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A fallacy, in the strict sense, is an invalid form of argument. Thus fallacy, or unsoundness in reasoning, is distinguished from simple falsity in that a single statement or belief may be false, but what is fallacious is the transition from a set of premises to a conclusion. However, this distinction is often slurred over; and we call other kinds of mistakes or confusion that are more or less closely related to faults in reasoning fallacies, in an extended sense. Indeed, we sometimes give the title of "fallacy" to what is little more than a particular type of false belief. At the same time, we usually count as fallacies only those invalid forms of argument, or related kinds of error, that are plausible and into which people frequently and easily fall. Fallacy is different from sophistry, which is the deliberate use of unsound reasoning or of related errors. A fallacy used with intent to deceive or to win an argument unfairly, to carry conviction without justification, or to defeat proper discussion becomes a sophistic device.

This article will survey and classify the main kinds of fallacies, explaining and illustrating many that have been traditionally recognized and named, and noting especially those that are of particular importance in philosophy; and it will touch on the conditions in which fallacies flourish and the means by which they may be avoided or detected.

In classifying fallacies, we shall take first fallacies in the strict sense, forms of argument in which the conclusion does not follow from the premise or premises. These are divided into formal fallacies, errors in the formal reasoning itself, and informal fallacies, in which the reasoner either argues invalidly without using any precise logical form or goes wrong in putting a thought or an ordinary language statement into logical form or in translating back from logical form into thought or ordinary language. (It is a consequence of this division that if anyone commits an informal fallacy, there would be a formal fallacy somewhere in the argument that would be obtained if his intended premises, conclusion, and intermediate steps were put correctly and consistently into some logical form; but it is useful to distinguish informal fallacies in order to indicate how the mistakes have occurred.)

Next we shall take fallacies in nondeductive reasoning and in observation. We cannot speak accurately of fallacies in this case, since we no longer have strictly valid arguments with which to contrast them; but in a looser way we can contrast good procedures and patterns of reasoning that confirm hypotheses with ones that fail to confirm or are likely to produce errors.

Third, we shall examine fallacies in discourse. Such faults as inconsistency, circularity, prejudice, irrelevance, and unfair interrogationwhich include some of the best-known fallaciesare not mistakes in reasoning from premises, or evidence, to a conclusion but are to be condemned on some other ground. Philosophical fallacies do not constitute a special group apart from those already mentioned, but some of these have been singled out for special notice.

Fallacies in the Strict Sense

formal fallacies

Formal fallacies may be arranged by reference to the logical systems, or parts of a logical system, whose valid argument forms they mimic or distort.

Hypothetical and disjunctive reasoning

Hypothetical and disjunctive reasoning is systematized by the calculus of propositions. The p, q, and other terms in the forms given below stand for variables that range over complete statements or propositions, and the phrases "If then" and "Either or" stand either for the corresponding truth operators or for any operators that, with respect to the arguments into which they enter, obey substantially the same calculus. The following fallacies are common in reasoning of this kind.

Asserting the consequent : If p then q, and q, therefore p.

Denying the antecedent : If p then q, and not p, therefore not q.

Converting a conditional : If p then q, therefore if q then p. For example, "If this equation holds, so does that one; therefore, if that equation holds, so does this one."

Negating antecedent and consequent : If p then q, therefore if not p then not q. For example, "If the nations disarm, there will be peace; so if the nations do not disarm, there will not be peace."

These invalid forms of argument are plausible partly because they are distortions of valid forms. The first two are distortions of modus ponens (If p then q, and p, therefore q ) and modus tollens (If p then q, and not q, therefore not p ). Similarly, the third and fourth both mimic the valid form transposition (If p then q, therefore if not q then not p ). However, concrete arguments of these invalid forms may also be explained as informal fallacies due to ambiguity (discussed under "Ambiguous Words and Phrases" below). An expression that actually asserts only a proposition of the form "If p then q " may be wrongly taken as asserting "q if and only if p, " and if each of the conditionals above were replaced by the corresponding biconditional, each fallacy would become a valid form of argument.

It is also easy to fall into these fallacies when one is working in a field in which corresponding statements of the forms "If p then q " and "If q then p " are frequently both true or both false. This is the case in certain areas of mathematics, and indeed this fact is used in the procedure for discovering proofs that is sometimes called geometrical analysis. We assume the truth of what we wish to prove, and work out its consequences; if among these we find something that is already known or that can be proved independently, we try to construct a proof by retracing the previous steps. We assume that p, we deduce in a series of steps that q, we prove independently that q, and hence, reversing the previous deduction, that p. However, this final proof will be valid only if each of the steps in the analysis is reversible. Geometrical analysis is a useful heuristic procedure because this is often the case, but this utility in many geometric arguments may tempt us to assume, wrongly, that such steps are always reversible and that wherever we have established "If p then q, " we are entitled to infer, from this alone, "If q then p. "

Another common fallacy is that of asserting an alternative : Either p or q, and p, therefore not q. This is a distortion of the disjunctive syllogism (Either p or q, and not p, therefore q ). However, concrete examples may also be explained as due to the ambiguity of disjunctive expressions, for if "Either p or q " were replaced by the strong disjunction "Either p or q but not both," this would be a valid form of argument.

There are also fallacies that are distortions of De Morgan's rules. Thus, "Not both p and q " is equivalent to "Either not p or not q, " but we may invalidly infer from it "Both not p and not q "; and from "Either not p or not q " we may invalidly infer "Not either p or q. "

Use of arguments

If a conclusion follows validly from a premise or set of premises, we can use this fact correctly in either of two ways. Given that the premises are true, we can infer that the conclusion is true; or, given that the conclusion is false, we can infer that at least one of the premises is false. However, these correct inferences may be replaced by the following fallacious ones:

  1. The conclusion is true; therefore the premise is true (or therefore all the premises are true).
  2. The premise (or at least one of the premises) is false; therefore the conclusion is false.

The first of these can contribute to confusion between the confirmation of a hypothesis and a proof of it; for when a hypothesis is confirmed, a conclusion drawn from it as a premise is found to be true, and the fallacy would make us infer from this that the hypothesis is itself true.

  • (3) The conclusion is false; therefore all the premises are false.

We might take as a variant of the above inference a fallacy noted by Aristotle and inappropriately named non causa pro causa. In this variant, an assumption is rejected because an argument in which it is used as a premise leads validly to a false or self-contradictory conclusion. This unsatisfactory conclusion is not due to this assumption, however, and would have followed from the other premises used without this assumption. In practice, one may slip into such an improper reductio ad absurdum (or ad falsum ) either through not noticing that other premises besides the assumption are used, or through too easily taking them to be correct.

