philosophy of logic and critical reasoning

Internet Encyclopedia of Philosophy

Critical thinking.

Critical Thinking is the process of using and assessing reasons to evaluate statements, assumptions, and arguments in ordinary situations. The goal of this process is to help us have good beliefs, where “good” means that our beliefs meet certain goals of thought, such as truth, usefulness, or rationality. Critical thinking is widely regarded as a species of informal logic, although critical thinking makes use of some formal methods. In contrast with formal reasoning processes that are largely restricted to deductive methods—decision theory, logic, statistics—the process of critical thinking allows a wide range of reasoning methods, including formal and informal logic, linguistic analysis, experimental methods of the sciences, historical and textual methods, and philosophical methods, such as Socratic questioning and reasoning by counterexample.

The goals of critical thinking are also more diverse than those of formal reasoning systems. While formal methods focus on deductive validity and truth, critical thinkers may evaluate a statement’s truth, its usefulness, its religious value, its aesthetic value, or its rhetorical value. Because critical thinking arose primarily from the Anglo-American philosophical tradition (also known as “analytic philosophy”), contemporary critical thinking is largely concerned with a statement’s truth. But some thinkers, such as Aristotle (in Rhetoric ), give substantial attention to rhetorical value.

The primary subject matter of critical thinking is the proper use and goals of a range of reasoning methods, how they are applied in a variety of social contexts, and errors in reasoning. This article also discusses the scope and virtues of critical thinking.

Critical thinking should not be confused with Critical Theory. Critical Theory refers to a way of doing philosophy that involves a moral critique of culture. A “critical” theory, in this sense, is a theory that attempts to disprove or discredit a widely held or influential idea or way of thinking in society. Thus, critical race theorists and critical gender theorists offer critiques of traditional views and latent assumptions about race and gender. Critical theorists may use critical thinking methodology, but their subject matter is distinct, and they also may offer critical analyses of critical thinking itself.

Table of Contents

The process of evaluating a statement traditionally begins with making sure we understand it; that is, a statement must express a clear meaning. A statement is generally regarded as clear if it expresses a proposition , which is the meaning the author of that statement intends to express, including definitions, referents of terms, and indexicals, such as subject, context, and time. There is significant controversy over what sort of “entity” propositions are, whether abstract objects or linguistic constructions or something else entirely. Whatever its metaphysical status, it is used here simply to refer to whatever meaning a speaker intends to convey in a statement.

The difficulty with identifying intended propositions is that we typically speak and think in natural languages (English, Swedish, French), and natural languages can be misleading. For instance, two different sentences in the same natural language may express the same proposition, as in these two English sentences:

Jamie is taller than his father. Jamie’s father is shorter than he.

Further, the same sentence in a natural language can express more than one proposition depending on who utters it at a time:

I am shorter than my father right now.

The pronoun “I” is an indexical; it picks out, or “indexes,” whoever utters the sentence and, therefore, expresses a different proposition for each new speaker who utters it. Similarly, “right now” is a temporal indexical; it indexes the time the sentence is uttered. The proposition it is used to express changes each new time the sentence is uttered and, therefore, may have a different truth value at different times (as, say, the speaker grows taller: “I am now five feet tall” may be true today, but false a year from now). Other indexical terms that can affect the meaning of the sentence include other pronouns (he, she, it) and definite articles (that, the).

Further still, different sentences in different natural languages may express the same proposition . For example, all of the following express the proposition “Snow is white”:

Snow is white. (English)

Der Schnee ist weiss. (German)

La neige est blanche. (French)

La neve é bianca. (Italian)

Finally, statements in natural languages are often vague or ambiguous , either of which can obscure the propositions actually intended by their authors. And even in cases where they are not vague or ambiguous, statements’ truth values sometimes vary from context to context. Consider the following example.

The English statement, “It is heavy,” includes the pronoun “it,” which (when used without contextual clues) is ambiguous because it can index any impersonal subject. If, in this case, “it” refers to the computer on which you are reading this right now, its author intends to express the proposition, “The computer on which you are reading this right now is heavy.” Further, the term “heavy” reflects an unspecified standard of heaviness (again, if contextual clues are absent). Assuming we are talking about the computer, it may be heavy relative to other computer models but not to automobiles. Further still, even if we identify or invoke a standard of heaviness by which to evaluate the appropriateness of its use in this context, there may be no weight at which an object is rightly regarded as heavy according to that standard. (For instance, is an object heavy because it weighs 5.3 pounds but not if it weighs 5.2 pounds? Or is it heavy when it is heavier than a mouse but lighter than an anvil?) This means “heavy” is a vague term. In order to construct a precise statement, vague terms (heavy, cold, tall) must often be replaced with terms expressing an objective standard (pounds, temperature, feet).

Part of the challenge of critical thinking is to clearly identify the propositions (meanings) intended by those making statements so we can effectively reason about them. The rules of language help us identify when a term or statement is ambiguous or vague, but they cannot, by themselves, help us resolve ambiguity or vagueness. In many cases, this requires assessing the context in which the statement is made or asking the author what she intends by the terms. If we cannot discern the meaning from the context and we cannot ask the author, we may stipulate a meaning, but this requires charity, to stipulate a plausible meaning, and humility, to admit when we discover that our stipulation is likely mistaken.

2. Argument and Evaluation

Once we are satisfied that a statement is clear, we can begin evaluating it. A statement can be evaluated according to a variety of standards. Commonly, statements are evaluated for truth, usefulness, or rationality. The most common of these goals is truth, so that is the focus of this article.

The truth of a statement is most commonly evaluated in terms of its relation to other statements and direct experiences. If a statement follows from or can be inferred from other statements that we already have good reasons to believe, then we have a reason to believe that statement. For instance, the statement “The ball is blue” can be derived from “The ball is blue and round.” Similarly, if a statement seems true in light of, or is implied by, an experience, then we have a reason to believe that statement. For instance, the experience of seeing a red car is a reason to believe, “The car is red.” (Whether these reasons are good enough for us to believe is a further question about justification , which is beyond the scope of this article, but see “ Epistemic Justification .”) Any statement we derive in these ways is called a conclusion . Though we regularly form conclusions from other statements and experiences—often without thinking about it—there is still a question of whether these conclusions are true: Did we draw those conclusions well? A common way to evaluate the truth of a statement is to identify those statements and experiences that support our conclusions and organize them into structures called arguments . (See also, “ Argument .”)

An argument is one or more statements (called premises ) intended to support the truth of another statement (the conclusion ). Premises comprise the evidence offered in favor of the truth of a conclusion. It is important to entertain any premises that are intended to support a conclusion, even if the attempt is unsuccessful. Unsuccessful attempts at supporting a proposition constitute bad arguments, but they are still arguments. The support intended for the conclusion may be formal or informal. In a formal, or deductive, argument, an arguer intends to construct an argument such that, if the premises are true, the conclusion must be true. This strong relationship between premises and conclusion is called validity . This relationship between the premises and conclusion is called “formal” because it is determined by the form (that is, the structure) of the argument (see §3). In an informal, or inductive , argument, the conclusion may be false even if the premises are true. In other words, whether an inductive argument is good depends on something more than the form of the argument. Therefore, all inductive arguments are invalid, but this does not mean they are bad arguments. Even if an argument is invalid, its premises can increase the probability that its conclusion is true. So, the form of inductive arguments is evaluated in terms of the strength the premises confer on the conclusion, and stronger inductive arguments are preferred to weaker ones (see §4). (See also, “ Deductive and Inductive Arguments .”)

Psychological states, such as sensations, memories, introspections, and intuitions often constitute evidence for statements. Although these states are not themselves statements, they can be expressed as statements. And when they are, they can be used in and evaluated by arguments. For instance, my seeing a red wall is evidence for me that, “There is a red wall,” but the physiological process of seeing is not a statement. Nevertheless, the experience of seeing a red wall can be expressed as the proposition, “I see a red wall” and can be included in an argument such as the following:

This is an inductive argument, though not a strong one. We do not yet know whether seeing something (under these circumstances) is reliable evidence for the existence of what I am seeing. Perhaps I am “seeing” in a dream, in which case my seeing is not good evidence that there is a wall. For similar reasons, there is also reason to doubt whether I am actually seeing. To be cautious, we might say we seem to see a red wall.

To be good , an argument must meet two conditions: the conclusion must follow from the premises—either validly or with a high degree of likelihood—and the premises must be true. If the premises are true and the conclusion follows validly, the argument is sound . If the premises are true and the premises make the conclusion probable (either objectively or relative to alternative conclusions), the argument is cogent .

Here are two examples:

In example 1, the premises are true. And since “larger than” is a transitive relation, the structure of the argument guarantees that, if the premises are true, the conclusion must be true. This means the argument is also valid. Since it is both valid and has true premises, this deductive argument is sound.

  Example 2:

In example 2, premise 1 is true, and let us assume premise 2 is true. The phrase “almost always” indicates that a majority of days in Montana are sunny, so that, for any day you choose, it will probably be a sunny day. Premise 2 says I am choosing days in February to visit. Together, these premises strongly support (though they do not guarantee) the conclusion that it will be sunny when I am there, and so this inductive argument is cogent.

In some cases, arguments will be missing some important piece, whether a premise or a conclusion. For instance, imagine someone says, “Well, she asked you to go, so you have to go.” The idea that you have to go does not follow logically from the fact that she asked you to go without more information. What is it about her asking you to go that implies you have to go? Arguments missing important information are called enthymemes . A crucial part of critical thinking is identifying missing or assumed information in order to effectively evaluate an argument. In this example, the missing premise might be that, “She is your boss, and you have to do what she asks you to do.” Or it might be that, “She is the woman you are interested in dating, and if you want a real chance at dating her, you must do what she asks.” Before we can evaluate whether her asking implies that you have to go, we need to know this missing bit of information. And without that missing bit of information, we can simply reply, “That conclusion doesn’t follow from that premise.”

The two categories of reasoning associated with soundness and cogency—formal and informal, respectively—are considered, by some, to be the only two types of argument. Others add a third category, called abductive reasoning, according to which one reasons according to the rules of explanation rather than the rules of inference . Those who do not regard abductive reasoning as a third, distinct category typically regard it as a species of informal reasoning. Although abductive reasoning has unique features, here it is treated, for reasons explained in §4d, as a species of informal reasoning, but little hangs on this characterization for the purposes of this article.

3. Formal Reasoning

Although critical thinking is widely regarded as a type of informal reasoning, it nevertheless makes substantial use of formal reasoning strategies. Formal reasoning is deductive , which means an arguer intends to infer or derive a proposition from one or more propositions on the basis of the form or structure exhibited by the premises. Valid argument forms guarantee that particular propositions can be derived from them. Some forms look like they make such guarantees but fail to do so (we identify these as formal fallacies in §5a). If an arguer intends or supposes that a premise or set of premises guarantee a particular conclusion, we may evaluate that argument form as deductive even if the form fails to guarantee the conclusion, and is thus discovered to be invalid.

Before continuing in this section, it is important to note that, while formal reasoning provides a set of strict rules for drawing valid inferences, it cannot help us determine the truth of many of our original premises or our starting assumptions. And in fact, very little critical thinking that occurs in our daily lives (unless you are a philosopher, engineer, computer programmer, or statistician) involves formal reasoning. When we make decisions about whether to board an airplane, whether to move in with our significant others, whether to vote for a particular candidate, whether it is worth it to drive ten miles faster the speed limit even if I am fairly sure I will not get a ticket, whether it is worth it to cheat on a diet, or whether we should take a job overseas, we are reasoning informally. We are reasoning with imperfect information (I do not know much about my flight crew or the airplane’s history), with incomplete information (no one knows what the future is like), and with a number of built-in biases, some conscious (I really like my significant other right now), others unconscious (I have never gotten a ticket before, so I probably will not get one this time). Readers who are more interested in these informal contexts may want to skip to §4.

An argument form is a template that includes variables that can be replaced with sentences. Consider the following form (found within the formal system known as sentential logic ):

This form was named modus ponens (Latin, “method of putting”) by medieval philosophers. p and q are variables that can be replaced with any proposition, however simple or complex. And as long as the variables are replaced consistently (that is, each instance of p is replaced with the same sentence and the same for q ), the conclusion (line 3), q , follows from these premises. To be more precise, the inference from the premises to the conclusion is valid . “Validity” describes a particular relationship between the premises and the conclusion, namely: in all cases , the conclusion follows necessarily from the premises, or, to use more technical language, the premises logically guarantee an instance of the conclusion.

