true. But is it a valid form of argument?

It is not. How can you tell? Because the following argument is of the same form, and it has true premises but a false conclusion:

• If Socrates was a horse (this corresponds to P), then Socrates was warm-blooded (this corresponds to Q).
• Socrates was warm-blooded (Q).
• So Socrates was a horse (P).

Since this second argument has true premises and a false conclusion, it must be invalid. And since the first argument has the same form as the second argument (both are of the form If P then Q. Q. So P. ), both arguments must be invalid.

If an argument aims to be deductive, but is invalid, it won’t give us any reason to believe its conclusion. (Though, as we said, it may be that the conclusion nonetheless happens to be true.)

If you take a class in Formal Logic, you’ll study which forms of argument are valid and which are invalid. We won’t devote much time to that study in this class. I only want you to learn what the terms “valid” and “invalid” mean, and to be able to recognize a few clear cases of valid and invalid arguments when you see them.

As we mentioned before, sometimes an author will not explicitly state all the premises of his argument. There’s something he needs to be assuming, but he hasn’t identified it and labeled as a premise. This will render the author’s argument invalid as it is written. But if it’s clear what the author meant or needs to be relying on, we can often “fix up” the argument by supplying that missing premise. For instance, as it stands, the argument:

• All engineers enjoy ballet.
• Therefore, some males enjoy ballet.

is invalid. But it’s clear how to fix it up. We just need to supply the implicit premise :

• Some engineers are male.

You should become adept at filling in such missing premises, so that you can see the underlying form of an argument more clearly.

Sometimes a premise is left out because the author takes it to be obvious, as in the engineer argument and the exploding car argument. But sometimes the missing premise is very contentious, as in the abortion argument. In these cases, the author may not yet recognize that they’re relying on the assumption. Or they may not appreciate how contentious it is. Occasionally, they may realize these things, but just hope they can trick their readers into not noticing.

An argument is sound just in case it’s valid and all its premises are in fact true.

The argument:

• If the moon is made of green cheese, then cows jump over it.
• The moon is made of green cheese.
• Therefore, cows jump over the moon.

is an example of a valid argument which is not sound.

We said above that a valid argument can never take you from true premises to a false conclusion. So, if you have a sound argument for a given conclusion, then, since the argument has true premises, and since the argument is valid, and valid arguments can never take you from true premises to a false conclusion, the argument’s conclusion must be true. Sound arguments always have true conclusions.

This means that if you read Philosopher X’s deductive argument and you disagree with her conclusion, then you’re committed to the claim that her argument is unsound. Either X’s conclusion does not actually follow from her premises — there is a problem with her reasoning or logic — or at least one of X’s premises is false.

When you’re doing philosophy, it is never enough simply to say that you disagree with someone’s conclusion, or that their conclusion is wrong. If your opponent’s conclusion is wrong, then there must be something wrong with their argument, and you need to say what you think it is.

Terminology : The Philosophical Glossary discusses when to say someone “proved” something versus when to say they merely “argued for” it. The former words communicate that you think the author succeeded. The latter leave it open whether their arguments are convincing or sound:

You should not say that Locke has proven some claim, or shown or demonstrated that something is the case, unless you think that Locke’s arguments for his claim are successful. If Locke has proven a claim, then the claim must be true.

If you doubt or want to leave it open whether Locke’s arguments for a claim are successful, then you should say instead Locke argues that… or Locke defends the claim that… or Locke tries to prove that… or something of that sort.

Merely having a sound argument is not yet enough to have the persuasive force of reason on your side. It may be that your premises are true, but it’s hard to recognize that they’re true.

Consider the following two arguments:

Either God exists, or 2+2=5. 2+2 does not equal 5. So God exists.

Either God does not exist, or 2+2=5. 2+2 does not equal 5. So God does not exist.

