2. PARALOGISM AND SOPHISM.

“Fallacy” comes from the Latin fallacia, meaning deceptive or erroneous, and therefore a fallacy in logic is any error in reasoning which has an appearance of correctness. If the writer or speaker is himself deceived by the fallacy, then such is called a Paralogism; but if the fallacy is committed by him for the expressed purpose of deceiving others, then such becomes a Sophism. During the time of the Schoolmen the Sophism was in such high repute that it required even a Socrates to puncture this ignominious bubble of vain trickery. In fact, Socrates, the greatest of all pagan educators, led the crusade which has relegated to the “logical dust bin” the notion that skill in the art of framing sophisms is a scholarly accomplishment. Many believe modern sophistry to be the chief social and commercial evil of the day, and to Socrates must be given the credit for teaching us to look upon those who would practice sophism with righteous indignation and pronounced disgust. However, paralogism and not sophism is the more legitimate field for the student of logic; his problem being, “What are the common errors whichI, as a writer and speaker, must strive to avoid?”

3. A DIVISION OF THE DEDUCTIVE FALLACIES.

The mistakes of induction will occupy our attention in a later chapter. We are now concerned with the fallacies of deduction. Any classification or division of the deductive fallacies must of necessity be faulty. Even the labors of Aristotle in this regard are now pronounced crude and unsatisfactory. This is due to the divergence of opinion as to the signification of some of the fallacies, as well as to the fact that no division is free from the fault of an overlapping of the species. As a result of this lack of unanimity in definition and lack of ability in making the species mutually exclusive, any division of the deductive fallacies must be more or less illogical.

Aristotle divides the fallacies of deduction into two groups: (1)Fallacies in dictione, or formal fallacies. (2)Fallacies extra dictionem, or material fallacies. This division has received universal approval and though many distinctions made by him have been abandoned, yet most logicians retain his phraseology. Since many of the technical terms which Aristotle used have lived through the generations under the conventional meaning which he assigned to them, it becomes less confusing to adhere as closely as possible to these terms. Therefore, in the attending division only those changes have been made which progress and experience have forced upon us. What remains of this chapter will be devoted to explaining these fallacies as they appear in this division. For the sake of clearness and definiteness it is strongly recommended that the student study the outline extensively enough to be able to reproduce it.

4. GENERAL DIVISIONS EXPLAINED.

The formal fallacies are those which concern the form of the argument rather than the meaning. These fallacies arise from an improper use of words as arbitrary signs of thought, not from any inconsistency in the thought itself. To commit a formal fallacy we must violate one of the specific rules of logic. For this reason the formal fallacies are easier of comprehension. Moreover, because of this definiteness logicians are better able to come to some agreement as to their content and import. Classing the fallacies of immediate inference as formal is somewhat of an innovation; but since they occur because of the breaking of certain definite rules, and since immediate inference is a matter of changing the form without altering the meaning, we believe there is some justification for this position. Some would class “immediate inference” fallacies with the material fallacies of language.

The material fallacies are fallacies of meaning and not of form. They are those arising from inconsistency in thought, and from imperfect ways of interpreting this thought as it appears in language. No very specific rules of logic are violated by them and for this reason there are those who would entirely eliminate the material fallacies from the field of logic. But since thought is even more subtle than form in its deceitful machinations, we believe that the material fallacy calls for special attention on the part of the logician.

Material fallacies are divided into two kinds. First, those which have reference to wrong thinking, or fallacies in thought; and, second, those which are due mainly to an incorrect interpretation of words, or fallacies in language. The former result from inconsistency and unreasonableness in thought, whereas the latter come from lack of precision in expression.

5. FALLACIES OF IMMEDIATE INFERENCE.

Fallacies of immediate inference arise from some violation of the rules which this topic enunciates.

(1) Opposition.

Among other statements opposition posits these two: (1)When the particular is true its opposing universal is indeterminate; (2)A universal negative does not necessarily contradict a universal affirmative.

