This lesson is from Bachhuber, Andrew H., S.J. 1957. "Chapter 10: Fallacies," An Introduction to Logic. New York: Appleton-Century-Crofts, Inc. Pp. 176-97.
A fallacy is a deceptive argument; that is, an argument that seems to be conclusive but is actually not conclusive. Either its sequence seems to be valid but is actually invalid, or else its premises seem to be true but are actually false. The word fallacy is derived from the Latin word fallo, which means to deceive. An appearance of validity and truth is essential to a fallacy, for it would deceive no one unless it at least seemed to be valid and true. Violations of the rules of the syllogism were not traditionally regarded as fallacies because it was thought that they would deceive no one; but nowadays the term “fallacy” is also applied to them, and we speak of the fallacy of an undistributed middle, the fallacy of an illicit process of the major term, and so on. Mere errors in fact or principle are not fallacies in the Aristotelian sense.
The term “fallacy” is sometimes applied to ambiguous statements that are not actually parts of an argument. The reason for this is that they might be understood in a sense in which they are not true and thus be an occasion of deception. Strictly speaking, though, such statements are not fallacies but merely occasions of fallacies.
An intended fallacy is called a “sophism.” It gets this name because it was a favorite device of the ancient Greek Sophists, who claimed to be able to prove either side of any question.
Should logic treat of fallacies? Logic is the science and art of correct thinking. Fallacies are bad thinking; consequently you might suppose that the treatment of fallacies has no place in logic. Moreover, logic treats primarily of the formal conditions of valid inference. Many fallacies, on the other hand, arise from the matter of inference rather than from defective form and might consequently seem to lie outside the scope of logic.
Yet, in spite of these objections, ever since the time of Aristotle, treatises on logic have always included a discussion of fallacies, and many good reasons can be advanced in support of this traditional practice.
In the first place, correct forms of inference are often best illustrated and explained by contrasting them with incorrect forms. Indeed, you cannot know the correct forms of thought without simultaneously knowing the incorrect forms; you necessarily know both of them together. A physician aims at procuring health but nevertheless studies diseases; so, too, a logician, who aims at attaining correctness of thought, must also study the pathology of thought. You cannot think correctly unless you avoid thinking incorrectly; and you can neither avoid incorrect thinking yourself nor detect incorrect thinking in others unless you are skilled in recognizing in¬ correct forms of thought.
Secondly, the study of fallacies will serve as a review of much of what we have already seen. You should not consider fallacies in isolation from the other parts of logic, but as intimately connected with them. When you study the various kinds of fallacies, you should make a special effort to note which of the general rules of inference are violated by each of them.
Thirdly, a readiness in recognizing fallacies will help you apply the principles of logic to everything you read or hear and put you on your guard against the more common sources of deception. Books, magazines, newspapers, and spoken discourse are full of fallacies; if you are skilled in recognizing them, you are less likely to be duped.
Finally, the ability to call a fallacy by name will give you a great advantage over an opponent in discussion and debate. A person unfamiliar with fallacies often has a vague suspicion that an argument is defective or even knows for certain that it has some flaw, but still cannot say exactly what is wrong with it. A person familiar with fallacies, on the contrary, can put his finger right on the flaw and thus protect himself from being embarrassed and abused by sophisms.
No classification of fallacies is entirely satisfactory. In the first place, no classification is exhaustive. Indeed, it is probably impossible to draw up a complete list of fallacies; all we hope to do is to list the more common and more important types. In the second place, the members of the classification overlap, because the same fallacious argument can generally be referred to various headings as it is considered from different points of view. This difficulty of classification springs from the very nature of fallacies. Fallacies are error, and error is multiple; the same argument can labor under manifold defects.
The following classification, which is substantially that of Aristotle, seems as satisfactory as any. It has the added advantage of having a long-established tradition behind it.
Aristotle divides fallacies into those of language and those not of language. In this classification we go beyond the confines of formal logic, and consider the thought content, as well as the form, of argumentation.
Aristotle lists six fallacies of language. The first five are various kinds of ambiguity and consist in using an expression in different senses in different parts of an argument but proceeding as though it were used in the same sense. A categorical syllogism in which any of these fallacies occurs has the equivalent of four terms. The middle term is the one that is most often used in two senses.
Aristotle’s sixth fallacy of language is an invalid argument that infers similarity of meaning from similarity of word construction.