There are also fallacious ways of using the fact that an argument is invalid, such as:

  • (4) The argument from this premise (or these premises) to that conclusion is invalid; therefore the conclusion is false.

Examples of the first and fourth fallacies in the use of argument can also be explained in another way. The correct inference in each case is that the conclusion is not supported by the proposed argument, and we may confuse "not supported" with "false." Indeed, where the conclusion is the subject of controversy and we have previously had both arguments tending to show that it is true and arguments tending to show that it is false, the demolition of a supporting argument will shift the balance between the opposing views and will leave our reasons for denying this conclusion relatively stronger than they were before.

Traditional logic

The simple conversion of an A-proposition (or universal affirmative) is a common fallacy having the form "all P are Q, therefore all Q are P. " For example, having agreed that whatever is conceivable is logically possible, we are liable to infer from this that anything that is logically possible is conceivable. An equivalent error is the negating of terms in an A-proposition, that is, arguing from "All P are Q " to "All not-P are not-Q ": "Whatever is conceivable is logically possible; therefore, anything that is not conceivable is not logically possible."

A similar fallacy is the conversion of an O-proposition : "Some P are not Q, therefore some Q are not P. " An example is "Some states with parliamentary government are not democratic; it follows that there are genuinely democratic states which lack parliamentary government."

We can give a complete list of the possible formal fallacies in the traditional syllogism and sorites because the following set of four rules (one of them in two parts) is such that every argument that has the form of a syllogism or a sorites is valid if it obeys all these rules and is invalid if it breaks any of them.

Rule I. Not more than one premise may be negative.

Rule II. If one premise is negative, the conclusion must be negative, and vice versa.

Rule III. Each middle term must be distributed at least once.

Rule IV. If a term is distributed in the conclusion, it must be distributed in the premise in which it occurs.

In interpreting these rules, we take the subjects of universal propositions and the predicates of negative propositions to be distributed, and the subjects of particular propositions and the predicates of affirmative propositions to be not distributed.

There are, then, the following possible formal fallacies:

Two negative premises.

Negative conclusion with no negative premise.

Negative premise with no negative conclusion.

Undistributed middle. A middle term is not distributed in either of the premises it is meant to connect.

Illicit major. The major term, the predicate of the conclusion, is distributed in the conclusion but not in its premise.

Illicit minor. The minor term, the subject of the conclusion, is distributed in the conclusion but not in its premise.

Fallacies of the last three kinds are the most common and important. The argument "All machines work in accordance with causal laws, and all human beings work in accordance with causal laws; therefore all human beings are machines" commits the fallacy of undistributed middle because the middle term, "things that work causally," is undistributed in each of the premises as the predicate of an affirmative proposition. This fallacy is more plausible if the reasoning is expressed hypothetically: "Machines are causally determined, so if human beings were causally determined, they would be mere machines."

The fallacy becomes yet more plausible if the argument is extended to form a sorites: "Machines are causally determined, and they are not morally responsible for what they do; therefore, if human beings were causally determined, they would be no more morally responsible than machines are." The syllogism "All matters of taste are subjective, and no moral judgments are matters of taste; therefore no moral judgments are subjective" contains the fallacy of illicit major, for the term subjective is distributed in the conclusion but not in its premise. The fallacy is not obvious here, and it is still less obvious in the sorites "Matters of taste are subjective, but we do not dispute about matters of taste; since we do dispute about moral judgments, they cannot be subjective." However, the fallacy may be easily seen in an argument of the same form on another subject, such as "All birds are egg-layers; no insects are birds; therefore no insects are egg-layers." Similarly, the argument "All Victorian Gothic buildings have nonfunctional features, and they are all ugly; therefore all buildings with nonfunctional features are ugly" is an example of the fallacy of illicit minor, for the term "buildings with nonfunctional features" is distributed in the conclusion but not in its premise.

There are fallacies that consist in the mishandling of complex (conjunctive and disjunctive) terms. These include distortions of the De Morgan rules for terms, corresponding to fallacies noted above. Thus, it is fallacious to argue from "No policy will both defend freedom and insure peace" (PeDI, which is equivalent by obversion to PaD̄Ī ) to "Every policy both fails to defend freedom and fails to insure peace" (PaD̄Ī ).

Two traditionally recognized fallacies are the fallacy of the accident and the converse fallacy of the accident, which is also called the fallacy a dicto secundum quid ad dictum simpliciter. The latter consists in going invalidly from a qualified statement to an unqualified onefor example, in arguing from "It is always wrong to take another person's property without his permission" to "It is always wrong to take another person's property." (It is similarly fallacious to go from a statement qualified in one way to a like statement qualified in another way; both these errors, when they occur in moral reasoning, amount to neglect of the principle that circumstances alter cases.) Considered formally, the converse fallacy of the accident consists in invalidly dropping a conjoined term, in arguing from "All PQ are R " to "All P are R. " It is always fallacious to drop a conjunct from a distributed term, and we might therefore extend the traditional name to cover all cases of this sort. But what, then, is the fallacy of which this is the converse? Adding a conjunct to a distributed term is generally valid, but it is always a fallacy to add a conjunct to an undistributed termfor example, to argue from "Some snakes are poisonous" to "Some snakes native to Madagascar are poisonous"and we may give this fallacy the traditional name of the fallacy of the accident. However, supposed examples of this are often really examples of the converse fallacy.

Parallel with the fallacies of dropping a conjunct from a distributed term and adding a conjunct to an undistributed term are the fallacies of dropping a disjunct from an undistributed term (All P are Q or R, therefore all P are Q ) and adding a disjunct to a distributed term (No P are Q, therefore no P are Q or R ).

Relational arguments

We may recognize certain arguments involving relations as being valid on account of some formal feature of these relations, such as symmetry or transitivity. There will then be a kind of fallacy that consists in treating a certain relation as if it had some formal feature that it does not have. Thus, it is fallacious to argue "Even an experienced doctor may be unable to distinguish diphtheria at an early stage from tonsillitis, or tonsillitis from an ulcerated throat; even an experienced doctor, therefore, may be unable to distinguish diphtheria at an early stage from an ulcerated throat," because the relation "is indistinguishable from" is not transitive. This invalid argument is plausible because this nontransitive relation can be confused with the transitive one "is exactly like."

Multiple and nonextensional operators

In multiply quantified statements, the order of two successive universal quantifiers can be changed. Thus, "Every man is always selfish" (which we can symbolize as Πm ΠtSmt "For every man, for every time, that man is selfish at that time") is equivalent to "At every time all men are selfish" (Πt ΠmSmt ). Similarly, "Someone at some time is selfish" (Σm ΣtSmt ) is equivalent to "There is a time at which someone is selfish" (Σt ΣmSmt ). However, "Every man is sometimes selfish" (Πm ΣtSmt ) is not equivalent to "Sometimes every man is selfish" (Σt ΠmSmt "There is a time such that every man is selfish at that time"); the latter implies the former but not vice versa. It is, therefore, a fallacy to change the order of successive quantifiers from universal-particular to particular-universal. Aristotle would have been guilty of this fallacy if he had argued directly from "Every activity aims at some good" to "There is a good at which every activity aims."