Notice we have said nothing yet about truth . As critical thinkers, we are interested, primarily, in evaluating the truth of sentences that express propositions, but all we have discussed so far is a type of relationship between premises and conclusion (validity). This formal relationship is analogous to grammar in natural languages and is known in both fields as syntax . A sentence is grammatically correct if its syntax is appropriate for that language (in English, for example, a grammatically correct simple sentence has a subject and a predicate—“He runs.” “Laura is Chairperson.”—and it is grammatically correct regardless of what subject or predicate is used—“Jupiter sings.”—and regardless of whether the terms are meaningful—“Geflorble rowdies.”). Whether a sentence is meaningful, and therefore, whether it can be true or false, depends on its semantics , which refers to the meaning of individual terms (subjects and predicates) and the meaning that emerges from particular orderings of terms. Some terms are meaningless—geflorble; rowdies—and some orderings are meaningless even though their terms are meaningful—“Quadruplicity drinks procrastination,” and “Colorless green ideas sleep furiously.”.

Despite the ways that syntax and semantics come apart, if sentences are meaningful, then syntactic relationships between premises and conclusions allow reasoners to infer truth values for conclusions. Because of this, a more common definition of validity is this: it is not possible for all the premises to be true and the conclusion false . Formal logical systems in which syntax allows us to infer semantic values are called truth-functional or truth-preserving —proper syntax preserves truth throughout inferences.

The point of this is to note that formal reasoning only tells us what is true if we already know our premises are true. It cannot tell us whether our experiences are reliable or whether scientific experiments tell us what they seem to tell us. Logic can be used to help us determine whether a statement is true, but only if we already know some true things. This is why a broad conception of critical thinking is so important: we need many different tools to evaluate whether our beliefs are any good.

Consider, again, the form modus ponens , and replace p with “It is a cat” and q with “It is a mammal”:

In this case, we seem to “see” (in a metaphorical sense of see ) that the premises guarantee the truth of the conclusion. On reflection, it is also clear that the premises might not be true; for instance, if “it” picks out a rock instead of a cat, premise 1 is still true, but premise 2 is false. It is also possible for the conclusion to be true when the premises are false. For instance, if the “it” picks out a dog instead of a cat, the conclusion “It is a mammal” is true. But in that case, the premises do not guarantee that conclusion; they do not constitute a reason to believe the conclusion is true.

Summing up, an argument is valid if its premises logically guarantee an instance of its conclusion (syntactically), or if it is not possible for its premises to be true and its conclusion false (semantically). Logic is truth-preserving but not truth-detecting; we still need evidence that our premises are true to use logic effectively.

            A Brief Technical Point

Some readers might find it worth noting that the semantic definition of validity has two counterintuitive consequences. First, it implies that any argument with a necessarily true conclusion is valid. Notice that the condition is phrased hypothetically: if the premises are true, then the conclusion cannot be false. This condition is met if the conclusion cannot be false:

This is because the hypothetical (or “conditional”) statement would still be true even if the premises were false:

It is true of this argument that if the premises were true, the conclusion would be since the conclusion is true no matter what.

Second, the semantic formulation also implies that any argument with necessarily false premises is valid. The semantic condition for validity is met if the premises cannot be true:

In this case, if the premise were true, the conclusion could not be false (this is because anything follows syntactically from a contradiction), and therefore, the argument is valid. There is nothing particularly problematic about these two consequences. But they highlight unexpected implications of our standard formulations of validity, and they show why there is more to good arguments than validity.

Despite these counterintuitive implications, valid reasoning is essential to thinking critically because it is a truth-preserving strategy: if deductive reasoning is applied to true premises, true conclusions will result.

There are a number of types of formal reasoning, but here we review only some of the most common: categorical logic, propositional logic, modal logic, and predicate logic.

a. Categorical Logic

Categorical logic is formal reasoning about categories or collections of subjects, where subjects refers to anything that can be regarded as a member of a class, whether objects, properties, or events or even a single object, property, or event. Categorical logic employs the quantifiers “all,” “some,” and “none” to refer to the members of categories, and categorical propositions are formulated in four ways:

A claims: All As are Bs (where the capitals “A” and “B” represent categories of subjects).

E claims: No As are Bs.

I claims: Some As are Bs.

O claims: Some As are not Bs.

Categorical syllogisms are syllogisms (two-premised formal arguments) that employ categorical propositions. Here are two examples:

There are interesting limitations on what categorical logic can do. For instance, if one premise says that, “Some As are not Bs,” may we infer that some As are Bs, in what is known as an “existential assumption”? Aristotle seemed to think so ( De Interpretatione ), but this cannot be decided within the rules of the system. Further, and counterintuitively, it would mean that a proposition such as, “Some bachelors are not married,” is false since it implies that some bachelors are married.

Another limitation on categorical logic is that arguments with more than three categories cannot be easily evaluated for validity. The standard method for evaluating the validity of categorical syllogisms is the Venn diagram (named after John Venn, who introduced it in 1881), which expresses categorical propositions in terms of two overlapping circles and categorical arguments in terms of three overlapping circles, each circle representing a category of subjects.

Venn diagram for claim and Venn diagram for argument

A, B, and C represent categories of objects, properties, or events. The symbol “ ∩ ” comes from mathematical set theory to indicate “intersects with.” “A∩B” means all those As that are also Bs and vice versa. 

Though there are ways of constructing Venn diagrams with more than three categories, determining the validity of these arguments using Venn diagrams is very difficult (and often requires computers). These limitations led to the development of more powerful systems of formal reasoning.

b. Propositional Logic

Propositional, or sentential , logic has advantages and disadvantages relative to categorical logic. It is more powerful than categorical logic in that it is not restricted in the number of terms it can evaluate, and therefore, it is not restricted to the syllogistic form. But it is weaker than categorical logic in that it has no operators for quantifying over subjects, such as “all” or “some.” For those, we must appeal to predicate logic (see §3c below).

Basic propositional logic involves formal reasoning about propositions (as opposed to categories), and its most basic unit of evaluation is the atomic proposition . “Atom” means the smallest indivisible unit of something, and simple English statements (subject + predicate) are atomic wholes because if either part is missing, the word or words cease to be a statement, and therefore ceases to be capable of expressing a proposition. Atomic propositions are simple subject-predicate combinations, for instance, “It is a cat” and “I am a mammal.” Variable letters such as p and q in argument forms are replaced with semantically rich constants, indicated by capital letters, such as A and B . Consider modus ponens again (noting that the atomic propositions are underlined in the English argument):

As you can see from premise 1 of the Semantic Replacement, atomic propositions can be combined into more complex propositions using symbols that represent their logical relationships (such as “If…, then…”). These symbols are called “operators” or “connectives.” The five standard operators in basic propositional logic are:

These operations allow us to identify valid relations among propositions: that is, they allow us to formulate a set of rules by which we can validly infer propositions from and validly replace them with others. These rules of inference (such as modus ponens ; modus tollens ; disjunctive syllogism) and rules of replacement (such as double negation; contraposition; DeMorgan’s Law) comprise the syntax of propositional logic, guaranteeing the validity of the arguments employing them.

Two Rules of Inference:

Two Rules of Replacement:

For more, see “ Propositional Logic .”

c. Modal Logic

Standard propositional logic does not capture every type of proposition we wish to express (recall that it does not allow us to evaluate categorical quantifiers such as “all” or “some”). It also does not allow us to evaluate propositions expressed as possibly true or necessarily true, modifications that are called modal operators or modal quantifiers .

Modal logic refers to a family of formal propositional systems, the most prominent of which includes operators for necessity (□) and possibility (◊) (see §3d below for examples of other modal systems). If a proposition, p , is possibly true, ◊ p , it may or may not be true. If p is necessarily true, □ p , it must be true; it cannot be false. If p is necessarily false, either ~◊ p or □~ p , it must be false; it cannot be true.

There is a variety of modal systems, the weakest of which is called K (after Saul Kripke, who exerted important influence on the development of modal logic), and it involves only two additional rules:

Necessitation Rule:   If  A  is a theorem of  K , then so is □ A .

Distribution Axiom:  □( A ⊃ B ) ⊃ (□ A ⊃□ B ).  [If it is necessarily the case that if A, then B , then if it is necessarily the case that A, it is necessarily the case that B .]

Other systems maintain these rules and add others for increasing strength. For instance, the (S4) modal system includes axiom (4):

(4)  □ A ⊃ □□ A   [If it is necessarily the case that A, then it is necessarily necessary that A.]

An influential and intuitive way of thinking about modal concepts is the idea of “possible worlds” (see Plantinga, 1974; Lewis 1986). A world is just the set of all true propositions. The actual world is the set of all actually true propositions—everything that was true, is true, and (depending on what you believe about the future) will be true. A possible world is a way the actual world might have been. Imagine you wore green underwear today. The actual world might have been different in that way: you might have worn blue underwear. In this interpretation of modal quantifiers, there is a possible world in which you wore blue underwear instead of green underwear. And for every possibility like this, and every combination of those possibilities, there is a distinct possible world.

If a proposition is not possible, then there is no possible world in which that proposition is true. The statement, “That object is red all over and blue all over at the same time” is not true in any possible worlds. Therefore, it is not possible (~◊P), or, in other words, necessarily false (□~P). If a proposition is true in all possible worlds, it is necessarily true. For instance, the proposition, “Two plus two equal four,” is true in all possible worlds, so it is necessarily true (□P) or not possibly false (~◊~P).

All modal systems have a number of controversial implications, and there is not space to review them here. Here we need only note that modal logic is a type of formal reasoning that increases the power of propositional logic to capture more of what we attempt to express in natural languages. (For more, see “ Modal Logic: A Contemporary View .”)

d. Predicate Logic

Predicate logic, in particular, first-order predicate logic, is even more powerful than propositional logic. Whereas propositional logic treats propositions as atomic wholes, predicate logic allows reasoners to identify and refer to subjects of propositions, independently of their predicates. For instance, whereas the proposition, “Susan is witty,” would be replaced with a single upper-case letter, say “S,” in propositional logic, predicate logic would assign the subject “Susan” a lower-case letter, s, and the predicate “is witty” an upper-case letter, W, and the translation (or formula ) would be: Ws.

In addition to distinguishing subjects and predicates, first-order predicate logic allows reasoners to quantify over subjects. The quantifiers in predicate logic are “All…,” which is comparable to “All” quantifier in categorical logic and is sometimes symbolized with an upside-down A: ∀ (though it may not be symbolized at all), and “There is at least one…,” which is comparable to “Some” quantifier in categorical logic and is symbolized with a backward E: ∃. E and O claims are formed by employing the negation operator from propositional logic. In this formal system, the proposition, “Someone is witty,” for example, has the form: There is an x , such that x has the property of being witty, which is symbolized: (∃ x)(Wx). Similarly, the proposition, “Everyone is witty,” has the form: For all x, x has the property of being witty, which is symbolized (∀ x )( Wx ) or, without the ∀: ( x )( Wx ).

Predicate derivations are conducted according to the same rules of inference and replacement as propositional logic with the exception of four rules to accommodate adding and eliminating quantifiers.

Second-order predicate logic extends first-order predicate logic to allow critical thinkers to quantify over and draw inferences about subjects and predicates, including relations among subjects and predicates. In both first- and second-order logic, predicates typically take the form of properties (one-place predicates) or relations (two-place predicates), though there is no upper limit on place numbers. Second-order logic allows us to treat both as falling under quantifiers, such as e verything that is (specifically, that has the property of being) a tea cup and everything that is a bachelor is unmarried .

e. Other Formal Systems

It is worth noting here that the formal reasoning systems we have seen thus far (categorical, propositional, and predicate) all presuppose that truth is bivalent , that is, two-valued. The two values critical thinkers are most often concerned with are true and false , but any bivalent system is subject to the rules of inference and replacement of propositional logic. The most common alternative to truth values is the binary code of 1s and 0s used in computer programming. All logics that presuppose bivalence are called classical logics . In the next section, we see that not all formal systems are bivalent; there are non-classical logics . The existence of non-classical systems raises interesting philosophical questions about the nature of truth and the legitimacy of our basic rules of reasoning, but these questions are too far afield for this context. Many philosophers regard bivalent systems as legitimate for all but the most abstract and purely formal contexts. Included below is a brief description of three of the most common non-classical logics.

Tense logic , or temporal logic, is a formal modal system developed by Arthur Prior (1957, 1967, 1968) to accommodate propositional language about time. For example, in addition to standard propositional operators, tense logic includes four operators for indexing times: P “It has at some time been the case that…”; F “It will at some time be the case that…”; H “It has always been the case that…”; and G “It will always be the case that….”

Many-valued logic , or n -valued logic, is a family of formal logical systems that attempts to accommodate intuitions that suggest some propositions have values in addition to true and false. These are often motivated by intuitions that some propositions have neither of the classic truth values; their truth value is indeterminate (not just undeterminable, but neither true nor false), for example, propositions about the future such as, “There will be a sea battle tomorrow.” If the future does not yet exist, there is no fact about the future, and therefore, nothing for a proposition to express.