These signify that neither an A nor an E must be assumed to be true when the corresponding I or O is true, and that E may not always contradict A, nor O contradict I.

ILLUSTRATIONS OF FALLACIES OF OPPOSITION.

There is little difference between fallacies like (1)and fallacies of converse accident. Concerning illustration (2), both statements are false; but to contradict we know that if one is false, the other must be true.

(2) Obversion.

“Two negatives are equivalent to one affirmative,” is the principle underlying obversion. The most common fallacy in obversion springs from using one negative instead of two.

ILLUSTRATIONS OF FALLACIOUS OBVERSION.

(3) Conversion.

Conversion involves the interchanging of the subject and predicate of a proposition without affecting the distribution; in consequence the usual fallacy incident to this interchange is distributing an undistributed term.

ILLUSTRATIONS OF FALLACY OF CONVERSION.

(4) Contraversion.

As this process involves the two steps of obversion and conversion, fallacies appertaining to contraversion would relate to these two steps.

ILLUSTRATIONS OF FALLACIES OF CONTRAVERSION.

The formal fallacies of categorical, hypothetical, and disjunctive arguments have received detailed treatment in chapters 11, 14 and 15; we may, therefore, devote our attention to the material fallacies without further delay.

6. FALLACIES OF LANGUAGE. (Equivocation.)

These are the fallacies of double meaning. It is known that an equivocal term is one which permits two or more interpretations; similarly a proposition which admits of two or more interpretations may be denominated equivocal. Thus the term equivocation has come to stand for all errors in language resulting from a possibility of more than one interpretation. This justifies the position of referring to all of the six fallacies in language as fallacies also of equivocation.

(1) Ambiguous middle.

Ambiguous middle explains itself. It is the fallacy of giving to the middle term a double meaning. In form the argument may contain but three terms, yet in meaning there are in reality four terms. For this reason ambiguous middle and the fallacy of four terms appear to be about one and the same thing; but in this treatment we shall regard them as mutually exclusive, and this is the distinction:

Invalid arguments of “ambiguous middle” have only three terms in form but four terms in meaning. This signifies that the middle term though identical in form is given a double meaning.

Invalid arguments of “four terms” always have four terms in both form and meaning; they are “logical quadrupeds” in every sense of the word.

ILLUSTRATIONS.

In the “four-term” fallacies, observe that the four terms occur in the premises. When a fourth term is introduced in the conclusion, the material fallacy of non sequitur has been committed.

(2) Amphibology (or amphiboly).

Amphibology is a fallacy resulting from an ambiguous proposition rather than from the ambiguity of any particular term. The fallacy of amphibology is committed when the spoken or written proposition conveys more than one meaning. The ancient oracles indulged in this sort of fallacy, the reason for such indulgence being obvious; the oracles were not too positive as to the outcome of their prognostications, and therefore were especially careful to cover every emergency.

A careless use of relative clauses and prepositional phrases often results in the fallacy of amphibology.

ILLUSTRATIONS OF THE FALLACY OF AMPHIBOLOGY.

(3) Accent.

This fallacy springs from placing undue emphasis on some word or group of words. Naturally such accentuation may convey a meaning entirely foreign to the author’s intent. Newspapers are guilty of this fallacy when they select a few words from a speech and use them as headlines without further explanation. Apolitician may quote a sentence uttered by an opponent and fail to relate it to what preceded or followed. Acartoonist may arouse the prejudice of public opinion by giving ridiculous emphasis to some idiosyncracy possessed by the subject of his attack.

ILLUSTRATIONS OF FALLACIES OF ACCENT.

(4) Composition.

The fallacy of composition is committed when it is assumed that what is true distributively is likewise true collectively. Aterm is used in a distributive sense when it is applied to each individual of the class; whereas a term is used in a collective sense when it is applied to the class considered as one whole. “All” meaning each one considered separately and “all” meaning the whole furnishes a frequent pitfall for this fallacy.