There are similarly invalid ways of changing the order of successive operators one or both of which are not quantifiers. "It is certain that someone will win" (which may be symbolized as V ΣxWx ) does not imply "There is someone who is certain to win" (ΣxVWx ), although the invalid inference from the first to the second is facilitated by the fact that "Someone is sure to win" is ambiguous between the two. George Berkeley's central argument (in Section 23 of the Principles of Human Knowledge and in the first of the Three Dialogues ) contains an example of this fallacy. He showed, correctly, that a statement which we can formulate as follows is necessarily false: "There is something which someone truly believes not to be thought of" (Σm ΣmBmNTx ). However, he thought he had demonstrated the necessary falsity of the different statement "Someone truly believes that there is something which is not thought of" (ΣmBm ΣxNTx ). Berkeley argued invalidly from the denial of the former statement to the denial of the latter, and so to the conclusion that it is absurd to maintain that material objects exist unconceived.

We should recognize, then, a fallacy of rearranging operators. Indeed, we could bring under this heading many fallacious forms of argument. Thus, the fallacies due to distortions of De Morgan's rules noted above consist in reversing the order of negation and conjunction, or of disjunction and negation. The invalid argument from "You are not obliged to resign" to "You are obliged not to resign" reverses the order of the deontic operator and negation; the fallacious "logical" proof of determinism, "Necessarily either you will go or you will stay; so either you will go necessarily or you will stay necessarily," reverses the order of the modal operator and disjunction; and so on.

Some operators set up nonextensional contexts, contexts in which terms or propositions that are extensionally equivalent cannot be validly substituted for one another. Whereas "Mrs. Jones shot the man in her bedroom," together with the fact that the man in her bedroom was her husband, entails "Mrs. Jones shot her husband," "Mrs. Jones intentionally shot the man in her bedroom" does not similarly entail "Mrs. Jones intentionally shot her husband." And even if "p " is logically equivalent to "q, " "Smith believes that p " does not entail "Smith believes that q. " It is still a matter of dispute how such contexts should be explained and classified, and what kinds of substitution are valid in each sort of context; however, we can recognize, as a further type of fallacy, extensional substitution in nonextensional contexts.

informal fallacies

Many informal fallacies are due to ambiguity or vagueness of expressions used to make statements. If the terms used are vague or ambiguous, the expressions in which they are used will be correspondingly vague or ambiguous. However, the whole expression may be vague or ambiguous even if the terms are not, principally because a sentence form may be indeterminate as to the logical form it represents. We may, therefore, distinguish fallacies that arise from the ambiguity or vagueness of expressions in representing logical form from those that arise from other sorts of ambiguity or vagueness. Ambiguity or vagueness is not in itself a fallacy, but it may lead to fallacy. For example, someone may move invalidly from one assertion to another, but not notice that he has made any move at all because he uses the same ambiguous expression for his premise and for his conclusion. Or he may use an ambiguous expression to assert a premise, and thus infer a conclusion that would follow from one possible sense of that expression but does not follow from the sense he intends to assert. Or, having validly inferred a certain conclusion, he may assert a different conclusion, using an expression ambiguous between the validly derived conclusion and the one asserted.

Indeterminacy of expressions

A sentence such as "Men are unwise" may be ambiguous between "All men are unwise" and "Some men are unwise." It suffers from suppressed quantification. Similarly, if someone says "Courage and wisdom go together" (or "always go together," or "are constantly conjoined"), is he saying that all the courageous are wise, that all the wise are courageous, or both of these? Some philosophical terminology is ambiguous in just this way. If we say that one thing is a criterion of another, do we mean that it is a necessary criterion, a sufficient one, or both? Such indeterminacy may facilitate an invalid move from one meaning to the other, and in actual cases we may be unable to decide whether an arguer has committed the formal fallacy of simply converting an A-proposition or the informal fallacy of going from one sense to the other of an ambiguous expression.

Conditional expressions are often similarly indeterminate. "You will succeed if you make an effort" may say what it would be literally taken as saying (m s ), but with a different emphasis or in a different context it may mean "You will succeed only if you make an effort" (s m ), or perhaps the conjunction of these two (s m ). Disjunctive expressions, while they are commonly used to express a weak disjunction, can be ambiguous between weak and strong disjunction; but logicians have themselves often fallen into a fallacy in supposing that whenever two disjoined terms are mutually exclusive, either necessarily or as a matter of fact, the disjunction is itself a strong (exclusive) disjunction. The truth is that when the disjoined terms are known to exclude one another, it makes no practical difference whether the disjunction itself is weak or strong.

The name of the fallacy of division has been given, by some modern writers, to attempts to argue from the premise that something is true of some whole, or of some class considered collectively, to the conclusion that the same is true of the parts of that whole, or of the class considered distributively (that is, of each of its members); and the name of the fallacy of composition has been given to arguments in the reverse direction. Either of these fallacies may be covered by an ambiguity of the word all between its collective and its distributive sense. This ambiguity of all leads us to commit the fallacy of division when we argue, for example, from the fact that all the citizens are strong enough to resist a tyrant (meaning that the citizen body considered as a whole has sufficient strength to do this) to the conclusion that all the citizens are strong enough to resist a tyrant (meaning that every citizen, considered individually, has sufficient strength to do this). We are in this case arguing from the statement made by a sentence in which "all" is used collectively to the statement made by the same sentence when "all" is used distributively. We are committing the fallacy of composition when we argue from the premise that every man can decide how he will act to the conclusion that the human race can decide how it will act (for example, with regard to the rate of increase of population or the choice between war and peace). In this case we move from the distributive to the collective sense of "all" in "All men can decide on their actions." This, or a similar fallacy, is committed whenever we assume, without adequate reason, that we can speak about groups in the same ways in which we can speak about their members, that we can speak of a nation having a will or interests, or of a society having problems. Of course, it may be possible to do this; there may be predicates applicable (in the same sense) to a group and to its members, but this cannot be assumed without evidence. It may also be possible to introduce a different but useful sense in which a predicate normally applied to individuals may be applied to a group; but if so, the new sense must be explained.