These six fallacies of language, with the exception of the fallacies of composition and division, are of less importance today than in ancient times when oral disputation according to set forms was more common than now. We shall treat of them very briefly.
a. Equivocation
Equivocation consists in using a word that has the same spelling or sound, but a different meaning, in different parts of an argument. The word need not be an equivocal term in the strict sense; the ambiguous use of an analogous term or a change in the way a term is used (that is, an illegitimate shift of supposition) can suffice. Puns illustrate this fallacy.
The essence of the fallacy consists in using a term in an acceptable sense in a premise, and thus tricking people into admitting the premise, and then drawing a conclusion as though the term had been used in that premise in an unacceptable sense.
Notice, for instance, the equivocal use of “natural” in the following example:
What is natural is good; but to make mistakes is natural; therefore to make mistakes is good.
In its first occurrence, the word “natural” means “constituting or perfecting a nature”; in its second occurrence, it means “due to the limitations of nature.” Only in the first sense of the word is it true that what is natural is good. (This syllogism also incurs the fallacy of four terms.)
Notice, too, the equivocal use of “violate a law” and of “man” in the following two examples:
He who violates a law should be punished; but when we illustrate fallacies we violate many laws; therefore when we illustrate fallacies we should be punished.
He who violates a moral law perhaps should be punished but hardly one who violates a law of logic.
"Man" can be predicated of many; but you are a man; therefore you can be predicated of many.
The concept "man" can be predicated of man; however, you are not the concept "man" but a real man.
b. Amphiboly
Amphiboly is syntactical ambiguity. It consists in using a phrase whose individual words are univocal but whose meaning is ambiguous because the grammatical construction can be interpreted in various ways.
When King Pyrrhus asked the oracle whether he would conquer the Romans, the oracle answered in the following Latin hexameter:
Aio te, Aeacide, Romanos vincere posse. (Pyrrhus the Romans can, I say, subdue.)
Who was to conquer whom? King Pyrrhus made the disastrous mistake of thinking that he was to conquer the Romans rather than that the Romans were to conquer him.
Similar to this is the response that the oracle gave to King Croesus when he was planning a war against the Persians.
If Croesus wages war against the Persians, he will destroy a mighty kingdom.
Whose kingdom? His own? Or the Persians? The oracle did not say, but the event proved that it was to be his own.
c. Composition
The fallacy of composition consists in taking words or phrases as a unit when they should be taken separately. Cajus falls into this fallacy when he admits that thieves and murderers are excluded from the kingdom of heaven, but then denies that he himself is excluded since he is only a thief but not a murderer. In the premise, the words “thieves and murderers” are taken distributively; that is, both thieves and murderers are excluded from the kingdom, so that you are excluded if you are either a thief or a murderer (or, of course, both). But Cajus makes the mistake of assuming that only those are excluded who are both thieves and murderers. He has taken words together and as a unit when he should have taken them separately, or distributively.
A classic example of the fallacy of composition is found in John Stuart Mill’s Utilitarianism:
No reason can be given why the general happiness is desirable, except that each person, as far as he believes it to be attainable, desires his own happiness. This, however, being a fact, we have not only all the proof the case admits of, but all which it is possible to require, that happiness is a good; that each person’s happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons.
The fallacy consists in arguing from the alleged fact that each individual man seeks his own happiness without any regard for the happiness of the aggregate of men to the conclusion that each individual seeks the happiness of the aggregate. From the alleged fact that A seeks Ha (happiness of A), B seeks Hb, C seeks Hc, D seeks Hd, and so on, he argues that A seeks Habcd, B seeks Habcd, C seeks Habcd, and D seeks Habcd.
d. Division
The fallacy of division is the converse of the fallacy of composition and consists in taking separately what should be taken together as a unit. Did one straw break the camel’s back? The two-millionth straw in composition with the other 1,999,999 did break the camel’s back; but the two-millionth straw in separation from the other 1,999,999 did not break it.
You fall into this fallacy when you argue:
All in this room weigh about two tons; but MaryAlice is in this room; therefore MaryAlice weighs about two tons.
“All in this room” is to be understood collectively in the major premise; but in the conclusion you proceed as though it had been taken distributively; you divide, or separate, what is true only when taken together as a unit.
e. Accent
The fallacy of accent consists in the ambiguous use of a word that has different meanings when it is accented differently. This fallacy is the same as equivocation except that, strictly speaking, words having different accents are not the same words.