ILLUSTRATIONS OF THE FALLACY OF COMPOSITION.

(5) Division.

The fallacy of division is committed when it is assumed that what is true collectively is true distributively. Division is the converse of composition. Composition is a fallacious procedure from a distributive to a collective use; while division is a fallacious procedure from a collective to a distributive use. The fallacy of division may be illustrated by giving the converse of the illustrations under composition:

(6) Figure of Speech.

This fallacy results from assuming that words of the same root have the same meaning. Since the same root-word may be used as a noun, verb, adjective, etc., it does not follow that in these various forms it retains a common meaning. “Address” as a noun and “address” as a verb convey two distinct meanings.

The following are examples of this fallacy:

These fallacies are not classed as those of “four terms” because two terms so closely resemble each other in form, and yet they are not fallacies of ambiguous middle; since the middle terms are not identical in form.

7. FALLACIES IN THOUGHT.

The fallacies in thought arise through a tendency to assume as true that which demands further proof. Any one who is more anxious to be right than to win will make sure that nothing has been taken for granted which should receive further investigation, or that no truth has been given a presumptuous twist in order to make it fit the particular case under discussion. Because these errors in thought may be attributed chiefly to undue assumptions, we may denominate them as the fallacies of assumption.

(1) Accident.

The fallacy of accident occurs when one reasons from a general truth to an accidental case. Doctrinaires and theoretic enthusiasts are partial to this fallacy. It is so easy to lay down a general formula or remedy and then attempt to apply it to every accidental circumstance. Grandmother with her catnip tea and mustard plaster, however we may cherish the memory of the dear old soul, was nevertheless guilty of the fallacy of accident. Applying maxims and proverbs to particular instances is still another way of committing the fallacy.

EXAMPLES OF FALLACIES OF ACCIDENT.

(2) Converse Accident.

As the title implies this is the fallacy of reasoning from an accidental case to a general truth. Illustrations:

Relative to both accident and converse accident, it may be said that they obtain because all general truths, such as rules, principles, definitions, maxims, etc., have their exceptions; and it is through these exceptions that the two fallacies are made possible.

Accident and Converse Accident Distinguished from Division and Composition.

The fallacy of accident, we have learned, occurs when one reasons from a general truth to an accidental case; whereas the fallacy of division obtains when one reasons from a collective use of a term to a distributive use; in both cases the procedure is from a larger unit to a smaller unit. Moreover, with converse accident and composition, the movement is from the smaller unit to the larger. Because of this similarity there is danger of confusing the two kinds of fallacies. As a matter of distinction between the fallacies of accident, and composition and division the attending comparative rÉsumÉ may be of value:

Irrelevant Conclusion (Ignoratio Elenchi).

The fallacy of irrelevant conclusion results when the argument does not squarely meet the point at issue. It is the fallacy of arguing to the wrong point either purposely or through ignorance. One in defense, who has a weak case, may be tempted to divert attention from the point in hand, realizing that a close analysis of the matter in dispute will tend to his undoing. In such instances (1)the lawyer will abuse the plaintiff, (2)the demagogue will tell humorous stories, (3)the teacher will take advantage of the ignorance of the pupil, (4)the scholar will refer to authority and (5)the magnate will fall back upon the power of position and wealth. These forms of “rhetorical thinking” are as harmful as they are popular, and furnish one of the chief reasons for giving to the common people a better understanding of “how to think” as well as “how not to think.”

Definite names have been given to the various forms of irrelevant conclusion which may be summarized as follows:

Argumentum ad populum.

This is the fallacy of appealing to the feelings, passions and prejudices of an audience rather than to their good sense and powers of reason. It is probably the most common of the group. To excite sympathy, the lawyer for the defense may speak feelingly of the suffering that an unfavorable verdict will bring to the wife and children of the accused.

Argumentum ad hominem.