However, what Aristotle called the fallacies of division and composition are different from these. He was speaking about changing the ways in which words are combined; for example, from "John is able-to-write while he is not writing" to "John is able to write-while-he-is-not-writing." In all such cases there is an ambiguity that conceals a fallacy of rearranging operators (the former example may be symbolized as ΣtKMWatNWat "At some time both it is possible that John is writing at that time and John is not writing at that time"and the latter as M ΣtKWatNWat "It is possible that at some time both John is writing at that time and John is not writing at that time"). The ambiguity of "All the men pushed, but could not move the stone" is really of this sort; the first clause is symbolized in one sense as Σt ΠmPmt "There is a time such that every man pushed at that time"and in another sense as Πm ΣtPmt "For every man, there is a time such that the man pushed at that time." There need not be any question of ascribing the activity of pushing to a totality of men. In either case there are only individual pushings; but the statement in one sense says that these were simultaneous and in the other sense it does not. This contrast might also be referred to as a distinction between collective and distributive senses. There are, therefore, at least two distinct pairs of fallacies that have been called fallacies of composition and division, but if we speak about collective and distributive senses we tend to run the two pairs together.

Ordinary language seems to lend itself to ambiguities about operator order. Does "You can fool all of the people some of the time" mean that there are times at which the whole populace can be deceived (ΣtM ΠmDmt using M for "It is possible that" and Dmt for "that man is deceived at that time")? Or that every person is occasionally foolable (Πm ΣtMDmt )? Does "You can fool some of the people all of the time" mean that some people are capable of being permanently deceived (ΣmM ΠtDmt ), or that at every time it is possible to fool some people (Πt ΣmMDmt or ΠtM ΣmDmt, these two being perhaps equivalent)?

However, in all the cases considered here, and in some of those to be considered in the next subsection, it may be questioned whether we should say simply that the fallacy is due to ambiguity or vagueness. We may fail to distinguish two kinds (or forms) of situations because we use the same expression to describe them, but it could also be that we use the same expression because we commonly fail to distinguish the two things. Informal fallacies, as considered here, are due to confusion as much as to ambiguity. We can conveniently explain them in terms of the ambiguity of various expressions, but we should not assume that the linguistic fact of ambiguity (or vagueness) is the sole or the primary cause of these errors.

Ambiguous words and phrases

Ambiguity is extremely common, but it is likely to lead to fallacy only in cases in which the different meanings of a word or phrase are close enough to be confused. One fallacy that can then arise is that of the ambiguous middle, that is, an argument may appear to have the form of a syllogism, but the expression we take as standing for a middle term may have different meanings in the two premises. For example, an authority on theology is more likely than other people to be right about theology, and a learned divine is an authority on theology. Does it follow that a learned divine has a better than ordinary chance of being right about theology? Not if the phrase "an authority on theology" means in the second premise an authority on the body of theological assertions but in the first premise means an authority on that which theological assertions are about. In such cases there is really no term common to the two premises, and therefore there is no genuine syllogism. There are also similar fallacies in which an expression is used in different senses in a premise and in the conclusion. Ambiguity often gives rise to these fallacies when the meaning of a word is fixed by its context, and the two different contexts give the word two different meanings. All these are instances of equivocation.

Some words are systematically ambiguous in a troublesome way. An observation may be either what is observed or the observing of it; a perception may be either a perceiving or what is perceived. There are similar indeterminacies about "experience," "sensation," and "belief." Such ambiguities constantly create difficulties in epistemology, the philosophy of science, and philosophical psychology.

There are also forms of speech that tempt us to confuse what we can say about words with what we can say about the corresponding things. A cause necessarily produces an effect, but only in the sense that it would not be called a cause if it did not. Similarly, murder is necessarily wrong, but not in the sense that there is a necessary connection or a rationally discoverable link between the kind of act called murder and its being wrong.

Sometimes when words are not ordinarily ambiguous, we perversely make them so; for example, by giving a word, in addition to its ordinary meaning, another meaning that is borrowed from a cognate word or a similarly formed word. If John Stuart Mill confused "is desirable" (meaning "ought to be desired") with "can be desired," deriving this second sense from the use of "is visible" to mean "can be seen" and "is audible" to mean "can be heard," he was making a mistake of this kind. Similar results are produced by an idiosyncratic use of language. It is hard to keep to a sense specially assigned to a word, and we are always liable to slip back into some more conventional use. When a psychologist has redefined "learning" in relation to some special procedure by which "learning" can be measured, he or his readers may think that what he then discovers is true also about learning in its ordinary, much broader sense.

Such unwarranted generalization, considered formally, exemplifies the fallacy a dicto secundum quid ; in practice, however, it is aided by various ambiguities and confusions. Thus, the words class and set may be confined to finite collections or may embrace infinite ones as well. We are liable to argue from the fact that something holds for all finite classes or sets to the conclusion that it holds for all classes or sets, including infinite ones, partly because the words are ambiguous, partly because we fail to notice that the wider concept is a different one, and partly because we generalize from specimen cases and choose specimens that are more easily visualized but are not fully representative.

As we have noted, errors may arise not only from ambiguity as such but also from the confusing of things that, although similar or related, are different. A classic example of this, of great importance in philosophical discussion, is the confusing of separation with distinction. Thus the distinction between analytic and synthetic statements may be attacked, fallaciously, on the ground that actual statements are difficult to assign, without reservations, to one category or the other. Confusion here is due partly to failure to see what sorts of things are being distinguishednot verbal forms, not sentences, but ways of using sentences to make statements.

When this obscurity is removed, however, we may still have to defend the distinction against the critic who says that because of indeterminacies in the use of component words, every concrete use of a sentence in order to make a statement lies somewhere between being analytic and being synthetic. Even if this critic were right, this would in no way count against the distinction. Indeed, such a status makes it particularly important to draw the distinction, in order to expose the common fallacy of arguing from a statement in which words are so used as to make the statement analytically true to a synthetic statement made by the same words in a different sense (as might be done with the statement "A change in the moral code means social disintegration").

This confusion can also be used in the opposite way. It may be argued that because two things can be distinguished, they must be separatefor example, to argue that since we can distinguish a motive from a cause, things that have causes cannot have motives, or that a person's having a certain motive cannot be a cause of his action.

Fallacies in Nondeductive Reasoning and in Observation

Outside the sphere of deductive reasoning, we can speak of fallacies only in an extended sense. For example, we can contrast genuine confirmation of hypotheses with something that is mistaken for it, probable arguments that give some support to their conclusions with ones that do not, and, in general, techniques and procedures that tend to give correct results with ones that tend to produce error. However, it would be pointless and misleading to call a piece of inductive reasoning, say, fallacious, merely because its conclusion turned out to be false.

induction and confirmation

We may note two fallacies about induction or confirmation: the mistaking of confirmation for proof, and the demanding of proof where no more than confirmation is possible. There are also fallacies in induction and confirmation. Where scientific or commonsense reasoning follows the lines of one of the eliminative methods of induction, failure to observe the requirements of that method will count as a fallacy. Thus, in reasoning along the lines of the method of agreement, it will be a fallacy to conclude that there is a causal relation between the phenomenon P and a certain feature A, merely because occurrences of P are repeatedly found to be accompanied or preceded by occurrences of A, without trying to discover other possibly relevant features common to these occurrences of P or, what amounts to the same thing, without trying to find occurrences of P that are as relevantly diverse as possible and then seeing whether A is present in them all. Thus, it is fallacious to conclude that William is allergic to strawberries from the evidence that his allergic symptoms have repeatedly appeared after he has eaten strawberries, if William has eaten strawberries only in one particular house, at a particular sort of gathering, and so on.