Fuzzy logic is a type of many-valued logic developed out of Lotfi Zadeh’s (1965) work on mathematical sets. Fuzzy logic attempts to accommodate intuitions that suggest some propositions have truth value in degrees, that is, some degree of truth between true and false. It is motivated by concerns about vagueness in reality, for example whether a certain color is red or some degree of red, or whether some temperature is hot or some degree of hotness.

Formal reasoning plays an important role in critical thinking, but not very often. There are significant limits to how we might use formal tools in our daily lives. If that is true, how do critical thinkers reason well when formal reasoning cannot help? That brings us to informal reasoning.

4. Informal Reasoning

Informal reasoning is inductive , which means that a proposition is inferred (but not derived) from one or more propositions on the basis of the strength provided by the premises (where “strength” means some degree of likelihood less than certainty or some degree of probability less than 1 but greater than 0; a proposition with 0% probability is necessarily false).

Particular premises grant strength to premises to the degree that they reflect certain relationships or structures in the world . For instance, if a particular type of event, p , is known to cause or indicate another type of event, q , then upon encountering an event of type p , we may infer that an event of type q is likely to occur. We may express this relationship among events propositionally as follows:

If the structure of the world (for instance, natural laws) makes premise 1 true, then, if premise 2 is true, we can reasonably (though not certainly) infer the conclusion.

Unlike formal reasoning, the adequacy of informal reasoning depends on how well the premises reflect relationships or structures in the world. And since we have not experienced every relationship among objects or events or every structure, we cannot infer with certainty that a particular conclusion follows from a true set of premises about these relationships or structures. We can only infer them to some degree of likelihood by determining to the best of our ability either their objective probability or their probability relative to alternative conclusions.

The objective probability of a conclusion refers to how likely, given the way the world is regardless of whether we know it , that conclusion is to be true. The epistemic probability of a conclusion refers to how likely that conclusion is to be true given what we know about the world , or more precisely, given our evidence for its objective likelihood.

Objective probabilities are determined by facts about the world and they are not truths of logic, so we often need evidence for objective probabilities. For instance, imagine you are about to draw a card from a standard playing deck of 52 cards. Given particular assumptions about the world (that this deck contains 52 cards and that one of them is the Ace of Spades), the objective likelihood that you will draw an Ace of Spades is 1/52. These assumptions allow us to calculate the objective probability of drawing an Ace of Spades regardless of whether we have ever drawn a card before. But these are assumptions about the world that are not guaranteed by logic: we have to actually count the cards, to be sure we count accurately and are not dreaming or hallucinating, and that our memory (once we have finished counting) reliably maintains our conclusions. None of these processes logically guarantees true beliefs. So, if our assumptions are correct, we know the objective probability of actually drawing an Ace of Spades in the real world. But since there is no logical guarantee that our assumptions are right, we are left only with the epistemic probability (the probability based on our evidence) of drawing that card. If our assumptions are right, then the objective probability is the same as our epistemic probability: 1/52. But even if we are right, objective and epistemic probabilities can come apart under some circumstances.

Imagine you draw a card without looking at it and lay it face down. What is the objective probability that that card is an Ace of Spades? The structure of the world has now settled the question, though you do not know the outcome. If it is an Ace of Spades, the objective probability is 1 (100%); it is the Ace of Spades. If it is not the Ace of Spades, the objective probability is 0 (0%); it is not the Ace of Spades. But what is the epistemic probability? Since you do not know any more about the world than you did before you drew the card, the epistemic probability is the same as before you drew it: 1/52.

Since much of the way the world is is hidden from us (like the card laid face down), and since it is not obvious that we perceive reality as it actually is (we do not know whether the actual coins we flip are evenly weighted or whether the actual dice we roll are unbiased), our conclusions about probabilities in the actual world are inevitably epistemic probabilities. We can certainly calculate objective probabilities about abstract objects (for instance, hypothetically fair coins and dice—and these calculations can be evaluated formally using probability theory and statistics), but as soon as we apply these calculations to the real world, we must accommodate the fact that our evidence is incomplete.

There are four well-established categories of informal reasoning: generalization, analogy, causal reasoning, and abduction.

a. Generalization

Generalization is a way of reasoning informally from instances of a type to a conclusion about the type. This commonly takes two forms: reasoning from a sample of a population to the whole population , and reasoning from past instances of an object or event to future instances of that object or event . The latter is sometimes called “enumerative induction” because it involves enumerating past instances of a type in order to draw an inference about a future instance. But this distinction is weak; both forms of generalization use past or current data to infer statements about future instances and whole current populations.

A popular instance of inductive generalization is the opinion poll: a sample of a population of people is polled with respect to some statement or belief. For instance, if we poll 57 sophomores enrolled at a particular college about their experiences of living in dorms, these 57 comprise our sample of the population of sophomores at that particular college. We want to be careful how we define our population given who is part of our sample. Not all college students are like sophomores, so it is not prudent to draw inferences about all college students from these sophomores. Similarly, sophomores at other colleges are not necessarily like sophomores at this college (it could be the difference between a liberal arts college and a research university), so it is prudent not to draw inferences about all sophomores from this sample at a particular college.

Let us say that 90% of the 57 sophomores we polled hate the showers in their dorms. From this information, we might generalize in the following way:

Is this good evidence that 90% of all sophomores at that college hate the showers in their dorms?

A generalization is typically regarded as a good argument if its sample is representative of its population. A sample is representative if it is similar in the relevant respects to its population. A perfectly representative sample would include the whole population: the sample would be identical with the population, and thus, perfectly representative. In that case, no generalization is necessary. But we rarely have the time or resources to evaluate whole populations. And so, a sample is generally regarded as representative if it is large relative to its population and unbiased .

In our example, whether our inference is good depends, in part, on how many sophomores there are. Are there 100, 2,000? If there are only 100, then our sample size seems adequate—we have polled over half the population. Is our sample unbiased? That depends on the composition of the sample. Is it comprised only of women or only of men? If this college is not co-ed, that is not a problem. But if the college is co-ed and we have sampled only women, our sample is biased against men. We have information only about female freshmen dorm experiences, and therefore, we cannot generalize about male freshmen dorm experiences.

How large is large enough? This is a difficult question to answer. A poll of 1% of your high school does not seem large enough to be representative. You should probably gather more data. Yet a poll of 1% of your whole country is practically impossible (you are not likely to ever have enough grant money to conduct that poll). But could a poll of less than 1% be acceptable? This question is not easily answered, even by experts in the field. The simple answer is: the more, the better. The more complicated answer is: it depends on how many other factors you can control for, such as bias and hidden variables (see §4c for more on experimental controls).

Similarly, we might ask what counts as an unbiased sample. An overly simple answer is: the sample is taken randomly, that is, by using a procedure that prevents consciously or unconsciously favoring one segment of the population over another (flipping a coin, drawing lottery balls). But reality is not simple. In political polls, it is important not to use a selection procedure that results in a sample with a larger number of members of one political party than another relative to their distribution in the population, even if the resulting sample is random. For example, the two most prominent parties in the U.S. are the Democratic Party and the Republican Party. If 47% of the U.S. is Republican and 53% is Democrat, an unbiased sample would have approximately 47% Republicans and 53% Democrats. But notice that simply choosing at random may not guarantee that result; it could easily occur, just by choosing randomly, that our sample has 70% Democrats and 30% Republicans (suppose our computer chose, albeit randomly, from a highly Democratic neighborhood). Therefore, we want to control for representativeness in some criteria, such as gender, age, and education. And we explicitly want to avoid controlling for the results we are interested in; if we controlled for particular answers to the questions on our poll, we would not learn anything—we would get all and only the answers we controlled for.

Difficulties determining representativeness suggest that reliable generalizations are not easy to construct. If we generalize on the basis of samples that are too small or if we cannot control for bias, we commit the informal fallacy of hasty generalization (see §5b). In order to generalize well, it seems we need a bit of machinery to guarantee representativeness. In fact, it seems we need an experiment, one of the primary tools in causal reasoning (see §4c below).

Argument from Analogy , also called analogical reasoning , is a way of reasoning informally about events or objects based on their similarities. A classic instance of reasoning by analogy occurs in archaeology, when researchers attempt to determine whether a stone object is an artifact (a human-made item) or simply a rock. By comparing the features of an unknown stone with well-known artifacts, archaeologists can infer whether a particular stone is an artifact. Other examples include identifying animals’ tracks by their similarities with pictures in a guidebook and consumer reports on the reliability of products.

To see how arguments from analogy work in detail, imagine two people who, independently of one another, want to buy a new pickup truck. Each chooses a make and model he or she likes, and let us say they decide on the same truck. They then visit a number of consumer reporting websites to read reports on trucks matching the features of the make and model they chose, for instance, the year it was built, the size of the engine (6 cyl. or 8 cyl.), the type of transmission (2WD or 4WD), the fuel mileage, and the cab size (standard, extended, crew). Now, let us say one of our prospective buyers is interested in safety —he or she wants a tough, safe vehicle that will protect against injuries in case of a crash. The other potential buyer is interested in mechanical reliability —he or she does not want to spend a lot of time and money fixing mechanical problems.

With this in mind, here is how our two buyers might reason analogically about whether to purchase the truck (with some fake report data included):

Are the features of these analogous vehicles (the ones reported on) sufficiently numerous and relevant for helping our prospective truck buyers decide whether to purchase the truck in question (the one on the lot)? Since we have some idea that the type of engine and transmission in a vehicle contribute to its mechanical reliability, Buyer 2 may have some relevant features on which to draw a reliable analogy. Fuel mileage and cab size are not obviously relevant, but engine specifications seem to be. Are these specifications numerous enough? That depends on whether anything else that we are not aware of contributes to overall reliability. Of course, if the trucks having the features we know also have all other relevant features we do not know (if there are any), then Buyer 2 may still be able to draw a reliable inference from analogy. Of course, we do not currently know this.

Alternatively, Buyer 1 seems to have very few relevant features on which to draw a reliable analogy. The features listed are not obviously related to safety. Are there safety options a buyer may choose but that are not included in the list? For example, can a buyer choose side-curtain airbags, or do such airbags come standard in this model? Does cab size contribute to overall safety? Although there are a number of similarities between the trucks, it is not obvious that we have identified features relevant to safety or whether there are enough of them. Further, reports of “feeling safe” are not equivalent to a truck actually being safe. Better evidence would be crash test data or data from actual accidents involving this truck. This information is not likely to be on a consumer reports website.

A further difficulty is that, in many cases, it is difficult to know whether many similarities are necessary if the similarities are relevant. For instance, if having lots of room for passengers is your primary concern, then any other features are relevant only insofar as they affect cab size. The features that affect cab size may be relatively small.

This example shows that arguments from analogy are difficult to formulate well. Arguments from analogy can be good arguments when critical thinkers identify a sufficient number of features of known objects that are also relevant to the feature inferred to be shared by the object in question. If a rock is shaped like a cutting tool, has marks consistent with shaping and sharpening, and has wear marks consistent with being held in a human hand, it is likely that rock is an artifact. But not all cases are as clear.

It is often difficult to determine whether the features we have identified are sufficiently numerous or relevant to our interests. To determine whether an argument from analogy is good, a person may need to identify a causal relationship between those features and the one in which she is interested (as in the case with a vehicle’s mechanical reliability). This usually takes the form of an experiment, which we explore below (§4c).

Difficulties with constructing reliable generalizations and analogies have led critical thinkers to develop sophisticated methods for controlling for the ways these arguments can go wrong. The most common way to avoid the pitfalls of these arguments is to identify the causal structures in the world that account for or underwrite successful generalizations and analogies. Causal arguments are the primary method of controlling for extraneous causal influences and identifying relevant causes. Their development and complexity warrant regarding them as a distinct form of informal reasoning.

c. Causal Reasoning

Causal arguments attempt to draw causal conclusions (that is, statements that express propositions about causes: x causes y ) from premises about relationships among events or objects. Though it is not always possible to construct a causal argument, when available, they have an advantage over other types of inductive arguments in that they can employ mechanisms (experiments) that reduce the risks involved in generalizations and analogies.

The interest in identifying causal relationships often begins with the desire to explain correlations among events (as pollen levels increase, so do allergy symptoms) or with the desire to replicate an event (building muscle, starting a fire) or to eliminate an event (polio, head trauma in football).

Correlations among events may be positive (where each event increases at roughly the same rate) or negative (where one event decreases in proportion to another’s increase). Correlations suggest a causal relationship among the events correlated.

But we must be careful; correlations are merely suggestive—other forces may be at work. Let us say the y-axis in the charts above represents the number of millionaires in the U.S. and the x-axis represents the amount of money U.S. citizens pay for healthcare each year. Without further analysis, a positive correlation between these two may lead someone to conclude that increasing wealth causes people to be more health conscious and to seek medical treatment more often. A negative correlation may lead someone to conclude that wealth makes people healthier and, therefore, that they need to seek medical care less frequently.

