Deductive Logic Part 50

-- 872. The 'argumentum ad baculum' is unquestionably a form of irrelevancy. To knock a man down when he differs from you in opinion may prove your strength, but hardly your logic.

A sub-variety of this form of irrelevancy was exhibited lately at a socialist lecture in Oxford, at which an undergraduate, unable or unwilling to meet the arguments of the speaker, uncorked a bottle, which had the effect of instantaneously dispersing the audience. This might be set down as the 'argumentum ad nasum.'

-- 873. We now come to the Fallacy of the Consequent, a term which has been more hopelessly abused than any. What Aristotle meant by it was simply the a.s.sertion of the consequent in a conjunctive proposition, which amounts to the same thing as the simple conversion of A (-- 489), and is a fallacy of distribution. Aristotle's example is this--

If it has rained, the ground is wet.

.'. If the ground is wet, it has rained.

This fallacy, he tells us, is often employed in rhetoric in dealing with presumptive evidence. Thus a speaker, wanting to prove that a man is an adulterer, will argue that he is a showy dresser, and has been seen about at nights. Both these things however may be the case, and yet the charge not be true.

-- 874. The Fallacy of Pet.i.tio or a.s.sumptio Principii [Greek: t en arche ateistai or lambanein] to which we now come, consists in an unfair a.s.sumption of the point at issue. The word [Greek: ateistai], in Aristotle's name for it points to the Greek method of dialectic by means of question and answer. This fact is rather disguised by the mysterious phrase 'begging the question.' The fallacy would be committed when you asked your opponent to grant, overtly or covertly, the very proposition originally propounded for discussion.

-- 875. As the question of the precise nature of this fallacy is of some importance we will take the words of Aristotle himself (Top. viii. 13. ---- 2, 3). 'People seem to beg the question in five ways. First and most glaringly, when one takes for granted the very thing that has to be proved. This by itself does not readily escape detection, but in the case of "synonyms," that is, where the name and the definition have the same meaning, it does so more easily. [Footnote: Some light is thrown upon this obscure pa.s.sage by a comparison with Cat. I. -- 3, where 'synonym' is defined. To take the word here in its later and modern sense affords an easy interpretation, which is countenanced by Alexander Aphrodisiensis, but it is flat against the usage of Aristotle, who elsewhere gives the name 'synonym,' not to two names for the same thing, but to two things going under the same name. See Trendelenberg on the pa.s.sage.]

Secondly, when one a.s.sumes universally that which has to be proved in particular, as, if a man undertaking to prove that there is one science of contraries, were to a.s.sume that there is one science of opposites generally. For he seems to be taking for granted along with several other things what he ought to have proved by itself.

Thirdly, when one a.s.sumes the particulars where the universal has to be proved; for in so doing a man is taking for granted separately what he was bound to prove along with several other things. Again, when one a.s.sumes the question at issue by splitting it up, for instance, if, when the point to be proved is that the art of medicine deals with health and disease, one were to take each by itself for granted.

Lastly, if one were to take for granted one of a pair of necessary consequences, as that the side is incommensurable with the diagonal, when it is required to prove that the diagonal is incommensurable with the side.'

-- 876. To sum up briefly, we may beg the question in five ways--

(1) By simply asking the opponent to grant the point which requires to be proved;

(2) by asking him to grant some more general truth which involves it;

(3) by asking him to grant the particular truths which it involves;

(4) by asking him to grant the component parts of it in detail;

(5) by asking him to grant a necessary consequence of it.

-- 877. The first of these five ways, namely, that of begging the question straight off, lands us in the formal fallacy already spoken of (-- 838), which violates the first of the general rules of syllogism, inasmuch as a conclusion is derived from a single premiss, to wit, itself.

-- 878. The second, strange to say, gives us a sound syllogism in Barbara, a fact which countenances the blasphemers of the syllogism in the charge they bring against it of containing in itself a pet.i.tio principii. Certainly Aristotle's expression might have been more guarded. But it is clear that his quarrel is with the matter, not with the form in such an argument. The fallacy consists in a.s.suming a proposition which the opponent would be ent.i.tled to deny. Elsewhere Aristotle tells us that the fallacy arises when a truth not evident by its own light is taken to be so. [Footnote: [Greek: otan t me di auto gnostn di auto tis epicheirae deiknunai, tot' ateitai t ex arches.]. a.n.a.l. Pr. II. 16. -- I ad fin.]

-- 879. The third gives us an inductio per enumerationem simplicem, a mode of argument which would of course be unfair as against an opponent who was denying the universal.

-- 880. The fourth is a more prolix form of the first.

-- 881. The fifth rests on Immediate Inference by Relation (-- 534).

-- 882. Under the head of pet.i.tio principii comes the fallacy of Arguing in a Circle, which is incidental to a train of reasoning. In its most compressed form it may be represented thus--

(1) B is A.

C is B.

.'. C is A.

(2) C is A.

B is C.

.'. B is A.

-- 883. The Fallacy of Non causa pro causa ([Greek: t me aition] or [Greek: aitoin]) is another, the name of which has led to a complete misinterpretation. It consists in importing a contradiction into the discussion, and then fathering it on the position controverted. Such arguments, says Aristotle, often impose upon the users of them themselves. The instance he gives is too recondite to be of general interest.

-- 884. Lastly, the Fallacy of Many Questions ([Greek: t ta deo erotemata en poiein]) is a deceptive form of interrogation, when a single answer is demanded to what is not really a single question. In dialectical discussions the respondent was limited to a simple 'yes'

or 'no'; and in this fallacy the question is so framed as that either answer would seem to imply the acceptance of a proposition which would be repudiated. The old stock instance will do as well as another--'Come now, sir, answer "yes" or "no." Have you left off beating your mother yet?' Either answer leads to an apparent admission of impiety.

A late Senior Proctor once enraged a man at a fair with this form of fallacy. The man was exhibiting a blue horse; and the distinguished stranger asked him--'With what did you paint your horse?'

EXERCISES.

These exercises should be supplemented by direct questions upon the text, which it is easy for the student or the teacher to supply for himself.

PART I.

CHAPTER I.

Cla.s.sify the following words according as they are categorematic, syncategorematic or acategorematic;--

come peradventure why through inordinately pshaw therefore circ.u.mspect puss grand inasmuch stop touch sameness back cage disconsolate candle.

CHAPTER II.

Cla.s.sify the following things according as they are substances, qualities or relations;--

G.o.d likeness weight blueness gra.s.s imposition ocean introduction thinness man air spirit Socrates raillery heat mortality plum fire.

CHAPTER III.

1. Give six instances each of-attribute, abstract, singular, privative, equivocal and relative terms.

2. Select from the following list of words such as are terms, and state whether they are (1) abstract or concrete, (2) singular or common, (3) univocal or equivocal:--

van table however enter decidedly tiresome very b.u.t.t Solomon infection bluff Czar short although Caesarism distance elderly Nihilist.

3. Which of the following words are abstract terms?--

quadruped event through hate desirability thorough fact expressly thoroughness faction wish light inconvenient will garden inconvenience volition grind.

4. Refer the following terms to their proper place under each of the divisions in the scheme:--