Both of these arguments have the form P or Q. Not-Q. So P. That’s a valid form of argument. So both of these arguments are valid. What’s more, at least one of the arguments is sound. If God exists, then all the premises of Argument A are true, and since Argument A is valid, it must also be sound. If God does not exist, then all the premises of Argument B are true, and since Argument B is valid, it must also be sound. Either way, one of the arguments is sound. But we can’t easily tell which of these arguments is sound and which is not. Hence neither argument is very persuasive .

In general, when you’re engaging in philosophical debate, you don’t just want valid arguments from premises that happen to be true. You want valid arguments from premises that are recognizable as true, or already accepted as true, by all parties to your debate.

Hence, we can introduce a third notion. This quality of argument doesn’t have a standard name, but we can naturally describe it like so:

A persuasive argument is a valid argument with plausible, or obviously true, or antecedently accepted, or sufficiently justified premises.

These are the sorts of arguments you should try to offer, and that you should expect to be given.

Their premises should be uncontentious — or at least, less contentious than the argument’s conclusion. If they aren’t obvious, they should at least be widely enough accepted by the parties to the debate, that they don’t need defending. Else the author has the responsibility to support or justify them — either with yet further argumnt, or in other, less conclusive ways.

In any event, an argument’s premises should be credible independently of its conclusion — in the sense that it’d be possible for someone to reasonably accept the premises even if they had not already accepted the conclusion.

Begging the question is a technical philosophical label for arguments that fail to do that. These arguments assume or rely on the very point at issue in attempting to argue for it. This may also be called “circular reasoning.” Here is an example of an argument with this vice:

We know that God exists, because it says so in the Bible. And we can trust the Bible on this matter because it’s the Word of God, and so must be correct.

This argument begs the question because one of its premises says that the Bible is the Word of God. Presumably, one would only accept this premise if one already believed that God exists. But that’s precisely what we’re supposed to be arguing for!

A good rule of thumb is the following: if an argument contains a premise or step that would not be accepted by a reasonable person who is initially prone to doubt the argument’s conclusion, then the argument begs the question.

We will seldom see obvious cases of begging the question in our readings. It’s the unobvious cases of begging the question which are really dangerous, because they’re so hard to spot.

The funny label “begging the question” for this vice comes from old mistranslations of a Latin phrase that should have been translated as “claiming the question,” that is, trying to grab without argument the very answer whose correctness you’re debating.

Ordinary people have started to use the expression “begging the question,” too. Usually they don’t mean what philosophers do. They mean something like “prompting or inviting a question.” This started out as a misunderstanding of the philosopher’s notion, but eventually, if ordinary people keep using the expression that way, maybe that’s what it will mean, at least for them.

Deductive arguments contrast with non-deductive arguments in that the former are ones whose premises conclusively entail their conclusions. If you accept the premises as true, the conclusion cannot be avoided: it has to be true as well. However , often (perhaps always) we won’t be in positions where the premises of an argument are absolutely indubitable and immune to philosophical challenge. So although we’re working with deductive arguments, these arguments usually won’t decisively settle the debates we’re considering. We’ll have to sort out how plausible and convincing different arguments’ premises are, to assess how much persuasive force those arguments should have.

We’ll discuss these issues more later .

This page tried to explain, and enable you to understand, the following concepts:

• deductive arguments
• what is it for an argument to be valid? sound? persuasive?
• implicit/hidden/missing premises
• what is it for an argument to “beg the question”?

Created and maintained by [email protected]

URL: http://www.jimpryor.net/teaching/vocab2/arguments.html

2024-01-15 11:54 EST

This work licensed under a Creative Commons License

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5.1: Philosophical Methods for Discovering Truth

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• Nathan Smith et al.

Learning Objectives

By the end of this section, you will be able to:

• Describe the role that dialectics plays in logic and reasoning.
• Define “argument” and “negation of a argument.”
• Define the laws of noncontradiction and the excluded middle.

Like most academic disciplines, the goal of philosophy is to get closer to the truth. Logic, reasoning, and argumentation are the predominant methods used. But unlike many other disciplines, philosophy does not contain a large body of accepted truths or canonical knowledge. Indeed, philosophy is often known for its uncertainty because it focuses on questions for which we do not yet have ways of definitively answering. The influential 20th-century philosopher Bertrand Russell explains that “as soon as definite knowledge concerning any subject becomes possible, the subject ceases to be called philosophy, and becomes a separate science” (1912, 240).

