Deductive Logic

-- 832. Aristotle himself only goes so far as the first step in the division of fallacies, being content to cla.s.s them according as they are in the language or outside of it. After that he proceeds at once to enumerate the infimae species under each of the two main heads. We shall presently imitate this procedure for reasons of expediency. For the whole phraseology of the subject is derived from Aristotle's treatise on Sophistical Refutations, and we must either keep to his method or break away from tradition altogether. Sufficient confusion has already arisen from retaining Aristotle's language while neglecting his meaning.

-- 833. Modern writers on logic do not approach fallacies from the same point of view as Aristotle. Their object is to discover the most fertile sources of error in solitary reasoning; his was to enumerate the various tricks of refutation which could be employed by a sophist in controversy. Aristotle's cla.s.sification is an appendix to the Art of Dialectic.

-- 834. Another cause of confusion in this part of logic is the identification of Aristotle's two-fold division of fallacies, commonly known under the t.i.tles of In dictione and Extra diotionem, with the division into Logical and Material, which is based on quite a different principle.

-- 835. Aristotle's division perhaps allows an undue importance to language, in making that the principle of division, and so throwing formal and material fallacies under a common head. Accordingly another cla.s.sification has been adopted, which concentrates attention from the first upon the process of thought, which ought certainly to be of primary importance in the eyes of the logician. This cla.s.sification is as follows.

-- 836. Whenever in the course of our reasoning we are involved in error, either the conclusion follows from the premisses or it does not. If it does not, the fault must lie in the process of reasoning, and we have then what is called a Logical Fallacy. If, on the other hand, the conclusion does follow from the premisses, the fault must lie in the premisses themselves, and we then have what is called a Material Fallacy. Sometimes, however, the conclusion will appear to follow from the premisses until the meaning of the terms is examined, when it will be found that the appearance is deceptive owing to some ambiguity in the language. Such fallacies as these are, strictly speaking, non-logical, since the meaning of words is extraneous to the science which deals with thought. But they are called Semi-logical. Thus we arrive by a different road at the same three heads as before, namely, (1) Formal or Purely Logical Fallacies, (2) Semi-logical Fallacies or Fallacies of Ambiguity, (3) Material Fallacies.

-- 837. For the sake of distinctness we will place the two divisions side by side, before we proceed to enumerate the infimae species.

|--In the language | (Fallacy of Ambiguity) Fallacy-| | |--In the Form.

|--Outside the language -| | |--In the Matter.

|--Formal or purely logical.

|--Logical -| Fallacy-| |--Semi-logical | (Fallacy of Ambiguity).

|--Material

838. Of one of these three heads, namely, formal fallacies, it is not necessary to say much, as they have been amply treated of in the preceding pages. A formal fallacy arises from the breach of any of the general rules of syllogism. Consequently it would be a formal fallacy to present as a syllogism anything which had more or less than two premisses. Under the latter variety comes what is called 'a woman's reason,' which a.s.serts upon its own evidence something which requires to be proved. Schoolboys also have been known to resort to this form of argument--'You're a fool.' 'Why?' 'Because you are.' When the conclusion thus merely rea.s.serts one of the premisses, the other must be either

839. The remaining rules of the syllogism are more able to be broken than the first; so that the following scheme presents the varieties of formal fallacy which are commonly enumerated--

|--Four Terms.

Formal Fallacy-|--Undistributed Middle.

|--Illicit Process.

|--Negative Premisses and Conclusion.

-- 840. The Fallacy of Four Terms is a violation of the second of the general rules of syllogism (-- 582). Here is a palpable instance of it--

All men who write books are authors.

All educated men could write books.

.'. All educated men are authors.

Here the middle term is altered in the minor premiss to the destruction of the argument. The difference between the actual writing of books and the power to write them is precisely the difference between one who is an author and one who is not.

-- 841. Since a syllogism consists of three terms, each of which is used twice over, it would be possible to have an apparent syllogism with as many as six terms in it. The true name for the fallacy therefore is the Fallacy of More than Three Terms. But it is rare to find an attempted syllogism which has more than four terms in it, just as we are seldom tendered a line as an hexameter, which has more than seven feet.