In English works on logic the name “fallacy of accent” is often applied to ambiguity that results from shifting emphasis from one word to another. For instance, in the proposition “John is not a depraved murderer,” if you emphasize “depraved,” you deny that John is depraved without stating whether or not he is a murderer; if you emphasize “murderer,” you deny that he is a murderer without, however, stating whether or not he is depraved.
Note the change in meaning in the following example as the emphasis is shifted from one to another of the italicized words or phrases. “Thou shalt not bear false witness against thy neighbor.” If you emphasize “shalt not bear,” you suggest that one should not tolerate false witness; if you emphasize “false,” you hint that it is all right to say evil things about your neighbor as long as they are true; if you emphasize “against,” you suggest that it might be licit to tell lies in his favor; and if you emphasize “neighbor,” you suggest that it might not be forbidden to tell lies about men who are not your neighbors.
The fallacy of accent in this second sense is a kind of amphiboly.
f. Figures of Speech
The fallacy of figures of speech is a special type of false analogy that consists in wrongly inferring similarity of meaning from similarity of word structure. Note the words “immaterial,” “insoluble,” and “inflammable” in the following example.
What is immaterial is not material and what is insoluble is not soluble; therefore what is inflammable is not flammable.
In “immaterial” and “insoluble” the prefix “im-” or “in-” is a negative particle; but in “inflammable” it is an intensive particle. The argument proceeds, though, as if the prefix must have the same meaning in its third occurrence that it had in the first and second.
One of the most famous examples of this fallacy is found in Mill’s Utilitarianism:
The only proof capable of being given that an object is visible is that people actually see it. The only proof that a sound is audible is because people hear it; and so of the other sources of our experience. In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.
This fallacy rests on the false assumption that, in the word “desirable, the suffix “-ible” (or “-able”) must mean “capable of be¬ ing ... since it has this meaning in “visible” and “audible.”
In order to avoid the fallacy of figures of speech, you must know the meanings of words.
Aristotle lists seven fallacies not of language. They have this in common, that all of them arise from some kind of confusion about the things that are spoken of. Either what is essential to a thing is confused with what is merely accidental to it, or what is true abso¬ lutely and without qualification is confused with what is true only with a qualification or limitation, or what is against a thesis is confused with what is not against it—and so on, as we shall explain in connection with each fallacy. After treating of these Aristotelian fallacies we shall add a few others that seem important enough to deserve special attention.
a. Accident
The fallacy of accident consists in affirming or denying of a thing what has been affirmed or denied only of some accidental modification or condition of the thing, or vice versa. This fallacy rests on a confusion of what is essential or necessary to a thing and what is merely accidental to it.
The sophist’s dialogue with the acquaintance of Coriscus illustrates this fallacy.
"Do you know Coriscus?" / "Yes." / "Do you know the man who is approaching with his face muffled?" / "No." / "But he is Coriscus; you have both affirmed and denied that you know Coriscus."
To have his face muffled is an accident in Coriscus; it is possible to know Coriscus without knowing him according to this particular accidental condition. (You can know him without always recognizing him.)
You illustrate the same fallacy when you argue:
"You say that you ate what you bought; but you bought raw meat; therefore you must have eaten raw meat."
You did not intend to assert a complete identity between what you ate and what you bought. All you wanted to say is that they were substantially the same; you did not intend to deny that the accidental condition of the meat was changed by cooking.
A common form of this fallacy consists in arguing that a thing itself should be forbidden or destroyed because its use sometimes leads to abuse. The abuse should be eliminated, of course; but it does not follow from this that the use should also be eliminated.
Alcoholic drinks lead to drunkenness and should therefore be forbidden.
You can construct a parallel argument which is obviously absurd.
Good food leads to overeating and should therefore be forbidden.
You might have a valid argument, though, if you show that the use of a thing is inseparable from its abuse and that the abuse always has serious evil consequences.
b. Confusion of Absolute and Qualified Statement
Under this heading we shall treat of two distinct but closely related fallacies. The first of these consists in using a principle that is restricted in its applicability as though it were an absolutely universal principle, and thus applying it to cases for which it was not intended. What is true only with qualification or limitation is taken to be true absolutely or without any qualification or limitation. We illustrate this fallacy when we argue:
Water boils at 212° Fahrenheit; therefore water boils at 212° Fahrenheit on the top of Mount Everest.