Because philosophy focuses on questions we do not yet have ways of definitively answering, it is as much a method of thinking as it is a body of knowledge. And logic is central to this method. Thinking like a philosopher involves thinking critically about alternative possibilities. To answer the question of whether there is a God (a question for which we lack a definitive method of answering), we can look at things we believe we know and then critically work through what those ideas entail about the existence or possible characteristics of God. We can also imagine God exists or God does not exist and then reason through what either possibility implies about the world. In imagining alternative possibilities, we must critically work through what each possibility must entail. Changing one belief can set off a cascade of implications for further beliefs, altering much of what we accept as true. And so, in studying philosophy, we need to get used to the possibility that our beliefs could be wrong. We use reason to do philosophy, and logic is the study of reason. Hence, logic helps us get closer to the truth.

Dialectics and Philosophical Argumentation

Philosophers love to argue. But this love does not mean that philosophy lectures are loud, contentious events. Most people think of an argument as a verbal disagreement, and the term evokes images of raised voices, heightened emotions, and possibly bad behavior. However, in philosophy, this word does not have a negative connotation. An argument in philosophy is a reasoned position—to argue is simply to offer a set of reasons in support of some conclusion. The goal of an individual argument is to support a conclusion. However, the long-term goal of argumentation between philosophers is to get closer to the truth. In contemporary academic philosophy, philosophers are engaged in dialogue with each other where they offer arguments in the publication of articles. Philosophers also engage in argument at conferences and in paper presentations and lectures. In this way, contemporary academic philosophers are engaged in a dialectic of sorts.

A traditional dialectic is a debate or discussion between at least two people who hold differing views. But unlike debate, participants in the discussion do not have the goal of “winning,” or proving that the other view is wrong. Rather, the goal is to get closer to the truth. Thus, dialectics make use of logic and reason, while debates often use rhetorical ploys or appeal to the emotions. Because of the tendency of participants to appeal to emotion and prejudice in many modern popular debates, philosophers often qualify their words and refer to reasoned debate when discussing proper public discourse between people. But even reasoned debates can become adversarial, while dialectics are mostly collaborative. The participants in a dialectic, whom philosophers refer to as “interlocuters,” enter into discourse with the aim of trading their poor or false beliefs for knowledge.

Dialectics usually start with a question. An interlocuter offers an answer to the question, which is then scrutinized by all participants. Reasons against the answer are given, and someone may offer a counterexample to the answer—that is, a case that illustrates that the answer is wrong. The interlocuters will then analyze why the answer is wrong and try to locate its weakness. The interlocuters may also examine what made the answer plausible in the first place. Next, someone offers another answer to the question—possibly a refined version of the previous answer that has been adjusted in light of the weaknesses and strengths identified in the analysis. This process is repeated over and over, with each iteration theoretically bringing participants closer to the truth.

While dialectics aims at the truth, the creation of knowledge is not its sole function. For example, a long, deep conversation with a friend about the meaning of life should not be viewed as a failure if you do not come up with a satisfactory answer to life’s purpose. In this instance, the process has as much value as the aim (getting closer to the truth). Contemporary academic philosophers view their practice in the same way.

Indian Dialectics and Debate

Dialectics played an important role in early Indian philosophy. The earliest known philosophical writings originate in India as sections of the Vedas, which have been dated as far back as 1500 BCE (Mark 2020). The Vedas are often considered religious texts, but it is more accurate to think of them as religious and philosophical texts since they explore what it means to be a human being, discuss the purpose and function of the mind, and attempt to identify the goal of life. The Upanishads, which are the most philosophical of the Vedic texts, often take the form of dialogues. These dialogues generally occur between two participants—one who knows a truth and the other who seeks to know and understand the truth. The Vedic dialectics explore fundamental concepts such as Brahman (the One without a second, which includes the universe as its manifestation), dharma (an individual’s purpose and duty), and atman (an individual’s higher self). As in many dialectics, questioning, reasoning, and realizations that arise through the dialogue are the aim of these texts.