Unfortunately, correlations can occur without any causal structures (mere coincidence) or because of a third, as-yet-unidentified event (a cause common to both events, or “common cause”), or the causal relationship may flow in an unexpected direction (what seems like the cause is really the effect). In order to determine precisely which event (if any) is responsible for the correlation, reasoners must eliminate possible influences on the correlation by “controlling” for possible influences on the relationship (variables).

Critical thinking about causes begins by constructing hypotheses about the origins of particular events. A hypothesis is an explanation or event that would account for the event in question. For example, if the question is how to account for increased acne during adolescence, and we are not aware of the existence of hormones, we might formulate a number of hypotheses about why this happens: during adolescence, people’s diets change (parents no longer dictate their meals), so perhaps some types of food cause acne; during adolescence, people become increasingly anxious about how they appear to others, so perhaps anxiety or stress causes acne; and so on.

After we have formulated a hypothesis, we identify a test implication that will help us determine whether our hypothesis is correct. For instance, if some types of food cause acne, we might choose a particular food, say, chocolate, and say: if chocolate causes acne (hypothesis), then decreasing chocolate will decrease acne (test implication). We then conduct an experiment to see whether our test implication occurs.

Reasoning about our experiment would then look like one of the following arguments:

There are a couple of important things to note about these arguments. First, despite appearances, both are inductive arguments. The one on the left commits the formal fallacy of affirming the consequent, so, at best, the premises confer only some degree of probability on the conclusion. The argument on the right looks to be deductive (on the face of it, it has the valid form modus tollens ), but it would be inappropriate to regard it deductively. This is because we are not evaluating a logical connection between H and TI, we are evaluating a causal connection—TI might be true or false regardless of H (we might have chosen an inappropriate test implication or simply gotten lucky), and therefore, we cannot conclude with certainty that H does not causally influence TI. Therefore, “If…, then…” statements in experiments must be read as causal conditionals and not material conditionals (the term for how we used conditionals above).

Second, experiments can go wrong in many ways, so no single experiment will grant a high degree of probability to its causal conclusion. Experiments may be biased by hidden variables (causes we did not consider or detect, such as age, diet, medical history, or lifestyle), auxiliary assumptions (the theoretical assumptions by which evaluating the results may be faulty), or underdetermination (there may be a number of hypotheses consistent with those results; for example, if it is actually sugar that causes acne, then chocolate bars, ice cream, candy, and sodas would yield the same test results). Because of this, experiments either confirm or disconfirm a hypothesis; that is, they give us some reason (but not a particularly strong reason) to believe our hypothesized causes are or are not the causes of our test implications, and therefore, of our observations (see Quine and Ullian, 1978). Because of this, experiments must be conducted many times, and only after we have a number of confirming or disconfirming results can we draw a strong inductive conclusion. (For more, see “ Confirmation and Induction .”)

Experiments may be formal or informal . In formal experiments, critical thinkers exert explicit control over experimental conditions: experimenters choose participants, include or exclude certain variables, and identify or introduce hypothesized events. Test subjects are selected according to control criteria (criteria that may affect the results and, therefore, that we want to mitigate, such as age, diet, and lifestyle) and divided into control groups (groups where the hypothesized cause is absent) and experimental groups (groups where the hypothesized cause is present, either because it is introduced or selected for).

Subjects are then placed in experimental conditions. For instance, in a randomized study, the control group receives a placebo (an inert medium) whereas the experimental group receives the hypothesized cause—the putative cause is introduced, the groups are observed, and the results are recorded and compared. When a hypothesized cause is dangerous (such as smoking) or its effects potentially irreversible (for instance, post-traumatic stress disorder), the experimental design must be restricted to selecting for the hypothesized cause already present in subjects, for example, in retrospective (backward-looking) and prospective (forward-looking) studies. In all types of formal experiments, subjects are observed under exposure to the test or placebo conditions for a specified time, and results are recorded and compared.

In informal experiments, critical thinkers do not have access to sophisticated equipment or facilities and, therefore, cannot exert explicit control over experimental conditions. They are left to make considered judgments about variables. The most common informal experiments are John Stuart Mill’s five methods of inductive reasoning, called Mill’s Methods, which he first formulated in A System of Logic (1843). Here is a very brief summary of Mill’s five methods:

(1) The Method of Agreement

If all conditions containing the event y also contain x , x is probably the cause of y .

For example:

“I’ve eaten from the same box of cereal every day this week, but all the times I got sick after eating cereal were times when I added strawberries. Therefore, the strawberries must be bad.”

(2) The Method of Difference

If all conditions lacking y also lack x , x is probably the cause of y .

“The organization turned all its tax forms in on time for years, that is, until our comptroller, George, left; after that, we were always late. Only after George left were we late. Therefore, George was probably responsible for getting our tax forms in on time.”

(3) The Joint Method of Agreement and Difference

If all conditions containing event y also contain event x , and all events lacking y also lack x , x is probably the cause of y .

“The conditions at the animal shelter have been pretty regular, except we had a string of about four months last year when the dogs barked all night, every night. But at the beginning of those four months we sheltered a redbone coonhound, and the barking stopped right after a family adopted her. All the times the redbone hound wasn’t present, there was no barking. Only the time she was present was there barking. Therefore, she probably incited all the other dogs to bark.”

(4) The Method of Concomitant Variation

If the frequency of event y increases and decreases as event x increases and decreases, respectively, x is probably the cause of y .

“We can predict the amount of alcohol sales by the rate of unemployment. As unemployment rises, so do alcohol sales. As unemployment drops, so do alcohol sales. Last quarter marked the highest unemployment in three years, and our sales last quarter are the highest they had been in those three years. Therefore, unemployment probably causes people to buy alcohol.”

(5) The Method of Residues

If a number of factors x , y , and z , may be responsible for a set of events A , B , and C , and if we discover reasons for thinking that x is the cause of A and y is the cause of B , then we have reason to believe z is the cause of C .

“The people who come through this medical facility are usually starving and have malaria, and a few have polio. We are particularly interested in treating the polio. Take this patient here: she is emaciated, which is caused by starvation; and she has a fever, which is caused by malaria. But notice that her muscles are deteriorating, and her bones are sore. This suggests she also has polio.”

d. Abduction

Not all inductive reasoning is inferential. In some cases, an explanation is needed before we can even begin drawing inferences. Consider Darwin’s idea of natural selection. Natural selection is not an object, like a blood vessel or a cellular wall, and it is not, strictly speaking, a single event. It cannot be detected in individual organisms or observed in a generation of offspring. Natural selection is an explanation of biodiversity that combines the process of heritable variation and environmental pressures to account for biomorphic change over long periods of time. With this explanation in hand, we can begin to draw some inferences. For instance, we can separate members of a single species of fruit flies, allow them to reproduce for several generations, and then observe whether the offspring of the two groups can reproduce. If we discover they cannot reproduce, this is likely due to certain mutations in their body types that prevent them from procreating. And since this is something we would expect if natural selection were true, we have one piece of confirming evidence for natural selection. But how do we know the explanations we come up with are worth our time?

Coined by C. S. Peirce (1839-1914), abduction , also called retroduction, or inference to the best explanation , refers to a way of reasoning informally that provides guidelines for evaluating explanations. Rather than appealing to types of arguments (generalization, analogy, causation), the value of an explanation depends on the theoretical virtues it exemplifies. A theoretical virtue is a quality that renders an explanation more or less fitting as an account of some event. What constitutes fittingness (or “loveliness,” as Peter Lipton (2004) calls it) is controversial, but many of the virtues are intuitively compelling, and abduction is a widely accepted tool of critical thinking.

The most widely recognized theoretical virtue is probably simplicity , historically associated with William of Ockham (1288-1347) and known as Ockham’s Razor . A legend has it that Ockham was asked whether his arguments for God’s existence prove that only one God exists or whether they allow for the possibility that many gods exist. He supposedly responded, “Do not multiply entities beyond necessity.” Though this claim is not found in his writings, Ockham is now famous for advocating that we restrict our beliefs about what is true to only what is absolutely necessary for explaining what we observe.

In contemporary theoretical use, the virtue of simplicity is invoked to encourage caution in how many mechanisms we introduce to explain an event. For example, if natural selection can explain the origin of biological diversity by itself, there is no need to hypothesize both natural selection and a divine designer. But if natural selection cannot explain the origin of, say, the duck-billed platypus, then some other mechanism must be introduced. Of course, not just any mechanism will do. It would not suffice to say the duck-billed platypus is explained by natural selection plus gremlins. Just why this is the case depends on other theoretical virtues; ideally, the virtues work together to help critical thinkers decide among competing hypotheses to test. Here is a brief sketch of some other theoretical virtues or ideals:

Conservatism – a good explanation does not contradict well-established views in a field.

Independent Testability – a good explanation is successful on different occasions under similar circumstances.

Fecundity – a good explanation leads to results that make even more research possible.

Explanatory Depth – a good explanation provides details of how an event occurs.

Explanatory Breadth – a good explanation also explains other, similar events.

Though abduction is structurally distinct from other inductive arguments, it functions similarly in practice: a good explanation provides a probabilistic reason to believe a proposition. This is why it is included here as a species of inductive reasoning. It might be thought that explanations only function to help critical thinkers formulate hypotheses, and do not, strictly speaking, support propositions. But there are intuitive examples of explanations that support propositions independently of however else they may be used. For example, a critical thinker may argue that material objects exist outside our minds is a better explanation of why we perceive what we do (and therefore, a reason to believe it) than that an evil demon is deceiving me , even if there is no inductive or deductive argument sufficient for believing that the latter is false. (For more, see “ Charles Sanders Peirce: Logic .”)

5. Detecting Poor Reasoning

Our attempts at thinking critically often go wrong, whether we are formulating our own arguments or evaluating the arguments of others. Sometimes it is in our interests for our reasoning to go wrong, such as when we would prefer someone to agree with us than to discover the truth value of a proposition. Other times it is not in our interests; we are genuinely interested in the truth, but we have unwittingly made a mistake in inferring one proposition from others. Whether our errors in reasoning are intentional or unintentional, such errors are called fallacies (from the Latin, fallax, which means “deceptive”). Recognizing and avoiding fallacies helps prevent critical thinkers from forming or maintaining defective beliefs.

Fallacies occur in a number of ways. An argument’s form may seem to us valid when it is not, resulting in a formal fallacy . Alternatively, an argument’s premises may seem to support its conclusion strongly but, due to some subtlety of meaning, do not, resulting in an informal fallacy . Additionally, some of our errors may be due to unconscious reasoning processes that may have been helpful in our evolutionary history, but do not function reliably in higher order reasoning. These unconscious reasoning processes are now widely known as heuristics and biases . Each type is briefly explained below.

a. Formal Fallacies

Formal fallacies occur when the form of an argument is presumed or seems to be valid (whether intentionally or unintentionally) when it is not. Formal fallacies are usually invalid variations of valid argument forms. Consider, for example, the valid argument form modus ponens (this is one of the rules of inference mentioned in §3b):

modus ponens (valid argument form)

In modus ponens , we assume or “affirm” both the conditional and the left half of the conditional (called the antecedent ): (p à q) and p. From these, we can infer that q, the second half or consequent , is true. This a valid argument form: if the premises are true, the conclusion cannot be false.

Sometimes, however, we invert the conclusion and the second premise, affirming that the conditional, (p à q), and the right half of the conditional, q (the consequent), are true, and then inferring that the left half, p (the antecedent), is true. Note in the example below how the conclusion and second premise are switched. Switching them in this way creates a problem.

To get an intuitive sense of why “affirming the consequent” is a problem, consider this simple example:

affirming the consequent

From the fact that something is a mammal, we cannot conclude that it is a cat. It may be a dog or a mouse or a whale. The premises can be true and yet the conclusion can still be false. Therefore, this is not a valid argument form. But since it is an easy mistake to make, it is included in the set of common formal fallacies.

Here is a second example with the rule of inference called modus tollens . Modus tollens involves affirming a conditional, (p à q), and denying that conditional’s consequent: ~q. From these two premises, we can validly infer the denial of the antecedent: ~p. But if we switch the conclusion and the second premise, we get another fallacy, called denying the antecedent .

Technically, all informal reasoning is formally fallacious—all informal arguments are invalid. Nevertheless, since those who offer inductive arguments rarely presume they are valid, we do not regard them as reasoning fallaciously.

b. Informal Fallacies

Informal fallacies occur when the meaning of the terms used in the premises of an argument suggest a conclusion that does not actually follow from them (the conclusion either follows weakly or with no strength at all). Consider an example of the informal fallacy of equivocation , in which a word with two distinct meanings is used in both of its meanings:

In this case, the argument’s premises are true when the word “law” is rightly interpreted, but the conclusion does not follow because the word law has a different referent in premise 1 (political laws) than in premise 2 (a law of nature). This argument equivocates on the meaning of law and is, therefore, fallacious.

