Deductive Logic Part 49

-- 849. The Fallacy of Composition [Greek: diairesis] is likewise a case of ambiguous construction. It consists, as expounded by Aristotle, in taking words together which ought to be taken separately, e.g.

'Is it possible for a man who is not writing to write?'

'Of course it is.'

'Then it is possible for a man to write without writing.'

And again--

'Can you carry this, that, and the other?' 'Yes.'

'Then you can carry this, that, and the other,'--

a fallacy against which horses would protest, if they could.

-- 850. It is doubtless this last example which has led to a convenient misuse of the term 'fallacy of composition' among modern writers, by whom it is defined to consist in arguing from the distributive to the collective use of a term.

-- 851. The Fallacy of Division ([Greek: diairesis]), on the other hand, consists in taking words separately which ought to be taken together, e.g.

[Greek: ego s' eteka dolon ont' eleuteron [Footnote: Evidently the original of the line in Terence's _Andria_, 37,--feci ex servo ut esses libertus mihi.],

where the separation of [Greek: dolon] from [Greek: ontra] would lead to an interpretation exactly contrary to what is intended.

And again--

[Greek: pentekont' andron ekatn lipe dios achilleus],

where the separation of [Greek: andron] from [Greek: ekatn] leads to a ludicrous error.

Any reader whose youth may have been nourished on 'The Fairchild Family' may possibly recollect a sentence which ran somewhat on this wise--'Henry,' said Mr. Fairchild, 'is this true? Are you a thief and a liar too?' But I am afraid he will miss the keen delight which can be extracted at a certain age from turning the tables upon Mr. Fairchild thus--Henry said, 'Mr. Fairchild, is this true? Are _you_ a thief and a liar too?'

-- 852. The fallacy of division has been accommodated by modern writers to the meaning which they have a.s.signed to the fallacy of composition. So that by the 'fallacy of division' is now meant arguing from the collective to the distributive use of a term. Further, it is laid down that when the middle term is used distributively in the major premiss and collectively in the minor, we have the fallacy of composition; whereas, when the middle term is used collectively in the major premiss and distributively in the minor, we have the fallacy of division. Thus the first of the two examples appended would be composition and the second division.

(1) Two and three are odd and even.

Five is two and three.

.'. Five is odd and even.

(2) The Germans are an intellectual people.

Hans and Fritz are Germans.

.'. They are intellectual people.

-- 853. As the possibility of this sort of ambiguity is not confined to the middle term, it seems desirable to add that when either the major or minor term is used distributively in the premiss and collectively in the conclusion, we have the fallacy of composition, and in the converse case the fallacy of division. Here is an instance of the latter kind in which the minor term is at fault--

Anything over a hundredweight is too heavy to lift.

These sacks (collectively) are over a hundredweight.

.'. These sacks (distributively) are too heavy to lift.

-- 854. The ambiguity of the word 'all,' which has been before commented upon (-- 119), is a great a.s.sistance in the English language to the pair of fallacies just spoken of.

-- 835. The Fallacy of Accent ([Greek: prosodia]) is neither more nor less than a mistake in Greek accentuation. As an instance Aristotle gives Iliad xxiii. 328, where the ancient copies of Homer made nonsense of the words [Greek: t men ou kataputetai ombro] by writing [Greek: o] with the circ.u.mflex in place of [Greek: ou] with the acute accent. [Footnote: This goes to show that the ancient Greeks did not distinguish in p.r.o.nunciation between the rough and smooth breathing any more than their modern representatives.] Aristotle remarks that the fallacy is one which cannot easily occur in verbal argument, but rather in writing and poetry.

-- 856. Modern writers explain the fallacy of accent to be the mistake of laying the stress upon the wrong part of a sentence. Thus when the country parson reads out, 'Thou shall not bear false witness _against_ thy neighbour,' with a strong emphasis upon the word 'against,' his ignorant audience leap [sic] to the conclusion that it is not amiss to tell lies provided they be in favour of one's neighbour.