-- 842. The Fallacies of Undistributed Middle and Illicit Process have been treated of under ---- 585, 586. The heading 'Negative Premisses and Conclusion' covers violations of the three general rules of syllogism relating to negative premisses (---- 590-593). Here is an instance of the particular form of the fallacy which consists in the attempt to extract an affirmative conclusion out of two negative premisses--

All salmon are fish, for neither salmon nor fish belong to the cla.s.s mammalia.

The accident of a conclusion being true often helps to conceal the fact that it is illegitimately arrived at. The formal fallacies which have just been enumerated find no place in Aristotle's division. The reason is plain. His object was to enumerate the various modes in which a sophist might s.n.a.t.c.h an apparent victory, whereas by openly violating any of the laws of syllogism a disputant would be simply courting defeat.

-- 843. We now revert to Aristotle's cla.s.sification of fallacies, or rather of Modes of Refutation. We will take the species he enumerates in their order, and notice how modern usage has departed from the original meaning of the terms. Let it be borne in mind that, when the deception was not in the language, Aristotle did not trouble himself to determine whether it lay in the matter or in the form of thought.

-- 844. The following scheme presents the Aristotelian cla.s.sification to the eye at a glance:--

| |--Equivocation.

| |--Amphiboly.

|--In the language -|--Composition.

| |--Division.

| |--Accent.

| |--Figure of Speech.

Modes of -| Refutation. | |--Accident.

| |--A dicto secundum quid.

| |--Ignoratio Elenchi.

|--Outside the language -|--Consequent.

| |--Pet.i.tio Principii.

| |--Non causa pro causa.

| |--Many Questions.

[Footnote: for "In the language": The Greek is [Greek: para ten lexin], the exact meaning of which is; 'due to the statement.']

-- 845. The Fallacy of Equivocation [Greek: monumia] consists in an ambiguous use of any of the three terms of a syllogism. If, for instance, anyone were to argue thus--

No human being is made of paper, All pages are human beings,.'. No pages are made of paper--

the conclusion would appear paradoxical, if the minor term were there taken in a different sense from that which it bore in its proper premiss. This therefore would be an instance of the fallacy of Equivocal Minor.

-- 846. For a glaring instance of the fallacy of Equivocal Major, we may take the following--

No courageous creature flies, The eagle is a courageous creature,.'. The eagle does not fly--

the conclusion here becomes unsound only by the major being taken ambiguously.

-- 847. It is, however, to the middle term that an ambiguity most frequently attaches. In this case the fallacy of equivocation a.s.sumes the special name of the Fallacy of Ambiguous Middle. Take as an instance the following--

Faith is a moral virtue.

To believe in the Book of Mormon is faith.

.'. To believe in the Book of Mormon is a moral virtue.

Here the premisses singly might be granted; but the conclusion would probably be felt to be unsatisfactory. Nor is the reason far to seek. It is evident that belief in a book cannot be faith in any sense in which that quality can rightly be p.r.o.nounced to be a moral virtue.

-- 848. The Fallacy of Amphiboly ([Greek: amphibolia]) is an ambiguity attaching to the construction of a proposition rather than to the terms of which it is composed. One of Aristotle's examples is this--

[Greek: t boulesthai labein me tous polemious]

which may be interpreted to mean either 'the fact of my wis.h.i.+ng to take the enemy,' or 'the fact of the enemies' wis.h.i.+ng to take me.' The cla.s.sical languages are especially liable to this fallacy owing to the oblique construction in which the accusative becomes subject to the verb. Thus in Latin we have the oracle given to Pyrrhus (though of course, if delivered at all, it must have been in Greek)--

Aio te, AEacida, Romanos vincere posse.

Pyrrhus the Romans shall, I say, subdue (Whately), [Footnote: Cicero, De Divinatione, ii. -- 116; Quintilian, Inst. Orat. vii 9, -- 6.]

which Pyrrhus, as the story runs, interpreted to mean that he could conquer the Romans, whereas the oracle subsequently explained to him that the real meaning was that the Romans could conquer him. Similar to this, as Shakspeare makes the Duke of York point out, is the witch's prophecy in Henry VI (Second Part, Act i, sc. 4),

The duke yet lives that Henry shall depose.

An instance of amphiboly may be read on the walls of Windsor Castle--Hoc fecit Wykeham. The king mas incensed with the bishop for daring to record that he made the tower, but the latter adroitly replied that what he really meant to indicate was that the tower was the making of him. To the same head may be referred the famous sentence--'I will wear no clothes to distinguish me from my Christian brethren.'