Buddhist philosophical texts that were part of early Indian philosophy also contain narrative dialogues (Gillon 2021). Logical argumentation is evident in these, and as time progressed, texts became more focused on argument, particularly those relying on analogical reasoning, or the use of analogies. Analogies use an object that is known to draw inferences about other similar objects. Over time, the analogical arguments used in Buddhist texts took on structure . When arguments have structure, they rely on a form that captures a specific manner of reasoning, such that the reasoning can be schematized. As an example, consider the following argument that appears in the Caraka-saṃhitā (CS 3.8.31) (Gillon 2021). The argument has been slightly altered to aid in understanding.

Soul Analogical Argument

• The soul is eternal.
• Space is eternal and it is unproduced.
• Therefore, the soul is eternal because it is unproduced.

Analogical Argument Form

• X has property P.
• Y has property P and property S.
• Therefore, X has property S because it has property P

As you will see later in the section on deductive argumentation, relying on argumentative structure is a feature of logical reasoning.

Classical Indian philosophical texts also refer to the occurrence of reasoned public debates. Public debate was a further method of rational inquiry and likely the main mode of rational inquiry that most people had access to. One mode of debate took the form of assemblies in which experts considered specific topics, including those in politics and law (Gillon 2021). Arguments are the public expression of private inferences, and only by exposing one’s private thoughts through argument can they be tested. Public arguments are a method to improve one’s reasoning when it is scrutinized by others.

Greek Dialectics and Debate

Ancient Greek philosophy is also known for its use of dialectic and debate. Socrates, perhaps the most famous ancient Greek philosopher, claimed that knowledge is true opinion backed by argument (Plato, Meno ). “Opinion” here means unjustified belief: your beliefs could be true, but they cannot count as knowledge unless you have reasons for them and can offer justifications for your beliefs when questioned by others. Furthermore, Socrates’s method of gaining knowledge was to engage in dialectics with others. All of what we know about Socrates is through the writings of others—particularly the writings of Plato. Quite appropriately, Plato uses dialogues in all his works, in which Socrates is almost always a participant.

Socrates never wrote anything down. In the Phaedrus , one of Plato’s dialogues, Socrates criticizes written works as being a dead discourse of sorts. Books cannot respond to you when you ask questions. He states, “You’d think they were speaking as if they had some understanding, but if you question anything that has been said because you want to learn more, it continues to signify just the very same thing forever” ( Phaedrus , 275e). Clearly, dialectics was central to Socrates’s philosophical method.

CONNECTIONS

Learn more about Socrates in the introduction to philosophy chapter .

Plato’s dialogues are a testament to the importance of public discourse as a form of rational inquiry in ancient Greece. Based on Greek philosophical writings, we can assume reasoned public debate took place and that Socrates preferred it as a method of teaching and learning. In Plato’s dialogues, many questions are asked, and Socrates’s interlocuters offer answers to which Socrates asks further clarifying questions. Through the process of questioning, false beliefs and inadequate understanding are exposed. Socrates’s goal was not simply to offer people truth. Rather, through questioning, Socrates guides people to discover the truth on their own, provided they are willing to keep an open mind and admit, when necessary, that they are in the wrong. In Plato’s dialogues, participants don’t always land on a determinate answer, but they as well as readers are always left with a clearer understanding of the correct way to reason .

If any ancient Greek philosopher most embodies the tie between dialectic and logic, it is Aristotle (c. 384–322 BCE), who was a student of Plato. Aristotle wrote books on the art of dialectic (Smith 2020). And he probably participated in gymnastic dialectic—a structured dialectic contest practiced in the Academy (the school founded by Plato, which Aristotle attended). But more importantly, Aristotle created a complex system of logic upon which skill in the art of dialectic relied. Aristotle’s logic is the earliest formal systematized account of inference we know of and was considered the most accurate and complete system until the late 19th century (Smith 2020). Aristotle’s system is taught in logic classes to this day.