-- 857. The Fallacy of Figure of Speech [Greek: t schema tes lexeos]

results from any confusion of grammatical forms, as between the different genders of nouns or the different voices of verbs, or their use as transitive or intransitive, e.g. [Greek: ugiainein] has the same grammatical form as [Greek: temnein] or [Greek: okodomein], but the former is intransitive, while the latter are transitive. A sophism of this kind is put into the mouth of Socrates by Aristophanes in the Clouds (670-80). The philosopher is there represented as arguing that [Greek: kapdopos] must be masculine because [Greek: Kleonumos] is. On the surface this is connected with language, but it is essentially a fallacy of false a.n.a.logy.

-- 858. To this head may be referred what is known as the Fallacy of Paronymous Terms. This is a species of equivocation which consists in slipping from the use of one part of speech to that of another, which is derived from the same source, but has a different meaning. Thus this fallacy would be committed if, starting from the fact that there is a certain probability that a hand at whist will consist of thirteen trumps, one were to proceed to argue that it was probable, or that he had proved it.

-- 859. We turn now to the tricks of refutation which lie outside the language, whether the deception be due to the a.s.sumption of a false premiss or to some unsoundness in the reasoning.

-- 860. The first on the list is the Fallacy of Accident ([Greek: t sumbebekos]). This fallacy consists in confounding an essential with an accidental difference, which is not allowable, since many things are the same in essence, while they differ in accidents. Here is the sort of example that Aristotle gives--

'Is Plato different from Socrates ?' 'Yes.' 'Is Socrates a man ?'

'Yes.' 'Then Plato is different from man.'

To this we answer--No: the difference of accidents between Plato and Socrates does not go so deep as to affect the underlying essence. To put the thing more plainly, the fallacy lies in a.s.suming that whatever is different from a given subject must be different from it in all respects, so that it is impossible for them to have a common predicate. Here Socrates and Plato, though different from one another, are not so different but that they have the common predicate 'man.'

The attempt to prove that they have not involves an illicit process of the major.

-- 861. The next fallacy suffers from the want of a convenient name. It is called by Aristotle [Greek: t aplos tode e pe legestai ka me kupios] or, more briefly, [Greek: t aplos e me], or [Greek: t pe kai aplos], and by the Latin writers 'Fallacia a dicto secundum quid ad dictum simpliciter.' It consists in taking what is said in a particular respect as though it held true without any restriction, e.g., that because the nonexistent ([Greek: t me on]) is a matter of opinion, that therefore the non-existent is, or again that because the existent ([Greek: t on]) is not a man, that therefore the existent is not. Or again, if an Indian, who as a whole is black, has white teeth, we should be committing this species of fallacy in declaring him to be both white and not-white. For he is only white in a certain respect ([Greek: pe]), but not absolutely ([Greek: aplos]). More difficulty, says Aristotle, may arise when opposite qualities exist in a thing in about an equal degree. When, for instance, a thing is half white and half black, are we to say that it is white or black? This question the philosopher propounds, but does not answer. The force of it lies in the implied attack on the Law of Contradiction. It would seem in such a case that a thing may be both white and not-white at the same time. The fact is--so subtle are the ambiguities of language--that even such a question as 'Is a thing white or not-white?' straightforward, as it seems, is not really a fair one. We are ent.i.tled sometimes to take the bull by the horns, and answer with the adventurous interlocutor in one of Plato's dialogues--'Both and neither.' It may be both in a certain respect, and yet neither absolutely.

-- 862. The same sort of difficulties attach to the Law of Excluded Middle, and may be met in the same way. It might, for instance, be urged that it could not be said with truth of the statue seen by Nebuchadnezzar in his dream either that it was made of gold or that it was not made of gold: but the apparent plausibility of the objection would be due merely to the ambiguity of language. It is not true, on the one hand, that it was made of gold (in the sense of being composed entirely of that metal); and it is not true, on the other, that it was not made of gold (in the sense of no gold at all entering into its composition). But let the ambiguous proposition be split up into its two meanings, and the stringency of the Law of Excluded Middle will at once appear--

(1) It must either have been composed entirely of gold or not.

(2) Either gold must have entered into its composition or not.

-- 863. By some writers this fallacy is treated as the converse of the last, the fallacy of accident being a.s.similated to it under the t.i.tle of the 'Fallacia a dicto simpliciter ad dictum secundum quid.' In this sense the two fallacies may be defined thus.