Consider, also, the informal fallacy of ad hominem , abusive, when an arguer appeals to a person’s character as a reason to reject her proposition:

“Elizabeth argues that humans do not have souls; they are simply material beings. But Elizabeth is a terrible person and often talks down to children and the elderly. Therefore, she could not be right that humans do not have souls.”

The argument might look like this:

The conclusion does not follow because whether Elizabeth is a terrible person is irrelevant to the truth of the proposition that humans do not have souls. Elizabeth’s argument for this statement is relevant, but her character is not.

Another way to evaluate this fallacy is to note that, as the argument stands, it is an enthymeme (see §2); it is missing a crucial premise, namely: If anyone is a terrible person, that person makes false statements. But this premise is clearly false. There are many ways in which one can be a terrible person, and not all of them imply that someone makes false statements. (In fact, someone could be terrible precisely because they are viciously honest.) Once we fill in the missing premise, we see the argument is not cogent because at least one premise is false.

Importantly, we face a number of informal fallacies on a daily basis, and without the ability to recognize them, their regularity can make them seem legitimate. Here are three others that only scratch the surface:

Appeal to the People: We are often encouraged to believe or do something just because everyone else does. We are encouraged to believe what our political party believes, what the people in our churches or synagogues or mosques believe, what people in our family believe, and so on. We are encouraged to buy things because they are “bestsellers” (lots of people buy them). But the fact that lots of people believe or do something is not, on its own, a reason to believe or do what they do.

Tu Quoque (You, too!): We are often discouraged from pursuing a conclusion or action if our own beliefs or actions are inconsistent with them. For instance, if someone attempts to argue that everyone should stop smoking, but that person smokes, their argument is often given less weight: “Well, you smoke! Why should everyone else quit?” But the fact that someone believes or does something inconsistent with what they advocate does not, by itself, discredit the argument. Hypocrites may have very strong arguments despite their personal inconsistencies.

Base Rate Neglect: It is easy to look at what happens after we do something or enact a policy and conclude that the act or policy caused those effects. Consider a law reducing speed limits from 75 mph to 55 mph in order to reduce highway accidents. And, in fact, in the three years after the reduction, highway accidents dropped 30%! This seems like a direct effect of the reduction. However, this is not the whole story. Imagine you looked back at the three years prior to the law and discovered that accidents had dropped 30% over that time, too. If that happened, it might not actually be the law that caused the reduction in accidents. The law did not change the trend in accident reduction. If we only look at the evidence after the law, we are neglecting the rate at which the event occurred without the law. The base rate of an event is the rate that the event occurs without the potential cause under consideration. To take another example, imagine you start taking cold medicine, and your cold goes away in a week. Did the cold medicine cause your cold to go away? That depends on how long colds normally last and when you took the medicine. In order to determine whether a potential cause had the effect you suspect, do not neglect to compare its putative effects with the effects observed without that cause.

For more on formal and informal fallacies and over 200 different types with examples, see “ Fallacies .”

c. Heuristics and Biases

In the 1960s, psychologists began to suspect there is more to human reasoning than conscious inference. Daniel Kahneman and Amos Tversky confirmed these suspicions with their discoveries that many of the standard assumptions about how humans reason in practice are unjustified. In fact, humans regularly violate these standard assumptions, the most significant for philosophers and economists being that humans are fairly good at calculating the costs and benefits of their behavior; that is, they naturally reason according to the dictates of Expected Utility Theory. Kahneman and Tversky showed that, in practice, reasoning is affected by many non-rational influences, such as the wording used to frame scenarios (framing bias) and information most vividly available to them (the availability heuristic).

Consider the difference in your belief about the likelihood of getting robbed before and after seeing a news report about a recent robbery, or the difference in your belief about whether you will be bitten by a shark the week before and after Discovery Channel’s “Shark Week.” For most of us, we are likely to regard their likelihood as higher after we have seen these things on television than before. Objectively, they are no more or less likely to happen regardless of our seeing them on television, but we perceive they are more likely because their possibility is more vivid to us. These are examples of the availability heuristic.

Since the 1960s, experimental psychologists and economists have conducted extensive research revealing dozens of these unconscious reasoning processes, including ordering bias , the representativeness heuristic , confirmation bias , attentional bias , and the anchoring effect . The field of behavioral economics, made popular by Dan Ariely (2008; 2010; 2012) and Richard Thaler and Cass Sunstein (2009), emerged from and contributes to heuristics and biases research and applies its insights to social and economic behaviors.

Ideally, recognizing and understanding these unconscious, non-rational reasoning processes will help us mitigate their undermining influence on our reasoning abilities (Gigerenzer, 2003). However, it is unclear whether we can simply choose to overcome them or whether we have to construct mechanisms that mitigate their influence (for instance, using double-blind experiments to prevent confirmation bias).

6. The Scope and Virtues of Good Reasoning

Whether the process of critical thinking is productive for reasoners—that is, whether it actually answers the questions they are interested in answering—often depends on a number of linguistic, psychological, and social factors. We encountered some of the linguistic factors in §1. In closing, let us consider some of the psychological and social factors that affect the success of applying the tools of critical thinking.

Not all psychological and social contexts are conducive for effective critical thinking. When reasoners are depressed or sad or otherwise emotionally overwhelmed, critical thinking can often be unproductive or counterproductive. For instance, if someone’s child has just died, it would be unproductive (not to mention cruel) to press the philosophical question of why a good God would permit innocents to suffer or whether the child might possibly have a soul that could persist beyond death. Other instances need not be so extreme to make the same point: your company’s holiday party (where most people would rather remain cordial and superficial) is probably not the most productive context in which to debate the president’s domestic policy or the morality of abortion.

The process of critical thinking is primarily about detecting truth, and truth may not always be of paramount value. In some cases, comfort or usefulness may take precedence over truth. The case of the loss of a child is a case where comfort seems to take precedence over truth. Similarly, consider the case of determining what the speed limit should be on interstate highways. Imagine we are trying to decide whether it is better to allow drivers to travel at 75 mph or to restrict them to 65. To be sure, there may be no fact of the matter as to which is morally better, and there may not be any difference in the rate of interstate deaths between states that set the limit at 65 and those that set it at 75. But given the nature of the law, a decision about which speed limit to set must be made. If there is no relevant difference between setting the limit at 65 and setting it at 75, critical thinking can only tell us that , not which speed limit to set. This shows that, in some cases, concern with truth gives way to practical or preferential concerns (for example, Should I make this decision on the basis of what will make citizens happy? Should I base it on whether I will receive more campaign contributions from the business community?). All of this suggests that critical thinking is most productive in contexts where participants are already interested in truth.

b. The Principle of Charity/Humility

Critical thinking is also most productive when people in the conversation regard themselves as fallible, subject to error, misinformation, and deception. The desire to be “right” has a powerful influence on our reasoning behavior. It is so strong that our minds bias us in favor of the beliefs we already hold even in the face of disconfirming evidence (a phenomenon known as “confirmation bias”). In his famous article, “The Ethics of Belief” (1878), W. K. Clifford notes that, “We feel much happier and more secure when we think we know precisely what to do, no matter what happens, than when we have lost our way and do not know where to turn. … It is the sense of power attached to a sense of knowing that makes men desirous of believing, and afraid of doubting” (2010: 354).

Nevertheless, when we are open to the possibility that we are wrong, that is, if we are humble about our conclusions and we interpret others charitably, we have a better chance at having rational beliefs in two senses. First, if we are genuinely willing to consider evidence that we are wrong—and we demonstrate that humility—then we are more likely to listen to others when they raise arguments against our beliefs. If we are certain we are right, there would be little reason to consider contrary evidence. But if we are willing to hear it, we may discover that we really are wrong and give up faulty beliefs for more reasonable ones.

Second, if we are willing to be charitable to arguments against our beliefs, then if our beliefs are unreasonable, we have an opportunity to see the ways in which they are unreasonable. On the other hand, if our beliefs are reasonable, then we can explain more effectively just how well they stand against the criticism. This is weakly analogous to competition in certain types of sporting events, such as basketball. If you only play teams that are far inferior to your own, you do not know how good your team really is. But if you can beat a well-respected team on fair terms, any confidence you have is justified.

c. The Principle of Caution

In our excitement over good arguments, it is easy to overextend our conclusions, that is, to infer statements that are not really warranted by our evidence. From an argument for a first, uncaused cause of the universe, it is tempting to infer the existence of a sophisticated deity such as that of the Judeo-Christian tradition. From an argument for the compatibilism of the free will necessary for moral responsibility and determinism, it is tempting to infer that we are actually morally responsible for our behaviors. From an argument for negative natural rights, it is tempting to infer that no violation of a natural right is justifiable. Therefore, it is prudent to continually check our conclusions to be sure they do not include more content than our premises allow us to infer.

Of course, the principle of caution must itself be used with caution. If applied too strictly, it may lead reasoners to suspend all belief, and refrain from interacting with one another and their world. This is not, strictly speaking, problematic; ancient skeptics, such as the Pyrrhonians, advocated suspending all judgments except those about appearances in hopes of experiencing tranquility. However, at least some judgments about the long-term benefits and harms seem indispensable even for tranquility, for instance, whether we should retaliate in self-defense against an attacker or whether we should try to help a loved one who is addicted to drugs or alcohol.

d. The Expansiveness of Critical Thinking

The importance of critical thinking cannot be overstated because its relevance extends into every area of life, from politics, to science, to religion, to ethics. Not only does critical thinking help us draw inferences for ourselves, it helps us identify and evaluate the assumptions behind statements, the moral implications of statements, and the ideologies to which some statements commit us. This can be a disquieting and difficult process because it forces us to wrestle with preconceptions that might not be accurate. Nevertheless, if the process is conducted well, it can open new opportunities for dialogue, sometimes called “critical spaces,” that allow people who might otherwise disagree to find beliefs in common from which to engage in a more productive conversation.

It is this possibility of creating critical spaces that allows philosophical approaches like Critical Theory to effectively challenge the way social, political, and philosophical debates are framed. For example, if a discussion about race or gender or sexuality or gender is framed in terms that, because of the origins those terms or the way they have functioned socially, alienate or disproportionately exclude certain members of the population, then critical space is necessary for being able to evaluate that framing so that a more productive dialogue can occur (see Foresman, Fosl, and Watson, 2010, ch. 10 for more on how critical thinking and Critical Theory can be mutually supportive).

e. Productivity and the Limits of Rationality

Despite the fact that critical thinking extends into every area of life, not every important aspect of our lives is easily or productively subjected to the tools of language and logic. Thinkers who are tempted to subject everything to the cold light of reason may discover they miss some of what is deeply enjoyable about living. The psychologist Abraham Maslow writes, “I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail” (1966: 16). But it is helpful to remember that language and logic are tools, not the projects themselves. Even formal reasoning systems depend on axioms that are not provable within their own systems (consider Euclidean geometry or Peano arithmetic). We must make some decisions about what beliefs to accept and how to live our lives on the basis of considerations outside of critical thinking.

Borrowing an example from William James (1896), consider the statement, “Religion X is true.” James says that, while some people find this statement interesting, and therefore, worth thinking critically about, others may not be able to consider the truth of the statement. For any particular religious tradition, we might not know enough about it to form a belief one way or the other, and even suspending judgment may be difficult, since it is not obvious what we are suspending judgment about.

If I say to you: ‘Be a theosophist or be a Mohammedan,’ it is probably a dead option, because for you neither hypothesis is likely to be alive. But if I say: ‘Be an agnostic or be a Christian,’ it is otherwise: trained as you are, each hypothesis makes some appeal, however small, to your belief (2010: 357).

Ignoring the circularity in his definition of “dead option,” James’s point seems to be that if you know nothing about a view or what statements it entails, no amount of logic or evidence could help you form a reasonable belief about that position.

We might criticize James at this point because his conclusion seems to imply that we have no duty to investigate dead options, that is, to discover if there is anything worth considering in them. If we are concerned with truth, the simple fact that we are not familiar with a proposition does not mean it is not true or potentially significant for us. But James’s argument is subtler than this criticism suggests. Even if you came to learn about a particularly foreign religious tradition, its tenets may be so contrary to your understanding of the world that you could not entertain them as possible beliefs of yours . For instance, you know perfectly well that, if some events had been different, Hitler would not have existed: his parents might have had no children, or his parents’ parents might have had no children. You know roughly what it would mean for Hitler not to have existed and the sort of events that could have made it true that he did not exist. But how much evidence would it take to convince you that, in fact, Hitler did not exist, that is, that your belief that Hitler did exist is false ? Could there be an argument strong enough? Not obviously. Since all the information we have about Hitler unequivocally points to his existence, any arguments against that belief would have to affect a very broad range of statements; they would have to be strong enough to make us skeptical of large parts of reality.

