after it, and the other 'bought in the market' with some such phrase as 'and cooked at home' understood after it. The Fallacy of Accident as defined above includes both the Fallacia a dicto simpliciter ad dictum secundum quid and the Fallacia a dicto secundum quid ad dictum simpliciter,—that is, both the fallacy of arguing from a simple statement to a statement under a certain condition, and the fallacy of arguing from a statement under a certain condition to a simple statement. There is another fallacy of a similar nature, in which the reasoning proceeds from a statement under a certain condition to a statement under a different condition. All the three forms of the Fallacy of Accident are due to the ambiguity of language and may be easily avoided by stating the meaning of the propositions in clear and unambiguous language.

In conclusion, it appears that all the different kinds of Semilogical Fallacies arising from ambiguous language are really different forms of the fallacy of Ambiguous Middle, and, in rare cases, of Ambiguous Extreme. In some the middle term is in itself ambiguous, having two meanings in the same form or in different forms or parts of speech. In others the ambiguity arises from some of the words being ambiguous, or from the grammatical structure of the sentence being ambiguous. But an ambiguous term, whatever be the source of its ambiguity, is really equivalent to two terms; and all the forms of ambiguous middle and of ambiguous extreme are really transgressions of the first syllogistic rule, that is, they are all fallacies of four

terms.

§ 5. (2) The fallacies or faults arising from the violation of the rules of Logical Division and Definition have been already explained under those subjects, and do not require any separate treatment here.

B.-NON-LOGICAL OR MATERIAL FALLACIES.

These fallacies do not properly belong to Deductive Logic, as they are concerned about the subject-matter of reasoning. The more important of them are: (1) the Petitio Principii, including

the 'Argument in a Circle,' and 'Begging the Question'; (2) the Falsity of Premiss; and (3) the Ignoratio Elenchi, or the Fallacy of Irrelevancy, or, as it is sometimes called, the Irrelevant Conclusion.

6. (I)-Of the Petitio Principii.

This fallacy in its simplest form occurs when a proposition is proved by another proposition, and this other is again proved by the first. For example, 'A is, because B is; and B is, because A is.' Here the conclusion is proved by the premiss, and the premiss by the conclusion; and the fallacy is quite evident, and consists really in proving 'A is' by 'A is,'—the same by the same, idem per idem.

In the following example, the major premiss of the 1st syllogism is proved by the 2nd, and the major premiss of the 2nd by the 1st syllogism:—

Here 'S is P' is proved by a syllogism whose major premiss is 'M is P,' and this premiss is proved by a syllogism whose major premiss is 'S is P.' Thus, 'S is P' is proved with the aid of 'M is P,' and 'M is P' is proved with the aid of 'S is P': therefore 'S is P' is proved by 'S is P.' In this also the fallacy is almost quite evident. But if the two syllogisms here placed one after the other were, respectively, the first and the last of a long train of reasoning, it would not be so easy to detect the fallacy. And this difficulty is still further increased partly by the difference of language in which the same proposition may occur in different parts of the train, and partly by the omission of many intervening syllogisms. For example—

In this train of reasoning the final conclusion in the 4th syllogism is the same as the minor premiss of the 1st, that is, this premiss is proved by the 4th syllogism. But how is this final conclusion established? By using as a premiss the proposition 'A is E,' which has been itself proved by taking the final conclusion A is B' as a premiss in the first syllogism. Thus the final conclusion is really established by taking itself as à premiss in a part of the train of reasoning.

In the 1st syllogism, 'A is C' is proved by taking ‘A is B’ as a premiss.

In the 2nd, ‘A is D' is proved by taking ‘A is C’as a premiss, and therefore by indirectly taking ‘A is B' as a premiss.

In the 3rd, 'A is E' is proved by taking 'A is D' as a premiss, and therefore by taking indirectly 'A is B' as an ultimate premiss.

In the 4th, 'A is B' is proved by taking 'A is E' as a premiss, and therefore by taking indirectly 'A is B' as an ultimate premiss. That is, 'A is B' is proved by 'A is B.'