The premise is not true absolutely but only with the limitation “under an atmospheric pressure corresponding to 760 mm. of mercury.” Hence, when we use this premise to infer that water boils at 212° Fahrenheit on the top of Mount Everest, we are applying a principle to a case that it was not intended to cover. We do the same when we argue:
Germans are good musicians; therefore this German is a good musician.
The premise is true of Germans as a group or in general, but not of each individual German. (This example, if expressed in a complete syllogism, would incur the fallacy of undistributed middle since the middle term “German” would be particular in each occurrence.)
The other form of this fallacy consists in assuming that an absolute statement is implied in a qualified, or limited, statement when it is actually not implied therein. Compare the following propositions:
1. John is a good doctor; therefore John is a doctor.
2. He gave me $1000 of counterfeit money; therefore he gave me $1000.
"John is a good doctor” implies the absolute statement that John is a doctor; but “He gave me $1000 of counterfeit money” does not imply the absolute statement that he gave me $1000.
c. Ignoratio Elenchi
The fallacy of ignoratio elenchi consists in proving a conclusion other than the one that should be proved. It is called by various names; for instance, “the fallacy of irrelevant conclusion, ignorance of the question,” “ignoring the issue,” “missing the point, and so on.
The fallacy gets its name from the Latinized form of the Greek word elenchos, which means “refutation.” In order to refute a statement, you must establish its contradictory. Now if you establish something other than the contradictory of the statement to be refuted, you are said to be “ignorant of the refutation.”
Suppose, for instance, that someone uses the following argument to refute the Catholic claim that the pope is infallible.
There have been bad popes; therefore the pope is not infallible.
Suppose, too, that this opponent of papal infallibility has proven that there were a few bad popes. The question is, Is the fact that there have been a few bad popes really inconsistent with the pope's infallibility? Does this fact really involve the contradictory of “The pope is infallible”? Or can a pope be bad and still be infallible? Now, anyone who knows the exact technical sense in which Catholics claim infallibility for the pope will immediately see that the fact that there have been a few bad popes is irrelevant to the point at issue. The fact proves that the pope is not impeccable; but it does not prove that the pope is not infallible. In this example, as in many others, an ignoratio elenchi could have been avoided by clarifying the exact point at issue through precise definition.
[Note: Notice that on the assumption that no bad person can be infallible even by the special favor of God, the antecedent (“there have been bad popes”) would not be irrelevant to the conclusion (“therefore the pope is not infallible”). If the person using the argument would not admit that this assumption is false, he would incur, not the fallacy of ignoratio elenchi, but the non-Aristotelian fallacy of false assumption.]The following argument of the young lad who denied the guilt of his adult friend who had been sent to prison for murdering his wife also incurs an ignoratio elenchi:
He wasn’t guilty. He was nice to all the kids and very athletic. We played basketball and water-skied with him and had wonderful times. He’d do anything for anybody.
He could have been “nice to all the kids,” and so on, and nevertheless have murdered his wife. The question was not, Was he a pleasant companion, and so on, but, Did he, or did he not, murder his wife?
The prosecutor at a trial for murder commits this fallacy if he expatiates on how terrible murder is instead of proving that the accused is guilty.
The ignoratio elenchi is very common and assumes many minor forms. The following are the most important.
The argumentum ad hominem ignores the issue and attacks the person of an opponent instead. It includes such things as personal abuse, attacks on a man’s character or nationality or religion, “mud slinging,” “name calling,” “poisoning the wells,” charges of inconsistency, retorting an argument, and so on. Sometimes, of course, it is legitimate to question the credibility of a witness; for instance, if he has a criminal record, if he has perjured himself in the past, or if his testimony is inconsistent. Sometimes, too, it is legitimate to point out that a man’s present testimony is inconsistent with his conduct or with what he held in the past. Thus, Christ used a legitimate argumentum ad hominem when He silenced those who found fault with Him for healing on the Sabbath by asking, “Which of you shall have an ass or an ox fall into a pit, and will not immediately draw him up on the Sabbath?”
The argumentum ad populum (“appeal to the people”) is an appeal to popular prejudices rather than to reason. Every election year supplies altogether too many examples of this fallacy.
The argumentum ad misericordiam (“appeal to pity”) ignores the point at issue and appeals, instead, to our instinct to have compassion on the unfortunate. For instance, instead of proving that an accused person is innocent, the argument may be aimed at winning sympathy for him by portraying how unfortunate he has always been, how much his innocent and poverty-stricken family will suffer if he is convicted, and so on. Many arguments favoring divorce, contraception, abortion, euthanasia, and so on, illustrate this fallacy. They obscure the issue by playing on our emotions. Note, for instance, the following plea for euthanasia.