7. Approaches to Improving Reasoning through Critical Thinking

Recall that the goal of critical thinking is not just to study what makes reasons and statements good, but to help us improve our ability to reason, that is, to improve our ability to form, hold, and discard beliefs according to whether they meet the standards of good thinking. Some ways of approaching this latter goal are more effective than others. While the classical approach focuses on technical reasoning skills, the Paul/Elder model encourages us to think in terms of critical concepts, and irrationality approaches use empirical research on instances of poor reasoning to help us improve reasoning where it is least obvious we need it and where we need it most. Which approach or combination of approaches is most effective depends, as noted above, on the context and limits of critical thinking, but also on scientific evidence of their effectiveness. Those who teach critical thinking, of all people, should be engaged with the evidence relevant to determining which approaches are most effective.

a. Classical Approaches

The classic approach to critical thinking follows roughly the structure of this article: critical thinkers attempt to interpret statements or arguments clearly and charitably, and then they apply the tools of formal and informal logic and science, while carefully attempting to avoid fallacious inferences (see Weston, 2008; Walton, 2008; Watson and Arp, 2015). This approach requires spending extensive time learning and practicing technical reasoning strategies. It presupposes that reasoning is primarily a conscious activity, and that enhancing our skills in these areas will improve our ability to reason well in ordinary situations.

There are at least two concerns about this approach. First, it is highly time intensive relative to its payoff. Learning the terminology of systems like propositional and categorical logic and the names of the fallacies, and practicing applying these tools to hypothetical cases requires significant time and energy. And it is not obvious, given the problems with heuristics and biases, whether this practice alone makes us better reasoners in ordinary contexts. Second, many of the ways we reason poorly are not consciously accessible (recall the heuristics and biases discussion in §5c). Our biases, combined with the heuristics we rely on in ordinary situations, can only be detected in experimental settings, and addressing them requires restructuring the ways in which we engage with evidence (see Thaler and Sunstein, 2009).

b. The Paul/Elder Model

Richard Paul and Linda Elder (Paul and Elder, 2006; Paul, 2012) developed an alternative to the classical approach on the assumption that critical thinking is not something that is limited to academic study or to the discipline of philosophy. On their account, critical thinking is a broad set of conceptual skills and habits aimed at a set of standards that are widely regarded as virtues of thinking: clarity, accuracy, depth, fairness, and others. They define it simply as “the art of analyzing and evaluating thinking with a view to improving it” (2006: 4). Their approach, then, is to focus on the elements of thought and intellectual virtues that help us form beliefs that meet these standards.

The Paul/Elder model is made up of three sets of concepts: elements of thought, intellectual standards, and intellectual traits. In this model, we begin by identifying the features present in every act of thought. They use “thought” to mean critical thought aimed at forming beliefs, not just any act of thinking, musing, wishing, hoping, remembering. According to the model, every act of thought involves:

These comprise the subject matter of critical thinking; that is, they are what we are evaluating when we are thinking critically. We then engage with this subject matter by subjecting them to what Paul and Elder call universal intellectual standards. These are evaluative goals we should be aiming at with our thinking:

While in classical approaches, logic is the predominant means of thinking critically, in the Paul/Elder model, it is put on equal footing with eight other standards. Finally, Paul and Elder argue that it is helpful to approach the critical thinking process with a set of intellectual traits or virtues that dispose us to using elements and standards well.

To remind us that these are virtues of thought relevant to critical thinking, they use “intellectual” to distinguish these traits from their moral counterparts (moral integrity, moral courage, and so on).

The aim is that, as we become familiar with these three sets of concepts and apply them in everyday contexts, we become better at analyzing and evaluating statements and arguments in ordinary situations.

Like the classical approach, this approach presupposes that reasoning is primarily a conscious activity, and that enhancing our skills will improve our reasoning. This means that it still lacks the ability to address the empirical evidence that many of our reasoning errors cannot be consciously detected or corrected. It differs from the classical approach in that it gives the technical tools of logic a much less prominent role and places emphasis on a broader, and perhaps more intuitive, set of conceptual tools. Learning and learning to apply these concepts still requires a great deal of time and energy, though perhaps less than learning formal and informal logic. And these concepts are easy to translate into disciplines outside philosophy. Students of history, psychology, and economics can more easily recognize the relevance of asking questions about an author’s point of view and assumptions than perhaps determining whether the author is making a deductive or inductive argument. The question, then, is whether this approach improves our ability to think better than the classical approach.

c. Other Approaches

A third approach that is becoming popular is to focus on the ways we commonly reason poorly and then attempt to correct them. This can be called the Rationality Approach , and it takes seriously the empirical evidence (§5c) that many of our errors in reasoning are not due to a lack of conscious competence with technical skills or misusing those skills, but are due to subconscious dispositions to ignore or dismiss relevant information or to rely on irrelevant information.

One way to pursue this approach is to focus on beliefs that are statistically rare or “weird.” These include beliefs of fringe groups, such as conspiracy theorists, religious extremists, paranormal psychologists, and proponents of New Age metaphysics (see Gilovich, 1992; Vaughn and Schick, 2010; Coady, 2012). If we recognize the sorts of tendencies that lead to these controversial beliefs, we might be able to recognize and avoid similar tendencies in our own reasoning about less extreme beliefs, such as beliefs about financial investing, how statistics are used to justify business decisions, and beliefs about which public policies to vote for.

Another way to pursue this approach is to focus directly on the research on error, those ordinary beliefs that psychologists and behavioral economists have discovered we reason poorly, and to explore ways of changing how we frame decisions about what to believe (see Nisbett and Ross, 1980; Gilovich, 1992; Ariely, 2008; Kahneman, 2011). For example, in one study, psychologists found that judges issue more convictions just before lunch and the end of the day than in the morning or just after lunch (Danzinger, et al., 2010). Given that dockets do not typically organize cases from less significant crimes to more significant crimes, this evidence suggests that something as irrelevant as hunger can bias judicial decisions. Even though hunger has nothing to do with the truth of a belief, knowing that it can affect how we evaluate a belief can help us avoid that effect. This study might suggest something as simple as that we should avoid being hungry when making important decisions. The more we learn ways in which our brains use irrelevant information, the better we can organize our reasoning to avoid these mistakes. For more on how decisions can be improved by restructuring our decisions, see Thaler and Sunstein, 2009.

A fourth approach is to take more seriously the role that language plays in our reasoning. Arguments involve complex patterns of expression, and we have already seen how vagueness and ambiguity can undermine good reasoning (§1). The pragma-dialectics approach (or pragma-dialectical theory) is the view that the quality of an argument is not solely or even primarily a matter of its logical structure, but is more fundamentally a matter of whether it is a form of reasonable discourse (Van Eemeren and Grootendorst, 1992). The proponents of this view contend that, “The study of argumentation should … be construed as a special branch of linguistic pragmatics in which descriptive and normative perspectives on argumentative discourse are methodically integrated” (Van Eemeren and Grootendorst, 1995: 130).

The pragma-dialectics approach is a highly technical approach that uses insights from speech act theory, H. P. Grice’s philosophy of language, and the study of discourse analysis. Its use, therefore, requires a great deal of background in philosophy and linguistics. It has an advantage over other approaches in that it highlights social and practical dimensions of arguments that other approaches largely ignore. For example, argument is often public ( external ), in that it creates an opportunity for opposition, which influences people’s motives and psychological attitudes toward their arguments. Argument is also social in that it is part of a discourse in which two or more people try to arrive at an agreement. Argument is also functional ; it aims at a resolution that can only be accommodated by addressing all the aspects of disagreement or anticipated disagreement, which can include public and social elements. Argument also has a rhetorical role ( dialectical ) in that it is aimed at actually convincing others, which may have different requirements than simply identifying the conditions under which they should be convinced.

These four approaches are not mutually exclusive. All of them presuppose, for example, the importance of inductive reasoning and scientific evidence. Their distinctions turn largely on which aspects of statements and arguments should take precedence in the critical thinking process and on what information will help us have better beliefs.

8. References and Further Reading

Author Information

Jamie Carlin Watson Email: [email protected] University of Arkansas for Medical Sciences U. S. A.

An encyclopedia of philosophy articles written by professional philosophers.

What Is Logic? What Is Critical Thinking?

Strategies and skills for critical thinking, using logic.

Logic is the science of how to evaluate arguments and reasoning. Critical thinking is a process of evaluation which uses logic to separate truth from falsehood, reasonable from unreasonable beliefs. If you want to better evaluate the various claims, ideas, and arguments you encounter, you need a better understanding of basic logic and the process of critical thinking.

These are not trivial pursuits. They are essential to making good decisions and forming sound beliefs about our world.

Who Cares About Logic?

Is learning about logic and how to properly construct arguments really important? Most people may not need such skills in their day-to-day lives, but the truth is that almost everyone will benefit from learning how to think more critically.

This does not only apply to our own beliefs, but also to all the ideas and claims that we regularly encounter. Without the right mental tools, we have little hope of reliably separating truth from falsehood.

Unskilled and Unaware

Everyone makes mistakes. Quite often, what is most important is the ability to first recognize our mistakes and then what we do about it.

Unfortunately, there are fields where the worse a person is, the less likely they are to even recognize that they have made mistakes, much less will be able to fix them. Indeed, they are actually likely to accuse those who know more of being the ones who are wrong.

Critical thinking and logic are one of these fields. Many people imagine that they are already quite good at it and thus don't believe that they need to learn more. This prevents them from ever improving.

What Is Logic?

People use words like "logic" and "logical" a lot, often without really understanding what they mean.

Strictly speaking, logic is the science or study of how to evaluate arguments and reasoning. It's not a matter of opinion, it's a science of how arguments must be formed in order to be reasonable or correct. Obviously, a better understanding is critical for helping us reason and think better. Without it, it's too easy for us to fall into error.

What Is Critical Thinking?

The term "critical thinking" is used often but it isn't always properly understood. Put simply, critical thinking means developing reliable, rational evaluations of an argument or idea.

Critical thinking is a means for separating truth from falsehood and reasonable from unreasonable beliefs. It frequently involves finding flaws in the arguments of others, but that's not all that it's about. It's not simply about criticizing ideas, it is about developing the ability to think about ideas with greater critical distance.

Agreement and Disagreement

Arguments are about disagreement - people aren't likely to argue over things they agree on. As obvious as that may be, it isn't always as obvious what, exactly, people disagree on. This is especially true for those who are caught up in the midst of a disagreement.

This is a problem because disagreements can't be resolved if those involved don't recognize what their disagreement is really about - or worse yet, actually disagree on what they disagree about. If those involved don't work that out, the only thing they'll accomplish by arguing is to create more animosity.

Propaganda and Persuasion

Propaganda is any organized, coordinated effort to convince masses of people to adopt some particular idea, belief, attitude, or viewpoint.

It's easiest to see government propaganda in the context of wartime. The label is also applicable to the efforts of corporations to buy their products, to apologists trying to get people to adopt their religion and many other situations. Understanding the nature of propaganda and how it works is critical to being able to think more critically about it.

philosophy of logic and critical reasoning

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PHIL102: Introduction to Critical Thinking and Logic

Course introduction.

The course touches upon a wide range of reasoning skills, from verbal argument analysis to formal logic, visual and statistical reasoning, scientific methodology, and creative thinking. Mastering these skills will help you become a more perceptive reader and listener, a more persuasive writer and presenter, and a more effective researcher and scientist.

The first unit introduces the terrain of critical thinking and covers the basics of meaning analysis, while the second unit provides a primer in analyzing arguments. All of the material in these first units will be built upon in subsequent units, which cover informal and formal logic, Venn diagrams, scientific reasoning, as well as strategic and creative thinking.

First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.

philosophy of logic and critical reasoning

Unit 1: Introduction and Meaning Analysis

Critical thinking is a broad classification for a diverse array of reasoning techniques. In general, critical thinking works by breaking arguments and claims down to their basic underlying structure so we can see them clearly and determine whether they are rational. The idea is to help us do a better job of understanding and evaluating what we read, what we hear, and what we ourselves write and say. In this unit, we will define the broad contours of critical thinking and learn why it is a valuable and useful object of study. We will also introduce the fundamentals of meaning analysis: the difference between literal meaning and implication, the principles of definition, how to identify when a disagreement is merely verbal, the distinction between necessary and sufficient conditions, and problems with the imprecision of ordinary language.

Completing this unit should take you approximately 5 hours.

Unit 2: Argument Analysis

Arguments are the fundamental components of all rational discourse: nearly everything we read and write, like scientific reports, newspaper columns, and personal letters, as well as most of our verbal conversations contain arguments. Picking the arguments out from the rest of our often convoluted discourse can be difficult. Once we have identified an argument, we still need to determine whether or not it is sound. Luckily, arguments obey a set of formal rules that we can use to determine whether they are good or bad.  In this unit, you will learn how to identify arguments, what makes an argument sound as opposed to unsound or merely valid, the difference between deductive and inductive reasoning, and how to map arguments to reveal their structure.