Or the fallacy may be exposed thus:-A is C, because A is B; and A is B, because A is E (4th syllogism), and A is E, because A is D (3rd syllogism), and A is D, because A is C (2nd syllogism), therefore A is B, because A is C. Thus 'A is B' is proved by 'A is C,' and 'A is C' is proved by 'A is B.' Here the use of the symbols has enabled us to detect the fallacy easily; but if the language of the last syllogism were different from that of the first, and if, moreover, some of the intervening syllogisms were suppressed, the train being much longer than that represented above, it would not be so easy to detect the fallacy, and expose it by analysing the whole train.

The Petitio Principii in the stricter sense may, then, be defined as a fallacy in which the conclusion is proved by means of itself, or in which the conclusion is the same as one of the premisses. In the wider sense it includes also those fallacies in which the conclusion follows from, or is presupposed by, one premiss independently of the others. For example—

Those who are mortal are not immortal;

.. No man is immortal.

In order to prove the conclusion 'No man is immortal,' two premisses are advanced, and the argument is apparently stated in the form of a syllogism; but the conclusion really follows immediately from, or is presupposed by, the first or minor premiss 'All men are mortal,' which obverted gives the conclusion directly.

In the stricter sense, the Petitio Principii is called the Argument in a Circle because the final conclusion is the same as the first premiss, because the reasoning coming back whence it started, completes a circle. In the wider sense, including all forms, it is called Begging the Question, because it begs or surreptitiously takes for granted a proposition which is identical in meaning with, or is a consequence of, the very proposition to be proved.

§ 7. (2) Of the Falsity of Premiss.

The next fallacy under this head is the Falsity of Premiss. This fallacy occurs when one of the premisses is false; when something is regarded as a cause of an event, which is really not the cause, which is either merely a sign or an antecedent of it. It is also called Non causa pro causa, the assuming as a cause that which is not a cause, and Post hoc ergo propter hoc, or after this, and therefore on account of, or caused by, this.

Whately thus distinguishes the Petitio Principii from Non causa pro causa: "Let the name then of 'petitio principii' (begging the question)," he says, "be confined to those cases in which one of the Premisses either is manifestly the same in sense with the Conclusion, or is actually proved from it, or is such as the persons you ́are addressing are not likely to know, or to admit, except as an inference from the Conclusion; as, for example, if any one should infer the authenticity of a certain history, from its recording such and such facts, the reality of which rests on the evidence of that history. All other cases in which a Premiss (whether the expressed or the suppressed

one) has no sufficient claim to be admitted, I shall designate as the Fallacy of undue assumption of a Premiss1."

Whately gives the following as an example of "the Argument in a Circle":"Some mechanicians attempt to prove (what they ought to have laid down as a probable, but doubtful, hypothesis) that every particle of matter gravitates equally: 'why?' 'because those bodies which contain more particles ever gravitate more strongly or are heavier'; but (it may be urged) those which are heaviest are not always more bulky? 'no, but 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 2.'"

There is a smaller circle in the following instance: "If any one argues that you ought to submit to the guidance of himself, or his leader, or his party, &c., because these maintain what is right; and then argues that what is so maintained is right, because it is maintained by persons whom you ought to submit to, and that these are himself and his party"."

The fallacy of Non causa pro causa occurs when a sign is mistaken for a cause, or whenever the relation of cause and effect is reversed, the effect being regarded as the cause, and the cause as the effect, or when a premiss assumed is false. For instance, "A great deal of money in a country is a pretty sure proof of its wealth; and thence has been often regarded as a cause of it; whereas in truth it is an effect." "So also exposure to want and hardship in youth has been regarded as a cause of the hardy constitution of those men and brutes which have been brought up in barren countries of uncongenial climate. Yet the most experienced cattle-breeders know that animals are, cæteris paribus, the more hardy for having been well fed and sheltered in youth; while early hardships, by destroying all the tender, ensure