I have watched three loved ones and a dear friend die slowly and horribly of cancer. I saw their flesh turn yellow and shrivel into a hanging mass of vicious sickly design. I watched the light of reason die in their eyes and a haunting madness take its place. I heard their shrieks of agony and their desperate plea for death when opiates ceased to deaden their pain. . . . The Bible says, “Blessed are the merciful, for they shall obtain mercy.” Let the law-makers take this page and apply it in their courtrooms.
The question is not, Is a lingering death from cancer a terrible thing? All admit that it is. To dwell at length on the sufferings of the incurably ill is to befuddle the issue. The question is, Does God alone have dominion over the lives of innocent people? If he has, the direct killing of an innocent human being by another human being is always a serious crime.
The argumentum ad verecundiam (literally, “appeal to shame”) is an appeal to misplaced authority. It aims at overawing people by appealing to the dignity of those who hold an opinion rather than to their special competence in the matter under discussion. A mathematician, for instance, might be a genius in mathematics and still be an ignoramus in aesthetic matters; to accept his opinion in aesthetic matters on account of his pre-eminence in mathematics is to fall into this fallacy. This fallacy is a common device of advertisers who urge you to smoke a certain brand of cigarettes or drink a certain kind of whiskey because some famous person does. It is often introduced by phrases like “scientists say,” “informed people will tell you ...“surely you know . ..“everyone knows,” and so on.
The argumentum ad baculum (“appeal to the stick") is an appeal to physical force or moral pressure.
d. Begging the Question
The fallacy of begging the question, or petitio principii, consists in assuming under some form or other the conclusion that should be proved and then using it as a premise to prove the very same conclusion. This fallacy occurs in two forms.
The first form consists in using the same or an equivalent proposition as both premise and conclusion, as in the following examples.
Whiskey causes drunkenness because it is intoxicating.
The soul is immortal because it cannot die.
Morphine induces sleep because it has soporific effects.
Both the premises (the “because” clauses) and the conclusions state exactly the same thing and differ from one another only verbally.
The second form consists in using a premise that cannot be known to be true unless the conclusion is first known to be true, as in the following example:
All in this room are wearing shoes; but Martha is in this room; therefore Martha is wearing shoes.
The major premise is an enumerative universal and cannot be known to be true unless the conclusion is first known to be true. You cannot know that all in this room are wearing shoes unless you first know that Martha is wearing them.
The “vicious circle,” or “arguing in a circle,” is a special type of the fallacy of begging the question and consists in proving a proposition by a second proposition and then proving the second by the first. You have a vicious circle, for instance, if you prove that man has free will because he is responsible for his actions and then— generally a few pages later—prove that man is responsible for his actions because he has free will.
The fallacy of begging the question is incurred by the use of “question-begging epithets,” which imply that what is to be proved has already been proved. The prosecutor who refers to the man accused of murder as a murderer assumes precisely what he is supposed to prove. Or suppose that so-and-so, belonging to such-and-such an organization, has informed the police of its illegal activities. If you report his action by calling him a stool pigeon, you do more than merely report a fact; you insinuate a conclusion by using a weighted word with an unfavorable innuendo.
Akin to this is the practice of insinuating interpretations and conclusions into what is claimed to be an objective and impartial presentation of facts. An example of this can be found in Joseph P. Kamp’s We Must Abolish the United States. At the beginning of the book Mr. Kamp says:
Here then are the results of our researches. We present the facts as we find them, and our own conclusion as to their meaning. We have tried to be objective.
On the next page he continues:
Under the Constitution of the United States they [the American people] have the unalienable right to believe in, and to fight for, any idea, no matter how visionary, impractical, far-fetched, phony or screwball it may be.
Accordingly, since World War II an increasing number of forthright Americans, and some who call themselves Americans, have been spending their time, energy and money in furthering programs for World Government that are all of these things . . . and worse.
He has already told us what to think of certain programs although he has not yet given us a single fact about them. A page later, after presenting an outline “stripped of all pretense” of the position of his opponents, he adds to his list of derogatory epithets, or unfavorably weighted words, by asking:
Is such a sinister program too far-fetched, too asinine, and too plainly disloyal to win any real measure of public support?
