term must be dealt with as belonging either to the one or the other, and this is all that logical law professes to do.

Again, Mill gives us the following:

Every son of A is either B or C or D;

But a son of A is dead;

Therefore either B or C or D is dead.

The major proposition here, we are told, does not rest on the law of Excluded Middle, or on any necessity of thought, but on my knowledge of the fact. Did Mill really for a moment suppose that any one with common intelligence of the sphere of the Law of Excluded Middle ever imagined that the law informed him of this fact or any fact? At the same time, once the logician is furnished with this major, -that every son of A is either B or C or D,-the law of Identity will tell him, that every absolutely precludes more sons than those specified, that every cannot be interchanged with more than those specified. And on the strength of this Law and that of Excluded Middle, I am able to conclude that the dead son must be either B, C, or D, for if these were not thought as exhaustive, and as thus limiting the inference within them,-if there might be more,-the dead son need not be either B, C, or D, but possibly E.

But we are immediately told by Mill that the judgment, every animal is either a man or a brute, is founded on the Law of Excluded Middle. Such a judgment is not in any proper sense "founded" on this law; the law simply regulates the mutual exclusion of the terms. The true form of this judgment is,-every animal is either a man or not a man. That is all that the law says or can say. It does not enable us to identify not-man and brute. We must have the further knowledge, through comparison of the features of man and brute, that brute can be identified with what is not-man. The principle of Excluded Middle is here simply the scheme or form under which the otherwise known opposition of man and brute becomes logically available. Having found these, or having been given them, as opposed, we state the opposition in virtue of, or as a case of, the law of Exclusion between opposites.

§ 659. There is still a third form of Syllogism, which results from a major proposition which is at once hypothetical and disjunctive. Thus:-If A is, then either B or C is. Here the relation of the antecedent to the consequent is not affirmed directly, but only through mutually exclusive predicates. The reasoning then proceeds to sublate or remove the entire consequent :

If A is, then either B or C is;

But neither B nor Cis;

Therefore A is not.

We have now what is known as the Hypothetico-Disjunc

tive Syllogism, or the Dilemma, called also Cornutus or Horned Syllogism. It is called horned, because in the sumption the disjunctive members of the consequent are opposed like horns to the assertion of the adversary. With these we throw it from one side to the other in the subsumption, in order to toss it altogether away in the conclusion.2

§ 660. Krug gives the following cautions regarding the legitimacy of the Dilemma, and they are well deserving of consideration. In sifting a dilemma, we ought to ask

(1.) Whether a veritable consequence subsists between the antecedent and consequent of the sumption?

(2.) Whether the opposition in the consequent is thoroughgoing and valid?

(3.) Whether in the subsumption the disjunctive members are legitimately sublated?3

Krug gives the following example which violates those conditions:

If virtue were a habit worth acquiring, it must ensure either power, or wealth, or honour, or pleasure;

But virtue ensures none of these ;

Therefore virtue is not a habit worth acquiring.*

Ueberweg borrows from Krug the following, which he characterises as "a scientifically justifiable trilemma" :—

If the actually existing world were not the best of all possible worlds, then God did not either know the best, or could not create and preserve it, or did not wish to create or preserve it. But (because of the divine wisdom, omnipotence, and goodness) neither the first, second, nor third is true. Hence the actual world is the best of all possible worlds.5

§ 661. The older view of logicians regarding the Dilemma takes in more than this form. It was recognised by Hamilton as a reasoning having a conditional major premiss with several antecedents, and a disjunctive minor. This is the view, among others, of Whately and Mansel. Dilemma would properly indicate two antecedents, but it is used to include

1 Cf. Hamilton, Logic, iii. p. 350.

2 Krug, Logik, § 85; Hamilton, Logic, iii. p. 352.
3 Logik, § 87.

4 Cf. Hamilton, Logic, iii. pp. 352, 353.

5 See Krug, Logik, § 87; Ueberweg, Logic, p. 459.

more than two-and in this case may properly be Trilemma, Tetralemma, Polylemma.

§ 662. Its forms are as follow, and they are regulated by the combined laws of Hypothetical and Disjunctive Reasoning:

I. SIMPLE CONSTRUCTIVE.

If A is B, C is D, and if X is Y, C is D;
But either A is B, or X is Y;

Therefore C is D.

Here the common consequent is inferred.