Similarly, in reasoning along the lines of the method of difference, it will be a fallacy to conclude that A is even an indispensable part of a sufficient condition for P from a comparison of a case in which P and A are both present and a case where they are both absent, without checking that the two cases are otherwise relevantly alike, that no likely-to-be-relevant feature except A differentiates the case in which P occurs from the one in which it does not. In other words, it is fallacious to use a control case that differs from the experimental case in some unwanted respect. Thus, it is fallacious to infer that John's having recovered more rapidly than James is due to a drug that was given only to John, if John was also told that he was having a new treatment and the doctors and nurses all took special care of John because they were interested in the experiment. There can be correspondingly unsound experimental procedures, and corresponding errors in reasoning, in applications of the method of concomitant variation.

Post hoc ergo propter hoc is traditionally listed as a fallacy; but much respectable inductive reasoning would fall under this heading, and it is not to be condemned because it is not deductively valid. We argue, reasonably, that the one likely-to-be-relevant change causes the result that follows. We are, in effect, taking the "before" situation as the control case and the "after" situation as the experimental case. This is a fallacy only if we ignore other likely-to-be-relevant changes.

All such mistakes can be summed up as consisting in failures to test the hypothesis in questionthat A is (in some sense) the cause of P that is, in failure to look for what, if the hypothesis were false, would be most likely to reveal its falsity. If A is not the cause of P, we are most likely to reveal this by finding cases of P so diverse that A is not present in them all, or a control case so like the experimental case that P occurs in both, or occurs in neither, in spite of A 's being present in one and absent from the other.

Another inductive fallacy is to take a hypothesis as being confirmed by observations to which it is irrelevant, when without this hypothesis our other knowledge and beliefs would explain what is observed equally well. Further, since it is a basic principle of inductive reasoning that alternative hypotheses should be considered, and that to confirm one hypothesis we must eliminate its rivals or show them to be improbable, it is a fallacy to take a hypothesis as being confirmed by observations that are equally well confirmed by an intrinsically more probable alternative hypothesisfor example, to take the Michelson-Morley experiment as confirming the theory of relativity without eliminating the FitzGerald-Lorentz contraction and the emission hypothesis of the velocity of light.

We may add a fallacy of saving hypotheses. It is certainly a fault for a thinker to be so attached to a hypothesis that he notices only evidence that agrees with it and ignores or denies unfavorable evidence. Popular superstitions of all kinds are protected by this fallacy, but it is also common among scientists, historians, and philosophers. It may also be a mistake, when one finds evidence that is prima facie unfavorable, to introduce supplementary ad hoc hypotheses in order to protect the original one from falsification. Carried to an extreme, this procedure constitutes a linguistic change that makes the original hypothesis analytically true, and it can generate the fallacy described above of oscillating between an analytic and a synthetic use of the same expression. In less extreme cases, how can we systematically mark off this error from the respectable procedure of interpreting new observations in the light of an established theory? Perhaps in two ways: first, in the respectable procedure, we are working with a hypothesis that is already well confirmed, but it is a fallacy to "save" a hypothesis for which there is no strong independent support; and second, even if the original hypothesis was well confirmed, it may be appropriate to consider, after it has been "saved" by additional hypotheses (after the new observations have been interpreted in the light of the original hypothesis) or has been modified and qualified in various ways, whether some alternative hypothesis would account better for the whole body of evidence.


All arguments from analogy are fallacious in the sense that they are not deductively valid. However, we often want further to distinguish weak analogies from strong ones and to suggest that a weak analogy is completely fallacious but that a strong analogy has at least some force. In an analogy we compare two things, A and B ; we find some resemblances, say X, Y, Z, between them; and then we argue that since A has some further feature P, it is likely that B also has this feature. We are inclined to say that if the points of resemblance X, Y, Z are few or trivial, the analogy is weak or far-fetched, but that it is a strong analogy if there are many important points of resemblance. An alternative way of looking at the distinction is that to use this analogy is implicitly to frame and then use the hypothesis that all things that have the features X, Y, Z also have the feature P. The analogy will be weak if we already have evidence that falsifies this hypothesis or makes it implausible, but it will be strong if we have no such evidence and what we know about A somehow constitutes good inductive evidence for a connection between X, Y, Z, and P.


Faults in classification can in several ways give rise to fallacies in either the strict or the extended sense. If things are classified under headings where they simply do not belong, the classification implicitly asserts false propositions which may be used as premises in arguments that, even if formally valid, will therefore give no real support to their conclusions. If a classification is based on unimportant resemblances, this may give rise to weak analogies and to the framing of unlikely hypotheses, and inductive reasoning that uses such a classificationin the methods of agreement and difference, for examplewill give an appearance of support to conclusions that are not really supported by the evidence as a whole. Again, if the division of a class into subclasses is not exhaustive, it may be wrongly taken to be so, and this will provide a false premise for a disjunctive argument. Thus, if we divide trees into conifers and deciduous trees, we may infer that since eucalypts are not conifers, they are deciduous. Similarly, a division that is not exclusive may be wrongly taken to be so; the same division of the class "trees" may lead us to infer that larches, being conifers, are not deciduous.

Two important fallacies concerned with classification arise from the attempt to draw sharp distinctions where the facts show a continuous (or near continuous) gradation. Is a man bald if he has one hair on his head? or two? or three? And so on. Just what degree of mental disorder is to count as insanity? One fallacy consists in assimilating every intermediate case to one or the other of the extremes and is exemplified in the black-and-white thinking that divides people into normal individuals and lunatics or states into peace-loving nations and warmongers. The contrary, and more subtle, fallacy consists in arguing that because there is no break in the gradations, there is no distinction even between the extremesconcluding, for example, that we are all insaneas if the problem about when a man is bald showed that there is no difference between a man with a completely smooth scalp and one with a full head of hair.