Completing this unit should take you approximately 7 hours.

Unit 3: Basic Sentential Logic

This unit introduces a topic that many students find intimidating: formal logic. Although it sounds difficult and complicated, formal, or symbolic, logic is actually a fairly straightforward way of revealing the structure of reasoning. By translating arguments into symbols, you can more readily see what is right and what is wrong with them, and you can learn how to formulate better arguments. Advanced courses in formal logic focus on using rules of inference to construct elaborate proofs. Using these techniques, you can solve many complicated problems simply by manipulating symbols on the page. In this course, however, you will only be looking at the most basic properties of a system of logic. In this unit you will learn how to turn phrases in ordinary language into well-formed formulas, draw truth-tables for formulas, and evaluate arguments using those truth-tables.

Completing this unit should take you approximately 13 hours. 

Unit 4: Venn Diagrams

In addition to using predicate logic, the limitations of sentential logic can also be overcome by using Venn diagrams to illustrate statements and arguments. Statements that include general words like "some" or "few" as well as absolute words like "every" and "all" – so-called categorical statements – lend themselves to being represented on paper as circles that may or may not overlap.

Venn diagrams are especially helpful when dealing with the logical arguments called syllogisms. Syllogisms are a special type of three-step argument with two premises and a conclusion, which involve quantifying terms. In this unit, you will learn the basic principles of Venn diagrams, how to use them to represent statements, and how to use them to evaluate arguments.

Completing this unit should take you approximately 6 hours.

Unit 5: Fallacies

Now that you have studied the necessary structure of a good argument and can represent its structure visually, you might think it would be simple to pick out bad arguments. However, identifying bad arguments can be very tricky in practice. Very often what at first appears to be ironclad reasoning turns out to contain one or more subtle errors.

Fortunately, there are a large number of easily identifiable fallacies – mistakes of reasoning – that you can learn to recognize by their structure or content. In this unit, you will learn about the nature of fallacies, look at a couple of different ways of classifying them, and spend some time dealing with the most common fallacies in detail.

Completing this unit should take you approximately 3 hours.

Unit 6: Scientific Reasoning

Unlike the syllogistic arguments you explored in the last unit, which are a form of deductive argument, scientific reasoning is empirical. This means that it depends on observation and evidence, not logical principles. Although some principles of deductive reasoning do apply in science, such as the principle of contradiction, scientific arguments are often inductive, and for this reason, science often deals in confirmation and disconfirmation.

Nonetheless, there are general guidelines about what constitutes good scientific reasoning, and scientists are trained to be critical of their own inferences as well as those of others in the scientific community. In this unit, you will investigate some standard methods of scientific reasoning, some principles of confirmation and disconfirmation, as well as some techniques for identifying and reasoning about causation.

Completing this unit should take you approximately 4 hours.

Unit 7: Strategic Reasoning and Creativity

While the majority of this course has focused on the types of reasoning that is necessary to critique and evaluate existing knowledge, or to extend our knowledge in accordance with correct procedures and rules, there remains an enormous branch of our reasoning practice that runs in the opposite direction. Strategic reasoning, problem solving, and creative thinking all rely on an ineffable component of novelty supplied by the thinker.

Despite the seemingly mystical nature of such activity, problem solving and creative thinking are best approached by following a set of tried and tested procedures, which prompt our cognitive faculties to produce new ideas and solutions by extending our existing knowledge. In this unit, you will investigate techniques for problem solving, representing complex problems visually, making decisions in risky and uncertain scenarios, and creative thinking in general.

Completing this unit should take you approximately 2 hours.

Study Guide

This study guide will help you get ready for the final exam. It discusses the key topics in each unit, walks through the learning outcomes, and lists important vocabulary terms. It is not meant to replace the course materials!

philosophy of logic and critical reasoning

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Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses.

If you come across any urgent problems, email [email protected] or post in our discussion forum .

philosophy of logic and critical reasoning

Certificate Final Exam

Take this exam if you want to earn a free Course Completion Certificate.

To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.

Once you pass this final exam, you will be awarded a free Course Completion Certificate .

philosophy of logic and critical reasoning

Saylor Direct Credit

Take this exam if you want to earn college credit for this course . This course is eligible for college credit through Saylor Academy's Saylor Direct Credit Program .

The three Saylor Direct Credit quizzes are optional, but recommended to help you prepare for the final exam. You can take them at any time and they do not require a proctor. Quiz grades will not affect your grade on the final exam.

The Saylor Direct Credit Final Exam requires a proctoring fee of $5 . To pass this course and earn a Proctor-Verified Course Certificate and official transcript , you will need to earn a grade of 70% or higher on the Saylor Direct Credit Final Exam. Your grade for this exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again a maximum of 3 times , with a 14-day waiting period between each attempt.

We are partnering with SmarterProctoring to help make the proctoring fee more affordable. We will be recording you, your screen, and the audio in your room during the exam. This is an automated proctoring service, but no decisions are automated; recordings are only viewed by our staff with the purpose of making sure it is you taking the exam and verifying any questions about exam integrity. We understand that there are challenges with learning at home - we won't invalidate your exam just because your child ran into the room!


Once you pass this final exam, you will be awarded a Credit-Recommended Course Completion Certificate and can request an official transcript .

Saylor Direct Credit Exam

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Academic tools.

Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o’clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68–69; 1933: 91–92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot’s position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69–70; 1933: 92–93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond lane from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses. As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016a) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), Black (2012), and Blair (2021).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), Bailin et al. (1999b), and Willingham (2019).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

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Success Skills

Critical thinking and logic.

Critical thinking is fundamentally a process of questioning information and data. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says. You can also question a commonly-held belief or a new idea. With critical thinking, anything and everything is subject to question and examination.

Logic’s Relationship to Critical Thinking

The word logic comes from the Ancient Greek logike , referring to the science or art of reasoning. Using logic, a person evaluates arguments and strives to distinguish between good and bad reasoning, or between truth and falsehood. Using logic, you can evaluate ideas or claims people make, make good decisions, and form sound beliefs about the world. [1]

Questions of Logic in Critical Thinking

Let’s use a simple example of applying logic to a critical-thinking situation. In this hypothetical scenario, a man has a PhD in political science, and he works as a professor at a local college. His wife works at the college, too. They have three young children in the local school system, and their family is well known in the community.

The man is now running for political office. Are his credentials and experience sufficient for entering public office? Will he be effective in the political office? Some voters might believe that his personal life and current job, on the surface, suggest he will do well in the position, and they will vote for him.

In truth, the characteristics described don’t guarantee that the man will do a good job. The information is somewhat irrelevant. What else might you want to know? How about whether the man had already held a political office and done a good job? In this case, we want to ask, How much information is adequate in order to make a decision based on logic instead of assumptions?

The following questions, presented in Figure 1, below, are ones you may apply to formulating a logical, reasoned perspective in the above scenario or any other situation:

Infographic titled "Questions a Critical Thinker Asks." From the top, text reads: What's Happening? Gather the basic information and begin to think of questions (image of two stick figures talking to each other). Why is it Important? Ask yourself why it's significant and whether or not you agree. (Image of bearded stick figure sitting on a rock.) What Don't I See? Is there anything important missing? (Image of stick figure wearing a blindfold, whistling, walking away from a sign labeled Answers.) How Do I Know? Ask yourself where the information came from and how it was constructed. (Image of stick figure in a lab coat, glasses, holding a beaker.) Who is Saying It? What's the position of the speaker and what is influencing them? (Image of stick figure reading a newspaper.) What Else? What If? What other ideas exist and are there other possibilities? (Stick figure version of Albert Einstein with a thought bubble saying "If only time were relative...".

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philosophy of logic and critical reasoning

Logical Thinking vs Critical Thinking: Comparing and Breaking Down the Differences

the inner workings of a mind that thinks both logically and critically

Many people use the terms logical thinking and critical thinking interchangeably; however, there are subtle differences between the two. 

On the one hand, logical thinking is pretty straightforward. 

It’s a method of thinking that uses logic or analysis of information to evaluate a situation. 

Critical thinking, on the other hand, is a process that utilizes logical thinking but takes it a step further. 

To think critically is to question the face value, connect the dots, and seek the truth. 

20 Questions: Exercises in Critical Thinking

Get a Question-Based Critical Thinking Exercise—Free!

Introduce critical thinking gently & easily with thought-provoking exercises.

What Is Logical Thinking?

Logical thinking involves thinking in a disciplined manner. Everyday we come across situations where we need to determine what is going on and why. 

The process may be as simple as evaluating product information or as complex as embracing (or not) an opportunity that requires a significant life change. 

You probably don’t toss a coin in the air to make important life decisions. Instead, you analyze the facts and use reason to help you make good choices.

Let’s look at the example of a job opportunity in another state. 

It might sound like a fantastic career move, but applying a big of logical thinking before you take the leap can mean the difference between a positive outcome and one you’ll regret. 

Observing and analyzing all the facts and scenarios can help you come to a well reasoned conclusion—and that is logical thinking in a nutshell. 

What Is Critical Thinking?

Critical thinking is closely related to logical thinking. It involves the questioning of data, beliefs, and information to make a reasoned conclusion or decision. 

It’s the ability to take various ideas or pieces of information and make connections between them. 

philosophy of logic and critical reasoning

Using the example above, if you were offered a great job opportunity in another city, you still consider all the same factors previously mentioned.

However, with critical thinking, you move beyond hard facts and ask things like:

Let me put it another way by posing another question:

Do you take whatever you’re presented with and assume that it is just so? Precisely as described and portrayed?

Likewise, that new career may look good on paper, but what about the invisible factors that go beyond the facts and figures in your contract?

Seeking truthful answers to those not-so-black-and-white questions is the definition of critical thinking. 

Logical Reasoning vs Critical Thinking: The Relationship Between the Two

As touched on earlier, logical reasoning involves assessing facts to arrive at a valid conclusion.

With no assumptions being made and emotions removed from the equation, the principles of logic can be used much like you would use a math formula to solve a problem. 

There’s a clear distinction between right and wrong. 

In theory, given the same situation with the exact same information, two different people would arrive at the same conclusion.

On the other hand, critical thinking involves questioning the answers and information you get. 

For instance, you might investigate if the person providing the information has a vested interest in a particular outcome and how that influences the information provided. 

You may also ask yourself if you’re missing information or how reliable your source is. 

There’s definitely a blurred line between logical reasoning and critical thinking, but the connection is this:

Logical thought processes involve critical thinking, and using critical thinking skills involves a bit of logic.

Is Questioning and Reasoning the Same Thing?

Reasoning involves the use of both deductive and inductive processes to reach a conclusion. 

“Deductive” is just a fancy word for following a fact (or idea, statement, and so on) to its logical conclusion. 

“Inductive” reasoning provides room for one’s own experiences and observations along the pathway to a conclusion. 

In short, to reason is to use logical thinking to evaluate and determine then explain your approach to a problem.

Questioning, on the other hand, is different than—though part of—reaching a reasoned conclusion. 

Questions help you dig up more information so you can reason effectively to determine the truth of a matter. 

So essentially, questioning is just one part of reasoning. They are not one in the same. 

How to Strengthen Your Critical Thinking Skills

When a situation calls for forming your own opinion or making a decision, it’s important to know how to think as opposed to being told what to think.  

I t’s all too easy to be swayed by popular opinion. 

That being the case, it’s important to pause amid the clamor and think both logically and critically to ensure you know exactly what you believe instead of simply following the crowd. 

Doing so also equips you to make choices based on your personal values, beliefs, and goals.

You can strengthen your critical thinking skills by thinking through situations, one step at a time. 

You’ll gain knowledge as you gain real-world experience, but that database of knowledge isn’t going to serve up a solution for every problem you face. 

That’s where the ability to think critically becomes so important. 

Practice asking questions while questioning assumptions. 

(Here’s a list of fun critical thinking questions that are more lighthearted if you need help getting started.)

Pay attention to the processes you use to analyze information and reach conclusions.

Take time to break down any barriers to critical thinking that may exist.

Today, we are spoon-fed so much information on social media and the internet that thinking sometimes seems irrelevant, but oh what a dangerous path that is. 

If you don’t already, begin questioning the things you read and hear. 

Do your own research. 

Question commonly accepted facts. 

Analyze the information you receive and from whose mouth you receive it from.

Of course, not every little situation requires an in-depth analysis or use of critical thinking skills. 

Family and friends won’t appreciate being questioned about everything they say or do. 

Still, judicial use of logical thinking and critical thinking skills can help you become more informed about what is true and what is not.