The Use of Reason to Discover Truth

Reasoning allows us to hypothesize, work out consequences of our hypotheses, run thought experiments, assess the coherence of a set of beliefs, and generate plausible explanations of the world around us. As Chapter 1 explained, coherence is the property of consistency in a set of beliefs. Thus, when a set of beliefs is inconsistent, it is not possible for every belief in the set to be true. We must use reason to determine whether a set of beliefs is consistent and work out the logical implications of beliefs, given their truth. In this way, reason can be used to discover truth.

The rules of logic are like the rules of math; you cannot make 1 + 1 = 3. Indeed, math is a form of deductive reasoning that ensures truth. Answers to problems in math are derived using known functions and rules, which is also true in logic. Unlike math, however, not all of logic can guarantee correct answers. Nonetheless, logic supplies means by which to derive better answers—answers that are more likely to be true. Because logic is the study of proper reasoning, and proper reasoning is an essential tool for discovering truth, logic is foundational to the pursuit of learning.

Testing Hypotheses

A hypothesis is a proposed explanation for an observed process or phenomenon. Human beings formulate hypotheses because they wish to answer specific questions about the world. Usually, the sciences come to mind when we think of the word “hypothesis.” However, hypotheses can be created on many subjects, and chances are that you have created many hypotheses without realizing it. For example, if you often come home and find that one of your outside potted plants has been knocked over, you might hypothesize that “the wind must have knocked that one over.” In doing so, you answer the question, “Why is that plant often knocked over?” Generating and testing hypotheses engages different forms of reasoning— abduction, induction, and deduction—all of which will be explained in further detail below.

Clearly, simply coming up with a hypothesis isn’t enough for us to gain knowledge; rather, we must use logic to test the truth of our supposition. Of course, the aim of testing hypotheses is to get to the truth. In testing we often formulate if–then statements: “If it is windy, then my plant will get knocked over” or “If nitrogen levels are high in the river, then algae will grow.” If–then statements in logic are called conditionals and are testable. For example, we can keep a log registering the windy days, cross-checked against the days on which the plant was found knocked over, to test our if–then hypothesis.

Reasoning is also used to assess the evidence collected for testing and to determine whether the test itself is good enough for drawing a reliable conclusion. In the example above, if on no windy days is the plant knocked over, logic demands that the hypothesis be rejected. If the plant is sometimes knocked over on windy days, then the hypothesis needs refinement (for example, wind direction or wind speed might be a factor in when the plant goes down). Notice that logic and reasoning play a role in every step of the process: creating hypotheses, figuring out how to test them, compiling data, analyzing results, and drawing a conclusion.

We’ve been looking at an inconsequential example—porch plants. But testing hypotheses is serious business in many fields, such as when pharmaceutical companies test the efficacy of a drug in treating a life-threatening illness. Good reasoning requires researchers to gather enough data to compare an experimental group and control group (patients with the illness who received the drug and those who did not). If scientists find a statistically significant difference in positive outcomes for the experimental group when compared to the control group, they can draw the reasonable conclusion that the drug could alleviate illness or even save lives in the future.

Laws of Logic

Logic, like the sciences, has laws. But while the laws of science are meant to accurately describe observed regularities in the natural world, laws of logic can be thought of as rules of thought. Logical laws are rules that underlie thinking itself. Some might even argue that it is only by virtue of these laws that we can have reliable thoughts. To that extent, laws of logic are construed to be laws of reality itself. To see what is meant by this, let’s consider the law of noncontradiction .