We can deal here only with some elementary mistakes in statistical reasoning. One of these consists in paying attention to simple frequencies or proportions rather than to correlations. If a high proportion of atheists are honest, this in itself does not indicate any sort of causal connection between atheism and honesty; the first thing to discover is whether the proportion of honest people is higher among atheists than among nonatheists. Similarly, the frequency of persons who have both mathematical ability and artistic talent may be small in the population as a whole; but if only one person in ten has mathematical ability and only one in ten has artistic talent, then only one in a hundred would have both, even if there were no natural opposition between these gifts. Before we conclude that these abilities tend to occur separately, we must find whether artistic talent is more or less common among the mathematically able than among the rest of the population.

Another common statistical fallacy consists in directly inferring a causal connection from a positive correlation: given a positive correlation between cigarette smoking and lung cancer, it is a further question whether this is to be explained by a causal connection between them. An associated fallacy of confusion, which is becoming more common, is simply not to talk about causation but to use the word correlation as if it meant causal connection, for example, to infer predictions and practical recommendations directly from correlation statements. Another fallacy is the neglect of the requirements of significance. Essentially, this consists in taking as causally informative, or as representative of a similar correlation in a larger population, a correlation within a sample that could equally well be explained as a chance result. This is, therefore, an instance of the neglect of alternative hypotheses.

Even when there is good statistical evidence for a causal connection between two features A and B, it is a mistake to conclude immediately that one, say A, is the cause of the other without having considered and excluded the possibilities that B may tend to produce A, that A and B may be joint effects of some other cause, and that there may be causation in more than one direction. For example, a positive correlation between poverty and ill health might be due to the fact that poverty causes ill health, to the fact that ill health diminishes earning capacity and wastes resources, to the fact that stupidity, idleness, or drunkenness tends to produce both poverty and ill health, or to a combination of more than one of these causal tendencies.


Fallacies in reasoning about probability arise mainly from failure to attend to the fact that a probability is relative to certain evidence and changes as the evidence changes. The best-known is the gambler's fallacy. For example, since it is unlikely that a penny will fall heads up five times in a row, the gambler reasons, when it has fallen heads four times, that it is unlikely to fall heads at the next throw. But although the probability of five heads, relative to the knowledge that an unbiased penny is tossed in a random manner five times, is 1/32, the probability of this result, relative to the conjunction of this knowledge with the knowledge that it has fallen heads on the first four throws, is 1/2.


It is questionable whether we should follow Mill and speak of fallacies of observation. Many of the items so described consist of errors in reasoning rather than in observation, and so fall under other headings. We may, however, note the following principles:

First, there are errors of nonobservation, which may be due to deficiency of one's senses or sense apparatus, to carelessness, or to the tendency to see only what we want to see. This may include the nonobservation that is one way of saving hypotheses.

Second, any of the above-mentioned causes may equally produce misobservation.

Third, it is impossible to separate, and difficult even to distinguish, observation from interpretation: we always have some conceptual framework, some expectations that determine how we shall observe what we observe. For example, we expect an object that looks like an adult human being to be between five and six feet tall, and we therefore tend to see any such object as being at a distance that would agree with this. The actual material to which our prior concepts are applied may not conform to them, however, and then we may make wrong judgments through using these concepts. Also, if we do not realize how observation and interpretation are mixed together, we may give the authority of an observed fact to a judgment that really rests on our preconceptions.

Fourth, our perceptual mechanisms automatically allow for factors that have been constant or to which it is inconvenient to attend, and errors arise when allowances are made for what is no longer there; for example, the illusion that the land is moving when we first go ashore after becoming used to the rolling of a ship.

Fifth, we may in perception confuse relations, say of comparison, with intrinsic qualities. This explains the illusions of contrast. For example, if after having had one's left hand in cold water and one's right hand in hot water, one puts both hands into lukewarm water, the lukewarm water feels hot to the left hand and cold to the right hand because it really is hotter than the left hand (or than what it has just been feeling) and colder than the right hand (or than what it has just been feeling).

Sixth, we may mislocate what we observe. In particular, we have a tendency to project and to treat as objective, as belonging to some external state of affairs, the feeling that the state of affairs arouses in us (the pathetic fallacy ) or to mistake connections within our thoughts for connections between the corresponding objects. There is no room here for a full discussion of perceptual illusion and observational error, but it seems that many varieties of these can be explained by reference to one or more of these principles.

Fallacies in Discourse


A position or a system of thought cannot be sound if it contains incompatible statements or beliefs, and it is one of the commonest objections to what an opponent says that he is trying to have it both ways. Inconsistency has many possible sources, but one that is of special importance in philosophy is the case in which a thinker, in order to solve one problem or deal with a particular difficulty, denies or qualifies a principle he has previously adopted, although in other contexts he adheres to the principle and uses it without qualification.

Inconsistency is a formal feature and can be formally checked, although it may also be concealed by the use of different expressions with a single meaning. It is not the same as invalidity, however; indeed, any argument with incompatible (or self-contradictory) premises will be formally valid. It is particularly important to detect inconsistencies in a set of premises, for an argument with inconsistent premises, even though valid, gives no support to its conclusion; and using one is not a satisfactory way of establishing anything or of convincing an audience.

On the other hand, it is a formal fallacy to suppose that because your opponent has tried to have it both ways, he cannot have it either waythat every part of an inconsistent position must be false.

petitio principii

An argument that begs the question, that uses the conclusion as one of the premises, is always formally valid. A conclusion cannot fail to follow from a set of premises that includes it. This is also a fallacy only in the extended sense that such an argument gives no support to its conclusion. One kind of petitio principii consists in arguing in a circle, when one proposition is defended by reference to another, and the second is defended by reference to the first. For example, we may argue that a certain historian is trustworthy because he gives a balanced account of some episode, but also rely on that historian's account in order to decide what actually occurred in this episode, and hence to decide what would be a balanced account of it.

The larger and more complex a circle of argument is, the harder it is to detect the fallacy. One result of circularity is that the propositions that have been proved from one another appear to have been conclusively established, although no empirical evidence has been given for either of them. This can create an illusion that there are synthetic propositions that have no need of empirical support. This may be combined with a fallacy of confusion, of failing to distinguish the coherence or consequential character of a system from its trutha confusion that has developed into the coherence theory of truth and that is still encouraged by some eccentric uses of the word true or of such a phrase as "true within the system."

Circularity is common in moral reasoning, and here, too, it may make us think that moral conclusions can be rationally established without reliance on observations, intuitions, choices, or decisions. The exposure of such circularity compels us to give a more adequate account both of how moral judgments are to be supported and of how they are to be interpreted.

a priori fallacies

Under the heading of a priori fallacies Mill listed a number of natural prejudices, including the popular superstition that words have a magical power and such philosophical dogmas as that what is true of our ideas of things must be true of the things themselves; that differences in nature must correspond to our received (linguistic) distinctions; that whatever is, is rationally explicable; that there is no action at a distance; that every phenomenon has a single cause; and that effects must resemble their causes. These are all errors, but we can go further and recognize a general a priorist fallacy, which consists in trying to base knowledge of fundamental synthetic truths on anything other than empirical evidence. These examples illustrate how once we start looking for a priori truths, we are led to try to distill them from language or from our ideas (giving each of these an authority to which it is not entitled), or to confuse continuity with intelligibility and necessity, or to dignify with the title of a priori truths what are no more than sweeping generalizations from the simplest and most familiar observations.