The program may indeed be “visionary,” “impractical,” “far-fetched,” “phony,” and “screwball”; it may involve “pretense” and be “sinister,” “asinine,” and “disloyal”; nevertheless, this does not belong to the facts as facts but is a conclusion rightly or wrongly inferred from the facts. Mr. Kamp, of course, did not say that he would first present the facts and then his conclusions about them; still, by mingling his interpretations and conclusions with his presentation of the facts in such a way as to confound the two, he argues in a manner that is objectively fallacious.
e. False Cause
We must distinguish between the Aristotelian fallacy of false cause (non causa pro causa) and the much more important fallacv to which later logicians give the same name.
The Aristotelian fallacy of false cause consists in drawing an absurd conclusion from an assumption that is falsely imputed to an opponent or wrongly assumed to underlie a thesis. What is not the cause or reason for a thesis is assumed to be its cause or reason. Suppose, for example, that a sophist’s opponent has made the statement that the death penalty for murder is just, and the sophist argues as follows:
The claim that the death penalty for murder is just leads to an absurdity. If the death penalty for murder is just and if, moreover, punishment is just precisely insofar as it is an effective deterrent from crime, it would follow that it would be equally just to inflict the death penalty for pocket-picking.
The claim that the death penalty for murder is just actually rests on the principle that punishment should be proportionate to the gravity of a crime. But the sophist pretends that it rests on the assumption that punishment is just only insofar as it is an effective deterrent from crime, and then he draws his absurd conclusion from this falsely imputed assumption.
[Note: The Aristotelian fallacy of false cause often involves the additional fallacy of sublating the antecedent.]Later logicians give the name of “false cause” to various fallacies arising from a confusion of causal with non-causal relationships. Its commonest form is the post hoc, ergo propter hoc (“after this, therefore because of this”), which consists in mistaking a purely temporal sequence for a causal relationship.
Night comes before day; therefore night causes day.
I got well after taking a certain medicine; therefore I got well because I took that medicine.
The fallacy of false cause is also incurred by mistaking a mere condition or occasion of an event for its cause, as in the following example.
A man cannot think without his brain; therefore a man’s brain is the cause of his thought.
The fallacy of false cause in this modern sense is usually an ignoratio elenchi; sometimes, however, it rests on a false assumption and is not an Aristotelian fallacy at all.
f. Consequent
The fallacy of the consequent consists in inferring that an antecedent is true because its consequent is true, or that a consequent is false because its antecedent is false. This fallacy is based on the mistaken opinion that the relationship of an antecedent and its consequents in regard to truth and falsity is always reciprocal.
The best known forms of this fallacy are the invalid moods of the conditional syllogism. The first of these is called “positing the consequent” and is incurred by positing a consequent in the minor premise and then positing the antecedent in the conclusion; the second is called “sublating the antecedent” and is incurred by sublating the antecedent in the minor premise and then sublating the consequent in the conclusion. We treated of these adequately when we discussed the conditional syllogism.
The fallacy of the consequent can also be incurred in categorical syllogisms. Any notion included in the comprehension of a concept _whether as a constitutive note (genus and difference) or as a derived note (logical property)—is a consequent of that concept, and in relation to its consequents the concept itself is an antecedent. In this sense the notions “animal,” “organic,” “material,” and so on, are consequents of the antecedent “dog.” In the minor premise of the following syllogism the term “animal,” which is a consequent of “dog,” is predicated of the minor term “Moby Dick and in the conclusion its antecedent (“dog”) is predicated of the same term:
A dog is an animal; but Moby Dick is an animal; therefore Moby Dick is a dog.
This example not only incurs the fallacy of positing the consequent but also the formal fallacy of an undistributed middle term.
In the minor premise of the following syllogism the term “dog," which is an antecedent of “animal,” is denied of the minor term “Moby Dick” and in the conclusion its consequent is denied of the same term.
A dog is an animal; but Moby Dick is not a dog; therefore Moby Dick is not an animal.
This example not only incurs the fallacy of sublating the antecedent (“dog” is sublated with reference to Moby Dick) but also the formal fallacy of an illicit process of a major term.