Here the character of the opponent is defamed with a view of discrediting him with the court or audience. “Mud throwing” in times of political agitation is a good example of this fallacy.

Argumentum ad ignorantiam.

This fallacy comes from taking advantage of the ignorance of the opponent; the fallacy assumes that the original supposition has been proved if one is unable to prove the contradictory of the original. Illustration: Mars is inhabited because no one is able to prove that Mars is not inhabited.

Argumentum ad baculum.

In this all argumentation is made to give way to the forces of personal opposition and to the power of money. Illustration: Apolitical committee seating those delegates only, who will vote their way; and, doing this, not from the merits of the case, but because said committee happen to have a sufficient number of votes to “put the thing through.”

Argumentum ad verecundiam.

This fallacy comes from supposing that the whole thing may be settled by citing some noted authority who apparently substantiates the argument advanced.

Epitome of five forms of Irrelevant Conclusion:

Non Sequitur (False Consequent).

This is the fallacy of deriving a conclusion which does not follow from the premises. The fallacy obtains whenever material appears in the conclusion, which has no bearing on the case under discussion. “Irrelevant conclusion” pertains to the establishment of the premises while “non sequitur” is concerned with the conclusion only. We know that a logical thinker constructs the conclusion from material already presented by the premises; “Non sequitur” uses material in the conclusion which is found in neither premise.

“Non sequitur” differs from the fallacy of four terms in that the latter uses the fourth term in the premises while the former introduces the fourth term in the conclusion, and in a form so well obscured that it sometimes escapes notice. Illustration:

It does not follow that because a man is a thinking animal that he will become scholarly.

False Cause.

This is the fallacy of assuming that because two happenings have occurred together several times, the one is the cause of the other. This very common fallacy is due to lack of discrimination, and to the exaggerations incident to fear and superstition. Illustrations:

It is seen that “False Cause” is closely related to “Non Sequitur.”

Complex Question (Double Question).

This fallacy obtains when an assumption is put in the form of a question.

ILLUSTRATIONS:

Begging the Question (Petitio Principii).

This is a fallacy of deriving a conclusion from notions which in themselves demand proof.

The fallacy is not committed when the assertion is self-evident. It is easy to claim that our opponent is begging the question as soon as we see that he is getting the better of us. One may himself beg the question by being too ready to charge others with begging the question. When the opponent adopts premises which are commonly accepted, he does not beg the question. One commits the fallacy when he seems to prove the conclusion more satisfactorily than he really does. This he may accomplish by covertly taking for granted the truth of notions which have not the stamp of universal approval. The fallacy of begging the question assumes three forms:

(1) The assumption of an unproved premise (assumptio non probata).

In this either the major or the minor premise, or both may demand more substantial proof. It must be borne in mind, however, that the disputant must not ask for further proof after he has once accepted the premises, or after the opponent has met his demands to the satisfaction of commonly accepted authority.

Examples of begging the question by assuming unproved premises:

(2) Reasoning in a Circle (Circulus in probando).

This form of begging the question occurs, “When a conclusion is based upon a premise which in an earlier stage of the argument was itself based upon this very conclusion.” To put it in another way: Reasoning in a circle involves proving the truth of a conclusion by using a particular premise, and then proving the truth of the particular premise by using the conclusion. From premise to conclusion and from conclusion to premise completes the circle.

Examples of begging the question by reasoning in a circle:

(3) Question Begging Epithets and Appellations.

This is the fallacy of assuming the point at issue by means of a carefully selected epithet.

Scientists sometimes assume to clarify an inexplicable phenomenon by giving it a technical name. Politicians are exceedingly free with their epithets and appellations, and the records of religious disputes prove that the theologian often resorted to this device.

Examples of begging the question by using epithets and appellations:

It is seen that the use of these epithets and appellations is simply a rhetorical device for the purpose of creating either a favorable or unfavorable impression.

8. OUTLINE.

THE LOGICAL FALLACIES OF DEDUCTIVE REASONING.