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All X is Y ;
All Y is Z;
No X is Y;
All Y is Z; .:. No X is Z;
... No X is Z, it is not valid though we have merely substituted ‘ No’ for 'All' or 'No X' for ' All X' throughout, without affecting the jingle. Indeed if we had only said “No-X'instead of * No X’ the reasoning in the last case would have been precisely similar to that in the first and just as valid. Again
if we say
Five francs are a dollar;
Four shillings are a dollar; ... Five francs are four shillings, the inference is perfectly valid; but if we say in precisely similar form
Blades of grass are green;
Frogs are green; .:. Blades of grass are frogs, the inference is not valid. The reason is, of course, that the copula ‘are' is used in different senses in the two syllogisms; but when we do not stop to think of the sense, the familiar jingle, assisted perhaps in this case by some recollection of Euclid's axiom that “things equal to the same thing are equal to each other’, lures us on to danger.
In spite of a real confusion of meaning sometimes associated with some of these ' purely logical fallacies', they can hardly be called the result of bad thinking; because they are not the result of thinking at all, but only of a reflex act. On this account it might have been more appropriate to call them the Reflex Fallacies or the Jingle Fallacies.
As there are two classes of verbal fallacies, so also there
are two classes of the material or non-verbal fallacies, which may be called respectively Fallacies of the Forgotten Issue and Fallacies of the Ill-conceived of material
fallacies. Universe. Fallacies of the Forgotten Issue are not particularly characteristic of deduction; but some of them are usually discussed in connection with it, and therefore we shall speak of them in the next chapter. In the chapter after that we shall discuss Fallacies of the Ill-conceived Universe. These do not belong to the traditional field of deduction, because there are no rules for verbal manipulation which they break. Yet I have tried to show that all deductive inference depends upon the assumption that things have certain general relations, and that deductive fallacies occur when these relations are overlooked; and if this is correct these fallacies of the Ill-conceived Universe are essentially similar to the fallacies of deduction in their ultimate nature, though they may not be caused like them by a verbal jingle.
Nothing has been said in the foregoing pages about the fallacy known as 'Non Sequitur'. This name is really applicable, as the words imply, to every argument in which the conclusion does not follow, and in Sequitur. this sense of the words every fallacy is a Non Sequitur. But the phrase is often applied in a more restricted sense to those arguments only in which the conclusion does not even appear to follow, except perhaps to the most hasty and careless of reasoners; as in the following examples: The earth is round; therefore there is no atmosphere on the
Every one desires happiness, and virtuous people are happy, therefore every one desires to be virtuous.”
Episcopacy is of Scripture origin, the Church of England is the only established church in England; ergo the church established is the church that should be supported." subject requires no further consideration.
A Fallacy of the Forgotten Issue is committed when we forget what it was that an argument was intended to prove, and either take that very thing or something equivalent to it and quite as doubtful for granted, or else prove something which is not equivalent to the point at issue and then assume that we have proved the point itself. In the first case the fallacy is called Petitio Principii or Begging the Question. In the second it is called Ignoratio Elenchi, or a fallacy of Irrelevance. Each of these two fallacies of the forgotten issue takes several forms.
The fallacy of Petitio Principii is not committed unless there is a show of proof. Nobody commits it who merely Petitio
says “ I assume these conclusions to be true, and Principii.
I do not try to prove them'. But a person does commit it if he thinks he is proving his conclusions when he is really assuming them, or is assuming a premise that is not admitted or would not be admitted its real significance were understood. Often the premise is actually proved from the conclusion, or 'is such as would naturally and properly be so proved'. But in any case in which the fallacy is present the conclusion seems to be more fully proved by the argument than it really is, because it is not clearly understood how nearly equivalent is that which is taken for granted to that which is to be proved; e.g., Whoever refuses to believe in the inspiration of the Bible makes the Most High a deceiver; for has he not told us that ' All scripture is given by inspiration of God'?” Of course we have no reason to believe that it was really God who said that all scripture is given by his inspiration unless we already assume that the Bible or some part of it is inspired.
Whately directs attention to the fact that the English language is peculiarly“ suitable for the fallacy of Petitio Principii, from its being formed from two distinct languages, and thus abounding in synonymous expressions which have no resemblance in sound, and no connection in etymology; so that a Sophist may bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of Norman origin; e.g., ' To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the community, that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments'
A blunder of this same sort is committed when a student says that two chemicals are sure to unite since they have an affinity for each other; or that he knows unsupported objects will fall to the earth from the fact that they are attracted towards it.
“Connected with this fallacy is the rhetorical device [already discussed] of Question-begging Epithets. Thus, though the matter we are discussing is open to dispute, we may speak of a nefarious project, a laudable am
Includes bition, an astute act, a far-sighted policy, and epithets. so on, attempting, by means of a carefully selected epithet, to assume the point at issue, or at least to create an unfair prejudice in the mind of the hearer or reader whom we address. "'*
When a conclusion is based upon a premise which in an earlier stage of the argument was itself based upon this very conclusion, the reasoning is said
* Fowler's “ Deductive Logic" (Clarendon Press).
to be in a Circle (Circulus in Probando). Here are some
A is C;
C is B;
.:. A is B. Some mechanicians attempt to prove (what they ought to lay down as a probable but doubtful hypothesis) that every particle of matter gravitates equally; 'why?' because those bodies which contain more particles ēver gravitate more strongly, i.e., are heavier: 'but (it may be urged) those which are heaviest are not always more bulky; still they contain more particles, though more closely condensed ; ' “how do you know that ?''because they are heavier; ' "how does that prove it ?' 'because all particles of matter gravitating equally, that mass which is specifically the heavier must needs have the more of them in the same space' (Whately). Any man who would marry such a woman must have something wrong with him.' 'Why, what is the matter with his wife?' It is matter enough to be willing to marry such a man as he is.'
If there are a large number of intermediate steps and the argument is a long one it may be very difficult to detect the circle. This fallacy, like a good many others, can be best guarded against by making the shortest and simplest possible summary of any argument that claims our interest.
Ignoratio Elenchi or Irrelevance, the other fallacy of the forgotten issue, consists merely in arguing beside the point. “I am required by the circumstances of the case (no matter Ignoratio
why) to prove a certain conclusion; I prove,
not that, but one which is likely to be mistaken for it;—in this lies the fallacy. . . . For instance, instead of proving that this prisoner has committed an atrocious fraud', you prove that 'the fraud he is accused of is atrocious’; instead of proving, as in the well-known tale of Cyrus and the two coats, that 'the taller boy had a right