We must be on our guard against three common ways of incurring the fallacy of the consequent. First, we should not reject a thesis merely because one or the other of its proofs is inconclusive. The reason for this is that an antecedent can be false (or the sequence invalid) while the consequent is nevertheless true. Secondly, we should not assume that the arguments advanced in proof of a thesis must be conclusive because the thesis itself is known to be true. A true consequent can flow from a false antecedent. Thirdly, we should not assume that a hypothesis or theory must be true simply because its consequents have been verified. A hypothesis or theory is not proved conclusively by the mere verification of its consequents but only by showing that it is the only antecedent from which the verified consequents can flow.
g. Many Questions
The fallacy of many questions consists in asking either a multiple question as though it were a single question—or a question involving a supposition as though it involved no supposition—and then demanding a simple yes or no for an answer and thus tricking someone into making admissions he did not intend to make.
Consider the following multiple question which is proposed as though it were a single question.
Is he a democrat with socialistic tendencies?
If he is both a democrat and a man of socialistic tendencies, the answer may be a simple yes. If he is a democrat but does not have socialistic tendencies, if he is not a democrat but has socialistic tendencies, or if he is neither, the answer may be a vague and ambiguous no. A more definite answer would be: “He is a democrat but does not have socialistic tendencies,” or “He is not a democrat but has socialistic tendencies,” or “He is neither a democrat nor has socialistic tendencies.”
The following example is a favorite illustration of a question that has suppositions.
Have you stopped beating your wife?
Both yes and no will involve you in embarrassing admissions. The question rests on two suppositions; first, that you have a wife; and, second, that you have beaten her. If you have no wife, or if you have one but have never beaten her, you should deny the suppositions that are not fulfilled in your case.
h. Other Fallacies
The following fallacies are not included in Aristotle’s list of fallacies, but are important enough to merit a brief notice.
1) NON SEQUITUR is the Latin for “it does not follow.” In a sense every invalid argument is a non sequitur, just as every invalid argument is also an ignoratio elenchi; but the name “non sequitur” is generally restricted to a series of true but unrelated propositions that simulate the structure of a syllogism; for instance,
Cows give milk; but sheep have wool; therefore goats chew cud.
Most examples are rather trivial. We mention this fallacy only because its name is in rather common use and is included in most lists of fallacies.
2) The ARGUMENTUM AD IGNORANTIAM, or APPEAL TO IGNORANCE, infers that a statement is false because it cannot be proved, or true because it cannot be refuted. The assumption that a man is guilty until he proves himself not guilty is an example of this fallacy, as illustrated by a pamphleteer who lists a series of charges and then exclaims:
This is evidence that must be accepted because it cannot be refuted.
3) The fallacy of SUPPRESSING THE FACTS consists in selecting only the facts that favor an opinion and suppressing, or ignoring, all facts that are against it. By a careful selection of quotations you can often give the impression that a writer holds an opinion that is just the opposite of what he really holds.
4) The ARGUMENT FROM SILENCE infers that an alleged fact did not take place because it is not recorded in writings in which it would surely have been recorded if it had taken place. This argument can be legitimate, but is often misused. To know for certain that, if an event had taken place, it would have been recorded is often difficult and frequently impossible.
5) The FALLACY OF FALSE ASSUMPTION consists in using a false principle or false statement of fact as an unexpressed premise (or at least as a presupposition) of an argument. It is not a fallacy at all in the Aristotelian sense but an error. The fallacy of false assumption is incurred most frequently in enthymemes whose unexpressed member is false, as in the following example:
No one has ever seen a soul; therefore you cannot know for certain that you have a soul.
This argument rests on the false assumption that you cannot know anything for certain unless you can see (hear, touch, smell, or taste) it, and this false assumption is the reason for assenting to the conclusion. Unless the false assumption “causes” the conclusion, the fallacy of false assumption is not incurred.
6) Fallacies of ILLICIT GENERALIZATION consist in making a generalization on insufficient evidence. These fallacies are incident to induction.
7) The FALLACY OF FALSE ANALOGY will be treated in connection with induction. Actually it is an ignoratio elenchi.
The following sample answers will serve as models for the handling of fallacies. They will likewise clarify the differences between certain fallacies that are often confused with one another, and illustrate how the same fallacy can often be classified under various headings when considered from different points of view.
Sample 1. If there were no time, there would be no day; if it were not day, it would be night; but if it were night, there would be time; therefore, if there were no time, there would be time.
EQUIVOCATION. The word “day” is used in two senses: in its first occurrence it signifies a period of twenty-four hours; in its second occurrence it signifies “day” as opposed to “night.”