If you want to help your teen sharpen those skills, check out our award-winning curriculum, Philosophy Adventure .

philosophy of logic and critical reasoning

will your children recognize truth?

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How To Think

Critical reasoning, marianne talbot tells us how to use the ultimate in transferrable skills..

My mug is sitting to my right doing nothing. This is because it believes it is at the centre of the universe, and its desire to be at the centre of the universe is stronger than any of its other desires.

I expect you’ll reject this explanation of the behaviour of my mug. Why, you might ask, should we ever think the mug is acting for reasons ?

This is a good question. A human with this belief and this desire might have a reason to sit and do nothing; but a mug?

We might, of course, say a human with this belief and desire is irrational – that their reasons are bad ones. What makes them believe they are at the centre of the universe? Why do they want to be at the centre of the universe? Why do they want this more than anything else ? Weird. But we’d have no problem believing such a person is acting for reasons ; no problem with their being rational. In fact it is this possibility that makes it possible for them to be irrational . The mug, however, isn’t irrational: it is non-rational . It doesn’t act for reasons, good or bad. Only rational things can be irrational; only things that can act for reasons can act for bad reasons.

Aristotle thought human beings were the only rational animals. Without joining this debate we can certainly say that reason is central for human beings. Without reason all our decisions would be simple reactions to experience, or to memories of experiences. Not having reason means we would never reflect on our experience; for instance, ask ourselves, ‘Well, if this is the case, and that is the case, might it be the case quite generally that if this then that ?’ But not only can we pose such questions, our capacity for reason means we can also try, by means of argument or reason-designed experiment, to answer them.

The human capacity for reason is a species characteristic. It will develop in an individual human so long as that individual develops normally. It will develop as the individual acquires a language. It is interesting, in fact, to speculate how the two capacities are linked. Would reason be possible without language? Would language be possible without reason? What do you think?

The Attempt To Describe How To Reason Well

As with any of our natural capacities, attempts have been made to develop a theory of reasoning. This theory is called logical theory . Logical theory is normative , meaning it sets standards, tells us whether we are reasoning well or badly. And as with any theory of a practical capacity, theory and practice interact: we observe practice in order to develop the theory, then we use the theory to improve the practice.

Anyone can improve their capacity to reason by learning some logic. My experience has been that a lot of people are interested in improving their ability to reason. Given the centrality of reason to human life, this isn’t surprising.

Recognising Arguments

Probably the first thing you’ll learn on any critical reasoning course is how to recognize an argument. You might think this is easy. But it is amazing how many people think the following is an argument:

1) If she is a trained soprano then she will be able to reach top A

But this isn’t an argument, it’s a sentence. To be precise it is a conditional sentence: it has an ‘if’ clause, and a ‘then’ clause.

Arguments are constituted of at least two sentences. One of these sentences must be a claim being made (the conclusion ). The other(s) must be reasons for making that claim (the premises ). Our sentence is certainly constituted of two sentences (‘she is a soprano’ and ‘she will be able to reach top A’), together with the logical words ‘if’ and ‘then’; but these constituent sentences are not related as they would have to be in order for them to be an argument. Think about it: if someone were to assert this complex sentence, would they be claiming that either of the constituent sentences is true? Is either of these sentences a conclusion for which a premise is offered in support? Are they claiming that she is a trained soprano? Or that she is able to reach top A?

The answer is no. A person uttering sentence 1) is not asserting either of the constituent sentences. They are asserting only the whole complex sentence. They are saying that if she is a soprano, then she will be able to reach top A. They are not saying that she is a soprano, nor offering in support of such a claim the fact that she can reach top A.

Offering a conditional assertion and making an argument are two quite different things we do with language. Someone studying critical reasoning must learn that, and why, they are distinct.

Analysing Arguments

Having learned how to recognize an argument, our trainee critical thinker needs to learn how to analyse arguments: how to identify the parts of an argument – the conclusion and the premises. Here, for example, is the sort of thing you might read in your morning newspaper:

“Thankfully life can only get better. Agricultural yields are rising, thanks to new technology, and people are getting richer, thanks to globalisation and better communication. If people get richer the population will decrease and the world will get less crowded. There will be more wild places if agricultural yields rise, because we’ll need less land. If the world is less crowded and there are more wild places then life can only get better.” (Adapted from Matt Ridley in The Times , 12th September 2013)

There is an argument in here, but evaluating it as it stands is difficult. This is because the argument is hedged around with expressions of emotion (‘thankfully’) and claims intended to support the premises of the argument (‘thanks to new technology’, ‘thanks to globalization and better communication’) and emphases (‘and the world will get less crowded’).

In analysing an argument we get rid of everything extraneous to the argument, thereby revealing its logical structure. This argument, once analysed, becomes:

Argument One Premise one: Agricultural yields are rising Premise two: People are getting richer Premise three: If people get richer the population will decrease Premise four: If agricultural yields rise there will be more wild places Premise five: If there are more wild places and the population decreases then life will get better Conclusion: Life will get better

I hope you’ll agree that what is being asserted, and the reasons for asserting it, are much clearer now the argument is set out ‘logic-book style’.

Evaluating Arguments

Possibly the thing you’ll be most interested in if you are interested in learning how to reason critically is how to evaluate arguments; how to tell whether arguments are good or bad. You might already have decided whether or not the previous argument is a good argument. But on the basis of what have you decided?

Not, I hope, on the basis of your belief that the conclusion is true or false. The truth or falsehood of its conclusion is no guide to how good an argument is. There are good arguments with false conclusions, and there are bad arguments with true conclusions.

Here is a good argument with a false conclusion:

Argument Two Premise one: Whales are fish Premise two: All fish have scales Conclusion: Whales have scales

This is a good argument because if the premises were true the conclusion would have to be true. The truth of these premises would entail the truth of the conclusion: if the premises were true the conclusion couldn’t be false. However, the premises are not true.

And here is a bad argument with a true conclusion:

Argument Three Premise one: If whales have scales then whales are fish Premise two: Whales do not have scales Conclusion: Whales are not fish

This is a bad argument because the premises could both be true yet the conclusion false. The conclusion does not follow from the premises: whales could be scaleless fish. The conclusion is true – but we’d better not believe it on the basis of this argument.

Following From

You might want to protest that Argument Two can’t be a good argument. You might ask, “The premises of this argument are false, so how can the argument be good ?” But an argument’s being good or bad no more depends on the truth or falsehood of the premises than it does on the truth or falsehood of the conclusion. There are good arguments with false premises. And there are bad arguments with true premises.

Here is a good argument with false premises (and a true conclusion):

Argument Four Premise one: All fish have lungs Premise two: Whales are fish Conclusion: Whales have lungs

This is a good argument, despite the fact that both its premises are false, because the conclusion follows from the premises: if the premises were true the conclusion would have to be true.

And here is a bad argument with true premises (and a true conclusion):

Argument Five Premise one: All cats meow Premise two: The Queen’s corgi is not a cat Conclusion: The Queen’s corgi doesn’t meow

This is a bad argument, despite the fact its premises are both true and its conclusion is true. It is a bad argument because the conclusion does not follow from the premises. The truth of the conclusion is not guaranteed by the truth of the premises: the corgi might still meow despite not being a cat.

For an argument to be good, the only thing that matters is whether its conclusion follows from its premises. The actual truth-values of its premises and conclusion are irrelevant. A good argument is such that if its premises are true its conclusion must be true (or as we’ll see below, probably true).

If you thought the truth-value of the premises must be important for evaluating an argument, you are not wrong. We want our arguments to be good, such that their conclusion follows from their premises; but we also want them to be sound , meaning that their premises are true, and their conclusions follows from their premises.

We cannot logically require soundness of an argument. We often don’t know, after all, whether our premises are true or false. And sometimes their truth is a matter of dispute. Take the following argument:

Argument Six Premise one: Killing human beings is wrong Premise two: Therapeutic cloning involves killing human beings Conclusion: Therapeutic cloning is wrong

This is a good argument. If its premises are true then its conclusion will also be true. If you reject the conclusion of this argument, though, the very fact that it is a good argument tells you where to look to find the problem. The problem must be in the premises: if the conclusion of a good argument is false, then at least one of its premises must be false. The distinction between the argument’s being good and its being sound tells us how to go about questioning the conclusion of a good argument. In this case, both premises of this argument are matters of dispute. This means that we needn’t accept the conclusion of this argument, even though it is undoubtedly a good argument.

Deduction vs Induction

I have been talking about ‘following from’ as if it were the same in every case. In fact there are two sorts of ‘following from’. A conclusion may follow deductively from its premises, or it may follow inductively .

So far I have illustrated my case with deductive arguments. Deductive arguments when good are valid: if the premises are true the conclusions logically must be true. If an argument is deductively valid, and its premises are true, then it is logically impossible for the conclusion to be false. But I might have chosen to illustrate my case with inductive arguments.

Here is a good inductive argument:

Argument Seven Premise one: The sun has risen every day in the history of planet earth Conclusion: The sun will rise tomorrow

You will note immediately that whilst it would be hard to say the conclusion of this argument doesn’t follow from its premises, the argument is not valid . Its premise might be true yet its conclusion false.

No inductive argument is valid. For inductive arguments, the conclusion following from the premises is a matter of a strong probability that it is true, given the truth of the premises. Every inductive argument tacitly relies on what Scottish philosopher David Hume called ‘The Principle of the Uniformity of Nature’ (PUN): the belief that the future will be like the past.

The PUN ensures that, whilst every deductive argument is either good or bad, valid or invalid, inductive arguments are only good or bad to some degree . We don’t, therefore, talk of inductive validity, but of inductive strength . The example above is a strong inductive argument. Here is a weak one:

Argument Eight Premise one: I have seen Marianne twice and each time she was wearing earrings Conclusion: Next time I see Marianne she will be wearing earrings

Inductive arguments can be weak or they can be strong, or they can be anything in between. Induction doesn’t give us certainty, nor does it give us conclusivity. Conclusivity means that if a deductive argument is valid, then it will remain valid whatever else we might learn . An inductive argument, on the other hand, might go from being very strong to very weak (or vice versa ) as we acquire further knowledge. For example, I said that Argument Seven was a strong argument. But imagine if tonight we learn that a rogue black hole is just about to hit the sun – would we still be so confident of the truth of its conclusion? A new piece of knowledge could cause us to revise our belief that Argument Seven is a strong inductive argument. Inductive arguments are never conclusive.


Furthermore we have no method of logically testing inductive arguments. This is at least partly because inductive arguments can be evaluated only a posteriori – only in the light of experience. By contrast, any deductive argument can be evaluated a priori – without any experience of the world. If you doubt this, try evaluating this deductive argument:

Argument Nine Premise one: If widgets are holomo, then widgets are tralem Premise two: This widget is not tralem Conclusion: This widget is not holomo

I have little doubt that you will be able to tell that this is a good argument, even though you have no idea what it is about. That is because the only knowledge you need to evaluate it is linguistic and logical knowledge of the sort I know you have (or you wouldn’t have read this far). You have no need to look at the extra-linguistic world to evaluate this argument. It can be evaluated from your armchair.

This feature of some deductive arguments makes deduction the ultimate in transferable skills: it doesn’t matter what the subject matter of a deductive argument is, you will be able to tell whether it is a good argument or a bad one.

Induction is Ineliminable

Induction might not give us certainty, conclusivity or systematicity. It might also be such that we can evaluate an inductive argument only in the light of our background knowledge of the world. But we cannot do without it.

That this is the case became clear when the philosopher of science Karl Popper tried to argue that science can do without induction. Popper argued that we never inductively confirm a theory, and must instead be content with falsifying it. The only thing we can justifiable claim to know, he argued, is that a theory is false , never that it is true . However, in claiming this, Popper was tacitly relying on induction: after all, what makes us think that a theory that has been falsified on one occasion will be falsified on the next occasion, if it isn’t the inductive belief that the future will be like the past?

Induction is as important as deduction, but it is different. Understanding that and how it is different is an important part of sharpening your reasoning skills.

Reasoning is central to our notion of what it is to be human, but we can reason well or we can reason badly. Logical theory aims to identify what it is to reason well. By learning some logical theory, as you just have, you can improve your reasoning.

If you are interested in doing so further, you might be interested in the podcasts I made for the University of Oxford. These have several times been global number one in the iTunes download charts, and have been downloaded about four million times. They are completely free, and you can access them at . You might also be interested in my ebook Critical Reasoning: A Romp Through the Foothills of Logic . You can read more about it on my website: . Either way if you’d like to talk about critical reasoning come to my Facebook page: ( Marianne Talbot Philosophy ), or follow me on Twitter ( @oxphil_marianne ). I look forward to hearing from you.

© Marianne Talbot 2015

Marianne Talbot is Director of Studies in Philosophy at Oxford University’s Department for Continuing Education.

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