Noncontradiction

To understand the law of noncontradiction, we must first define a few terms. First, a statement is a sentence with truth value, meaning that the statement must be true or false. Statements are declarative sentences like “Hawaii is the 50th state to have entered the United States” and “You are reading an online philosophy book.” Sometimes philosophers use the term “proposition” instead of “statement,” and the latter term has a slightly different meaning. But for our purposes, we will use these terms as synonyms. Second, a negation of a statement is the denial of that statement. The easiest way to turn a statement into its negation is to add the qualifier “not.” For example, the negation of “My dog is on her bed” is “My dog is not on her bed.” Third, a contradiction is the conjunction of any statement and its negation. We may also say that any statement and its opposite are contradictory . For example, “My dog is on her bed” and “My dog is not on her bed” are contradictory because the second is the negation of the first. And when you combine a statement and its opposite, you get a contradiction: “My dog is on her bed and my dog is not on her bed.”

The law of noncontradiction is a law about truth, stating that contradictory propositions cannot be true in the same sense, at the same time . While my dog may have been on her bed earlier and now she’s off barking at squirrels, it cannot be true right now that my dog is both on her bed and not on her bed. However, some of you may be thinking about dogs who lie half on their beds and half on the floor (Josie, the dog belonging to the author of this chapter, is one of them). Can it not be true that such a dog is both on and not on their bed? In this instance, we must return to the phrase in the same sense . If we decide that “lying on the bed” means “at least 50% of your body is on the bed,” then we must maintain that definition when looking at propositions to determine whether they are contradictory. Thus, if Josie is half out of the bed with her head on the floor, we can still say “Josie is on the bed.” But notice that “Josie is not on the bed” remains false since we have qualified the meaning of “on the bed.”

For Aristotle, the law of noncontradiction is so fundamental that he claims that without it, knowledge would not be possible—the law is foundational for the sciences, reasoning, and language (Gottlieb 2019). Aristotle thought that the law of noncontradiction was “the most certain of all principles” because it is impossible for someone to believe that the same thing both is and is not (1989, 1005b).

The Excluded Middle

The law of the excluded middle is related to the law of noncontradiction. The law of the excluded middle states that for any statement, either that statement is true, or its negation is true. If you accept that all statements must be either true or false and you also accept the law of noncontradiction, then you must accept the law of the excluded middle. If the only available options for truth-bearing statements are that they are true or false, and if a statement and its negation cannot both be true at the same time, then one of the statements must be true while the other must be false. Either my dog is on her bed or off her bed right now .

Normativity in Logic

What if Lulu claims that she is 5 feet tall and that she is 7 feet tall? You’d think that she was joking or not being literal because this is tantamount to saying that she is both 5 feet tall and not 5 feet tall (which is implied by being 7 feet tall). The statement “I’m 5 feet tall and not 5 feet tall” is a contradiction. Surely Lulu does not believe a contradiction. We might even think, as Aristotle did, that it is impossible to believe a contradiction. But even if Lulu could believe a contradiction, we think that she should not . Since we generally believe that inconsistency in reasoning is something that ought to be avoided , we can say that logic is normative. Normativity is the assumption that certain actions, beliefs, or other mental states are good and ought to be pursued or realized. Normativity implies a standard (a norm) to which we ought to conform. Ethics is a normative discipline because it is the study of how we ought to act. And because we believe people ought to be logical rather than illogical, we label logic as normative.

While ethics is normative in the realm of actions and behavior, logic is normative in the realm of reasoning. Some rules of thought, like the law of noncontradiction, seem to be imperative (a command), so logic is a command of reasoning. Some philosophers argue that logic is what makes reasoning possible (MacFarlane 2002). In their view, logic is a constitutive norm of reasoning—that is, logic constitutes what reasoning is . Without norms of logic, there would be no reasoning. This view is intuitively plausible: What if your thoughts proceeded one after the other, with no connection (or ability to detect a connection) between them? Without logic, you would be unable to even categorize thoughts or reliably attach concepts to the contents of thoughts. Let’s take a closer look at how philosophers use special logical statements to organize their reasoning.

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• Authors: Nathan Smith
• Publisher/website: OpenStax
• Book title: Introduction to Philosophy
• Publication date: Jun 15, 2022
• Location: Houston, Texas
• Book URL: https://openstax.org/books/introduction-philosophy/pages/1-introduction
• Section URL: https://openstax.org/books/introduction-philosophy/pages/5-key-terms

© Dec 19, 2023 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.