DIVISION. The argument starts with the condition “if there were no time ’; but then it proceeds as though this condition had not been made, “dividing” the rest of the argument from the first portion. On the sup¬ position that there were no time, it would not be true that it would be night if it were not day, because on this supposition there would be neither day nor night.
Sample 2. The American worker shouldn’t kick; he’s much better off than his European brother.
IGNORATIO ELENCHI. The American worker could be much better off than his European brother and nevertheless have just grounds for complaint. Hence, the antecedent (“He’s much better off than his European brother”) is irrelevant to the conclusion (“The American worker shouldn’t kick”), and an ignoratio elenchi is incurred.
Is a so-called FALLACY OF FALSE ASSUMPTION incurred? Let us complete the argument, supplying a major premise that will render the argument formally valid:
Major: No one who is better off than anyone else can ever have just grounds for complaint;
Minor: but the American worker is better off than someone else (namely, his European brother);
Concl: therefore the American worker has no just grounds for complaint (shouldn’t kick).
If the principle expressed in the major premise were true, the evidence adduced in the minor premise would not be irrelevant to the conclusion but would clearly prove it. However, the major premise is obviously false. Now if this false principle actually caused the assent to the conclusion, the non-Aristotelian fallacy of false assumption would be incurred. However, in all likelihood the person using the argument in Sample 2 does not even advert to the general principle behind his argument and would promptly reject the principle if it were brought to his attention. In this case, the false principle would not cause the assent to the conclusion; and the fallacy incurred is not FALSE ASSUMPTION, but IGNORATIO ELENCHI. But if the person using the argument would think that the principle in the major premise were true, he would incur the non-Aristotelian fallacy of false assumption.
Sample 3. Labor unions cause strikes and should therefore be abolished. If we supply the missing parts and set up the argument in logical form, we get the following arrangement:
Major: Whatever causes strikes should be abolished;
Minor: but labor unions cause strikes;
Concl: therefore labor unions should be abolished.
The argument is formally valid but fallacious. The major premise is true only when two qualifications are added: that the strikes are UNJUST and that they are caused, not PER ACCIDENS, but PER SE. Passing to the minor premise, where the major is applied to labor unions, we find that labor unions cause, not unjust, but JUST strikes (at least from the point of view of the union) or, if they cause unjust strikes, they do this, not PER SE, but PER ACCIDENS.
Two fallacies are incurred: the fallacy of confusion of ABSOLUTE AND QUALIFIED STATEMENT, because a principle (the major premise) that is true only with the qualification made above is used as though it were true without qualification; and the fallacy of ACCIDENT, be¬ cause the argument concludes that the very existence of labor unions should be abolished, although all that has been proven is that their abuse (an accident) should be abolished.
Sample 4. Capital punishment is un-Christian, because the death penalty falls for the most part on obscure, impoverished, friendless or defective individuals and rarely on the well-to-do and educated.
If we supply the missing parts and set up the argument in logical form, we get the following syllogism:
Major: That punishment is un-Christian which falls for the most part on obscure, impoverished, friendless or defective individuals and rarely on the well-to-do and educated;
Minor: but the death penalty (or capital punishment) is such a punishment;
Concl: therefore capital punishment is un-Christian.
The evidence aims directly at proving that such punishment is unjust and only indirectly that it is un-Christian. Hence, we must supply the following syllogism as a proof of the major premise given above:
Major: What is unjust is un-Christian;
Minor: but a punishment that falls for the most part on obscure, impoverished, friendless or defective individuals and rarely on the well-to-do and educated is unjust;
Concl: therefore that punishment is un-Christian which falls for the most part on obscure, impoverished, friendless or defective individuals and rarely on the well-to-do or educated.
The syllogisms are both formally valid, but fallacies occur in the syllogism given as a proof of the main syllogism.
ACCIDENT. That such a punishment is unjust may be due to its faulty administration (an accident) rather than to its very nature. In other words, injustice might not be essential to capital punishment but accidental to it: if the accidental abuses would be eliminated, capital punishment would cease to be unjust.
IGNORATIO ELENCHI. Perhaps the obscure, impoverished, friendless or defective individuals commit more crimes that merit capital punishment than the well-to-do and educated. If this is true, then, not injustice, but the fact that more of them commit such crimes would be the reason why more of them receive capital punishment. In this case, the given antecedent is irrelevant to the conclusion, and the fallacy of ignoratio elenchi is incurred.