The Fallacy of Accident consists in a.s.suming that what holds true as a general rule will hold true under some special circ.u.mstances which may entirely alter the case. The Converse Fallacy of Accident consists in a.s.suming that what holds true under some special circ.u.mstances must hold true as a general rule.

The man who, acting on the a.s.sumption that alcohol is a poison, refuses to take it when he is ordered to do so by the doctor, is guilty of the fallacy of accident; the man who, having had it prescribed for him when he was ill, continues to take it morning, noon, and night, commits the converse fallacy.

-- 864. There ought to be added a third head to cover the fallacy of arguing from one special case to another.

-- 865. The next fallacy is Ignoratio Elenchi [Greek: elegchou agnoia]. This fallacy arises when by reasoning valid in itself one establishes a conclusion other than what is required to upset the adversary's a.s.sertion. It is due to an inadequate conception of the true nature of refutation. Aristotle therefore is at the pains to define refutation at full length, thus--

'A refutation [Greek: elegchos] is the denial of one and the same--not name, but thing, and by means, not of a synonymous term, but of the same term, as a necessary consequence from the data, without a.s.sumption of the point originally at issue, in the same respect, and in the same relation, and in the same way, and at the same time.'

The ELENCHUS then is the exact contradictory of the opponent's a.s.sertion under the terms of the law of contradiction. To establish by a syllogism, or series of syllogisms, any other proposition, however slightly different, is to commit this fallacy. Even if the substance of the contradiction be established, it is not enough unless the identical words of the opponent are employed in the contradictory. Thus if his thesis a.s.serts or denies something about [Greek: lopion], it is not enough for you to prove the contradictory with regard to [Greek: mation]. There will be need of a further question and answer to identify the two, though they are admittedly synonymous. Such was the rigour with which the rules of the game of dialectic were enforced among the Greeks!

-- 866. Under the head of Ignoratio Elenchi it has become usual to speak of various forme of argument which have been labelled by the Latin writers under such names as 'argumentum ad hominem,' 'ad populum,' 'ad verecundiam,' 'ad ignorantiam,' 'ad baculum'--all of them opposed to the 'argumentum ad rem' or 'ad judicium.'

-- 867. By the 'argumentum ad hominem' was perhaps meant a piece of reasoning which availed to silence a particular person, without touching the truth of the question. Thus a quotation from Scripture is sufficient to stop the mouth of a believer in the inspiration of the Bible. Hume's Essay on Miracles is a noteworthy instance of the 'argumentum ad hominem' in this sense of the term. He insists strongly on the evidence for certain miracles which he knew that the prejudices of his hearers would prevent their ever accepting, and then asks triumphantly if these miracles, which are declared to have taken place in an enlightened age in the full glare of publicity, are palpably imposture, what credence can be attached to accounts of extraordinary occurrences of remote antiquity, and connected with an obscure corner of the globe? The 'argumentum ad judicium' would take miracles as a whole, and endeavour to sift the amount of truth which may lie in the accounts we have of them in every age. [Footnote: On this subject see the author's _Attempts at Truth_ (Trubner & Co.), pp. 46-59.]

-- 868. In ordinary discourse at the present day the term 'argumentum ad hominem' is used for the form of irrelevancy which consists in attacking the character of the opponent instead of combating his arguments, as ill.u.s.trated in the well-known instructions to a barrister--'No case: abuse the plaintiff's attorney.'

-- 869. The 'argumentum ad populum' consists in an appeal to the pa.s.sions of one's audience. An appeal to pa.s.sion, or to give it a less question-begging name, to feeling, is not necessarily amiss. The heart of man is the instrument upon which the rhetorician plays, and he has to answer for the harmony or the discord that comes of his performance.

-- 870. The 'argumentum ad verecundiam' is an appeal to the feeling of reverence or shame. It is an argument much used by the old to the young and by Conservatives to Radicals.

-- 871. The 'argumentum ad ignorantiam' consists simply in trading on the ignorance of the person addressed, so that it covers any kind of fallacy that is likely to prove effective with the hearer.