More generally still, we can recognize a fallacy of prejudice, which consists in believing without evidence, in adopting or adhering to views on any subject without any relevant reason. It is worth noting that adopting a method of argument (other than a deductively valid form) is tantamount to adopting an assertion. For example, regularly to judge the rightness of actions by their utility is tantamount to adopting the principle that whatever maximizes utility is right; and, again, regularly to argue that because a statement cannot be verified, it is meaningless is tantamount to adopting a verifiability theory of meaning. This is a particularly easy way of committing the fallacy of prejudice.

ignoratio elenchi

The fallacy of ignoratio elenchi consists in missing the point, in arguing for something other than what is to be proved. However, we can speak in this way only if the context somehow determines what is to be proved. In the first place, the context may be a discussion between A and B, and B will commit this fallacy if he claims to be replying to what A has said but fails to come to grips with A 's argumentfor example, if he tries to disprove some proposition that A has not asserted either as a premise or as a conclusion. B is also guilty of this fallacy if he bluntly denies something that A has claimed to prove but does nothing to rebut A 's proof. Alternatively, it may be a thinker's general position or some long line of argument that makes it imperative for him to establish some point, and makes him guilty of irrelevance if he establishes something else instead.

There are a number of common and important types of irrelevance in discussion. If the question is whether a certain view is true or false, it is irrelevant to argue that adopting this view will be beneficial or pernicious. Thus, a body of religious doctrine may be irrelevantly defended on the ground that it makes people happier or better behaved. Similarly, the origin of a belief is in general irrelevant to the question of its truth; but if the fact that a belief is widely held has been used as evidence of its truth, then this reasoning may be relevantly rebutted by showing that the belief has come to be held for reasons or from causes that are independent of its truth. The truth of the belief and the account of its origin are in this case alternative explanatory hypotheses. That a view is held by certain people is also in general irrelevant to its truth, so that appeals to authority are usually examples of ignoratio elenchi. Cases in which the authority appealed to can be independently shown to be an authority in the sense of being likely to be well-informed about the point at issue are exceptions. Irrelevancy shades into prejudice; we may readily accept the doctrines of "our party" and reject those of "the enemy." In this, there may also be present a fallacy of confusion, in that we treat factual beliefs as if they were items of another categoryprinciples to which we can adhere or subscribe, or which we can reject, by choice.

Another form of irrelevance is the tu quoque, or "two wrongs" technique. If some action or view of one's own is criticized, one may reply by attacking some action or view of one's critic that is equally hard to defend. The argumentum ad hominem is similarwe reject what someone says on the irrelevant ground that he is in no position to say it. However, an argumentum ad hominem may quite properly point to an inconsistency, and may validly establish the limited conclusion that this man cannot consistently hold this viewa conclusion that may be of special interest in a moral discussion, where the problem may well be that of finding a policy that is both coherent and acceptable.

Related fallacies of irrelevance have been named argumentum ad verecundiam (appeal to authority or to feelings of reverence or respect), argumentum ad personam (appeal to personal interest), and argumentum ad populum (appeal to popular prejudice). Sometimes an argumentum ad ignorantiam or ad auditores is grouped with these, but these names seem to refer not to any specific fallacy but to the use of any unsound argument that is likely to deceive the actual audience.

fallacies of interrogation

There are two forms of the fallacy of many questions. In one, two or more questions are asked together, and a single answer is demanded to all of them. This is fallacious in that it unfairly prevents the person asked from giving different answers to the different questions. In the second form, the question asked has a presupposition that the answerer may wish to deny but which he would be accepting if he gave anything that would count as an answer. Thus, an answer of either "Yes" or "No" to the question "Have you left the party?" would be an admission of having been a party member, and any answer to the question "Why does such-and-such happen?" presupposes that such-and-such does happen. There is no fallacy, however, in merely asking a question that has a presupposition; the fallacy lies in demanding an answer in the narrow sense, in not permitting or in discouraging a reply that denies the presupposition. Again, it is an instance of the fallacy of prejudice to ask a question that has a presupposition without first investigating whether that presupposition is correct.

fallacies in explanation and definition

Just as a circular argument fails to give support, so a circular explanation fails to explain. There are concealed circularities of explanation; for example, some mental performance is explained by reference to a faculty, but further inquiry shows either that to say that this faculty exists is only to say that such performances occur or that, although more may be meant, there is, apart from such performances, no evidence for the existence of the faculty. Words like "tendency," "power," "disposition," and "capacity" lend themselves to circularities of this sort.

Similarly, a circular definition, in which the term to be defined recurs within the definiens, fails in its task. If it is intended as a stipulative definition, it fails to assign a meaning; and if it is intended as a reportive definition, it fails to inform anyone of the meaning with which the word is used.

Stipulative definitions can create ambiguity when we assign one meaning to a word but also retain another meaning. This amounts to an assertion that the two meanings go together, disguised as the innocent procedure of stipulation. Persuasive definition is an instance of this in which the retained meaning is an emotive one.

It is a fallacy, in the extended sense, to use words without meaning. But it is not a fallacy not to have defined one's terms, provided that they have a meaning that is known to the audience and is precise enough for the purpose in hand. On the contrary, since it is impossible to define all one's terms, it is a fallacy in discourse to demand that in all terms should be defined; a demand for definition can be a sophistic device for preventing the discussion of substantive issues.