II. COMPLEX CONSTRUCTIVE.

If A is B, C is D, and if X is Y, E is F;
But either A is B, or X is Y;

Therefore either C is D, or E is F.

The point of these two forms is, that whatever alternative be chosen, the same conclusion is inevitable.

III. DESTRUCTIVE.

If A is B, C is D, and if X is Y, E is F;
But either C is not D, or E is not F;
Therefore either A is not B, or X is not Y.

512

CHAPTER XXXVIII.

FALLACIES —FORMAL AND MATERIAL. (1.) FORMAL FALLACIES,

§ 663. Fallacy, in the widest sense of the term, includes every form of reasoning, or apparent reasoning, which leads to a conclusion either invalid, or such as ought not to be accepted, because of a fault in one or both of the premisses. A reasoning may be bad (1.) because the conclusion does not follow from the premisses; (2.) because the premiss or premisses are false in point of fact, or unduly assumed; (3.) because the conclusion is not the proof of the point which it is adduced to prove, or which the reasoner professes to prove.

§ 664. A fallacy is regarded either as a Paralogism or a Sophism, the former when the person reasoning is in error, either as to premiss or conclusion, and is at the same time unaware of it; the latter, when a reasoning, bad either in matter or form, or in both, is employed with a full consciousness of it on the part of the writer or speaker, and thus with the purpose of deceiving. This, of course, is of no logical importance. What the science of Logic professes to do is to deal with the essential character of the reasoning itself, -so far as its rules can reach it.

§ 665. Aristotle divides fallacies into two classes-viz., those παρὰ τὴν λέξιν and ἔξω τῆς λέξεως, or, as it was afterwards put, in dictione et extra dictionem-in the expression and beyond it. Under the first head-in Dictione-he classes six fallacies-viz. (1.) dμwvvμía (equivocation); (2.) åμpißoλía (ambiguity); (3.) oúvbeois (fallacia a sensu diviso ad sensum com

positum); (4.) diaípeois (fallacia a sensu composito ad sensum divisum) ; (5.) προσῳδία (accent); (6.) σχῆμα τῆς λέξεως (figura dictionis).

§ 666. Under the second head-extra Dictionem-he has seven classes: (1.) πapà тò ovμßeßŋkós (fallacia ratiocinationis ex accidente); (2.) tò ánλôs ʼn μỳ ánλws (a dicto simpliciter ad dictum secundum quid); (3.) ʼn Tоû èλéyxov äɣvola (ignoratio elenchi); (4.) Tарà тò éπóμevov (fallacia ratiocinationis ex consequente ad antecedens); (5.) τὸ ἐν ἀρχῇ λαμβάνειν αἰτεῖσθαι (petitio principii); (6.) тò μǹ aitiov is aÏTiov Tibévai (fallacia de non causa ut causa); (7.) τὸ τὰ πλείω ἐρωτήματα ἓν ποιεῖν (fallacia plurium interrogationum).1

§ 667. Aristotle has thus really anticipated all the forms of fallacy which have been dealt with by subsequent logicians. But the division into in Dictione et extra Dictionem is not satisfactory or well founded. The class, in Dictione, may properly be referred to fallacies in the inference,-to cases, in fact, in which the conclusion does not follow from the premisses, that is, Formal Fallacies.

§ 668. Those under the second head, extra Dictionem, may as a rule be referred either to the class of formal fallacies, or to that of Material Fallacies, in which the conclusion, while following from the premisses, is based on false or irrelevant premisses. This will appear as we proceed.

§ 669. There is, properly speaking, no specific class of the fallacies of language (in Dictione). Language may doubtless give rise to incorrect or invalid inference, but it does so because it leads to a violation of formal or logical law,— chiefly, in fact, to the making use of four instead of three terms in a reasoning. This is known as quaternio terminorum, or the logical quadruped. This is most commonly manifested in what is known as Ambiguous Middle; in other words, in the use of a term which indicates more than one notion, and which is taken in a double sense in the reasoning. For the ambiguity of a word does not necessarily lead to invalidity of inference, unless in so far as the ambiguity is made use of in the reasoning process.

§ 670. The only sound division of Fallacies accordingly is into―(1.) those in which the fault is in the reasoning process itself,-in other words, those in which the conclusion 1 Top. viii. 11; De Soph. Elench., § i., c. iv. v.