Philosophical Fallacies

the naturalistic fallacy

What G. E. Moore called the naturalistic fallacy is the identifying of goodness with any natural characteristic, such as pleasantness or being the object of desire. If there is a distinct property, goodness, it will of course be an error to identify it with any other feature, even if the two are coextensive, and this would be an example of the refusal to distinguish what we cannot separate; however, it must first be shown that there is such a property as Moore's goodness. Alternatively, if it is a question of how the word good is commonly used, then it would be an error to say that it is used to convey some natural description. However, if the naturalist is not trying to report the ordinary use, but is saying that this ordinary use is somehow unsatisfactory (and also that there is no such property as the one of which Moore speaks) and is therefore proposing a different use, where is his mistake? It is true that if he redefines "good" as the name of some natural characteristic, but still also uses the word in its ordinary evaluative or prescriptive sense, he will be slipping into a fallacy of ambiguity; but a consistent ethical naturalist may be committing no fallacy at all.

arguing from "is" to "ought"

An error exposed by David Hume, but still frequently committed, is that of arguing from premises that contain only descriptive terms, and no copula except "is," to a conclusion that contains an "ought." This is a fallacy in the strict sense; arguments of this sort cannot be valid, but they are often made plausible by the ambiguous use of such words as reasonable, fitting, authority, desirable, beneficial, courageous, temperate, just, right, and good itself, any one of which may be used first in a purely descriptive sense and then interpreted in a sense that is partly descriptive and partly prescriptive. A currently popular version of this fallacy combines it with one or more of the a priori fallacies. Since our concept of, say, courage or our ordinary use of the word courage combines a certain natural description with a certain prescription or evaluation, it is concluded that behavior that conforms to this natural description must be recommended or valued in just this way; that is, the move from is to ought is covered by an appeal to the supposed authority of our language or our ideas.

confusing relations with things or qualities

A group of philosophical errors that is less well known than the two just mentioned but at least as widespread and harmful consists in identifying a quality with a relation, in treating a relation as if it were an intrinsic quality of one of its terms, or in constructing fictitious entities out of relational situations. Presented linguistically, this means that a term is treated as standing both for a thing or a quality and for a relation, and this, like other ambiguities, can make synthetic connections appear necessary. Thus, an idea or a sense datum is supposed to be an object of which someone can be aware and to have this relationsomeone's being aware of itas part of its nature. This conflation generates a supposed matter of fact about which one can have infallible knowledge and thus gives rise to the pseudo problem of bridging the gap between this direct and infallible knowledge and ordinary fallible knowledge of objects that do not have being known built into their natures. Similarly, minds (or consciousness) have been treated as things that have as part of their nature the relation of being aware of something, and this generates difficulties in philosophical psychology. Also, errors that the naturalistic fallacy was meant to cover are better dealt with in this category. Goodness may be both treated as an intrinsic quality (natural or nonnatural) of, say, states of affairs and identified with or taken as logically including the relation of being pursued, aimed at, or recommended; indeed, it seems that it is just such a conflation of features that makes a quality nonnatural. Similarly, beauty may be both treated as an intrinsic quality and identified with or taken as logically including such relations as pleasing or being admired.

category mistakes

Philosophers now carefully distinguish different uses of language, different "language games"; the contrasting error is to confuse different ways of using words, to treat a term that belongs to one category as if it belonged to another. However, the concept of a use of language is itself ambiguous. In distinguishing uses, we may be noting differences that lie within language, differences in the relations between words and things, differences in the things to which our expressions apply; and it will be a mistake to confuse one kind of distinction with another. There is also a tendency to think that, at least in philosophy, we cannot employ this distinction between words and things; this view is supported by a variant of Berkeley's fallacy: Since we cannot talk about something except by using words in relation to it, it is supposed that we cannot talk about things as they are, apart from relations to words.

Avoidance and Detection of Fallacies

Popular discussions of fallacies rightly lay great stress on the psychological or emotional aspect of fallacious arguments. Under the influence of violent passions, thinking becomes more purely associative and less consequential, and we are more than usually ready not only to employ arguments, however unsound, that appear to support whatever cause we espouse but also to extend our favor to anything linked, however loosely, with what we already like, respect, or admire, and to extend our hostility to anything linked with what we already dislike, despise, or fear. Ridicule can also be used to brush aside relevant considerations and to condemn a person or a view without a hearing. All sorts of attachments, passions, and emotional prejudices can foster fallacies, and one of the chief means for the avoidance or detection of fallacies is to consider a problem calmly.

Precise formal statement often helps in the detection not only of fallacies in the strict sense but also of inconsistency, circularity, and irrelevance. However, since it is too laborious a task to state all our reasonings formally, we can use this device only when we already have reason to suspect a fallacy. Also, in cases involving equivocation or a category mistake, there is a danger that inaccurate formulation will conceal the fallacy instead of exposing it.

As Richard Whately remarked, "a very long discussion is one of the most effective veils of Fallacy; a Fallacy which when stated barely would not deceive a child, may deceive half the world if diluted in a quarto volume" (Elements of Logic, p. 151). Consequently, an important weapon against fallacy is condensation, extracting the substance of an argument from a mass of verbiage. But this device too has its dangers; it may produce oversimplification, that is, the fallacy a dicto secundum quid, of dropping relevant qualifications. When we suspect a fallacy, our aim must be to discover exactly what the argument is; and in general the way to do this is first to pick out its main outlines and then to take into account any relevant subtleties or qualifications.

See also Aristotle; Bentham, Jeremy; Berkeley, George; Conditionals; Definition; Hume, David; Induction; Logical Terms, Glossary of; Mill, John Stuart; Mill's Methods of Induction; Moore, George Edward; Probability; Truth and Falsity in Indian Philosophy; Whately, Richard.


The pioneer work on fallacies is the De Sophisticis Elenchis of Aristotle. Medieval and later logicians followed and expanded his account. Many textbooks on logic include a chapter on fallacies. Jeremy Bentham, throughout his writings, paid much attention to fallacious reasonings by which views that he opposed were supported, and he collected many of them in The Book of Fallacies, which is in Vol. II of his Works, edited by J. Bowring (Edinburgh, 1843). Richard Whately, in Ch. 3 of his Elements of Logic (London, 1826), gave a much improved classification and analysis of fallacies. John Stuart Mill devoted Book V of A System of Logic (London, 1843) to an account of fallacies, developing a new classification and concentrating on a priori fallacies (prejudices) and mistakes in observation and generalization.

Augustus De Morgan, in Ch. 13 of Formal Logic (London, 1847), rejected the attempt to list all possible ways of going wrong but gave a penetrating and well-illustrated analysis of many of the traditionally listed fallacies. Arthur Schopenhauer, in "The Art of Controversy," in Essays from the Parerga and Paralipomena, translated by T. B. Saunders (London, 1951), described stratagems that may be used in disputes, that is, both sophistic devices and ways of countering them. H. W. B. Joseph included in An Introduction to Logic (London, 1906) an appendix on fallacies based on the Aristotelian account.

M. R. Cohen and Ernest Nagel, in Ch. 19 of An Introduction to Logic and Scientific Method (New York, 1934), emphasized abuses of scientific method. R. H. Thouless in Straight and Crooked Thinking (London, 1930), Susan Stebbing in Thinking to Some Purpose (Harmondsworth, U.K., 1939), and W. W. Fearnside and W. B. Holther in FallacyThe Counterfeit of Argument (Englewood Cliffs, NJ, 1959), gave lively and readable accounts, illustrated with many examples of popular errors and of sophistry in practice, concentrating on political and social debate and propaganda, and stressing the emotional basis of a great deal of fallacy.

J. L. Mackie (1967)