[.'.] Death will overtake him.

The advantage of the Hypothetical form in argument is that it is simpler. It was much used in Mediaeval Disputation, and is still more popular than the Categorical Syllogism. Perhaps the prominence given to Hypothetical Syllogisms as syllogisms in Post-Renaissance text-books is due to the use of them in the formal disputations of graduands in the Universities. It was the custom for the Disputant to expound his argument in this form:--

If so and so is the case, such and such follows.

So and so is the case.

[.'.] Such and such follows.

To which the Respondent would reply: _Accipio antecedentem, nego consequentiam_, and argue accordingly. Petrus Hispanus does not give the Hypothetical Syllogism as a Syllogism: he merely explains the true law of Reason and Consequent in connexion with the Fallacia Consequentis in the section on Fallacies. (_Summulae. Tractatus Sextus._)

II.--DISJUNCTIVE SYLLOGISMS.

A Disjunctive Syllogism is a syllogism in which the Major Premiss is a DISJUNCTIVE PROPOSITION, _i.e._, one in which two propositions are declared to be mutually incompatible. It is of the form Either A is B, or C is D.[3]

If the disjunction between the alternatives is really complete, the form implies four hypothetical propositions:--

(1) If A is B, C is not D.

(2) If A is not B, C is D.

(3) If C is D, A is not B.

(4) If C is not D, A is B.

Suppose then that an antagonist has granted you a Disjunctive Proposition, you can, using this as a Major Premiss, extract from him four different Conclusions, if you can get him also to admit the requisite Minors. The Mode of two of these is technically called MODUS PONENDO TOLLENS, the mode that denies the one alternative by granting the other--A is B, _therefore_ C is not D; C is D, _therefore_ A is not B. The other Mode is also twice open, the MODUS TOLLENDO PONENS--A is not B, _therefore_ C is D; C is not D, _therefore_ A is B.

Fallacy is sometimes committed through the Disjunctive form owing to the fact that in common speech there is a tendency to use it in place of a mere hypothetical, when there are not really two incompatible alternatives. Thus it may be said "Either the witness is perjured, or the prisoner is guilty," when the meaning merely is that if the witness is not perjured the prisoner is guilty. But really there is not a valid disjunction and a correct use of the disjunctive form, unless four hypotheticals are implied, that is, unless the concession of either involves the denial of the other, and the denial of either the concession of the other. Now the prisoner may be guilty and yet the witness be perjured; so that two of the four hypotheticals, namely--

If the witness is perjured, the prisoner is not guilty, If the prisoner is guilty, the witness is not perjured--

do not necessarily hold. If, then, we would guard against fallacy, we must always make sure before assenting to a disjunctive proposition that there is really a complete disjunction or mutual incompatibility between the alternatives.

III.--THE DILEMMA.

A Dilemma is a combination of Hypothetical and Disjunctive propositions.

The word has passed into common speech, and its ordinary use is a clue to the logical structure. We are said to be in a dilemma when we have only two courses open to us and both of them are attended by unpleasant consequences. In argument we are in this position when we are shut into a choice between two admissions, and either admission leads to a conclusion which we do not like. The statement of the alternatives as the consequences hypothetically of certain conditions is the major premiss of the dilemma: once we admit that the relations of Antecedent and Consequent are as stated, we are in a trap, if trap it is: we are on the horns of the dilemma, ready to be tossed from one to the other.

For example:--

If A is B, A is C, and if A is not B, A is D. But A either is or is not B. Therefore, A either is C or is D.

If A acted of his own motive, he is a knave; if A did not act of his own motive, he is a catspaw. But A either acted of his own motive or he did not. Thereupon A is either a knave or a catspaw.

This is an example of the _Constructive_ Dilemma, the form of it corresponding to the common use of the word as a choice between equally unpleasant alternatives. The standard example is the dilemma in which the custodians of the Alexandrian Library are said to have been put by the Caliph Omar in 640 A.D.

If your books are in conformity with the Koran, they are superfluous; if they are at variance with it, they are pernicious. But they must either be in conformity with the Koran or at variance with it. Therefore they are either superfluous or pernicious.

Where caution has to be exercised is in accepting the clauses of the Major. We must make sure that the asserted relations of Reason and Consequent really hold. It is there that fallacy is apt to creep in and hide its head. The Alexandrian Librarians were rash in accepting the first clause of the conqueror's Major: it does not follow that the books are superfluous unless the doctrines of the Koran are not merely sound but contain all that is worth knowing. The propounder of the dilemma covertly assumes this. It is in the facility that it affords for what is technically known as _Petitio Principii_ that the Dilemma is a useful instrument for the Sophist. We shall illustrate it further under that head.

What is known as the _Destructive_ Dilemma is of a somewhat different form. It proceeds upon the denial of the Consequent as involving the denial of the Antecedent. In the Major you obtain the admission that if a certain thing holds, it must be followed by one or other of two consequences. You then prove by way of Minor that neither of the alternatives is true. The conclusion is that the antecedent is false.

We had an example of this in discussing whether the inference in the Hypothetical Syllogism is Immediate. Our argument was in this form:--

If the inference is immediate, it must be drawn either from the Major alone or from the Minor alone. But it cannot be drawn from the Major alone, neither can it be drawn from the Minor alone. Therefore, it is not immediate.

In this form of Dilemma, which is often serviceable for clearness of exposition, we must as in the other make sure of the truth of the Major: we must take care that the alternatives are really the only two open. Otherwise the imposing form of the argument is a convenient mask for sophistry. Zeno's famous dilemma, directed to prove that motion is impossible, covers a _petitio principii_.

If a body moves, it must move either where it is or where it is not. But a body cannot move where it is: neither can it move where it is not. Conclusion, it cannot move at all, _i.e._, Motion is impossible.

The conclusion is irresistible if we admit the Major, because the Major covertly assumes the point to be proved. In truth, _if_ a body moves, it moves neither where it is nor where it is not, but from where it is to where it is not. Motion consists in change of place: the Major assumes that the place is unchanged, that is, that there is no motion.

[Footnote 1: For the history of Hypothetical Syllogism see Mansel's _Aldrich_, Appendix I.]

[Footnote 2: It may be argued that the change is not merely grammatical, and that the implication of a general proposition in a hypothetical and _vice versa_ is a strictly logical concern. At any rate such an implication exists, whether it is the function of the Grammarian or the Logician to expound it.]

[Footnote 3: Some logicians prefer the form Either A is, or B is. But the two alternatives are propositions, and if "A is"

represents a proposition, the "is" is not the Syllogistic copula. If this is understood it does not matter: the analysis of the alternative propositions is unessential.]

CHAPTER VIII.

FALLACIES IN DEDUCTIVE ARGUMENT.--PETITIO PRINCIPII AND IGNORATIO ELENCHI.

The traditional treatment of Fallacies in Logic follows Aristotle's special treatise [Greek: Peri sophistikon elenchon]--Concerning Sophistical Refutations--Pretended Disproofs--Argumentative Tricks.

Regarding Logic as in the main a protection against Fallacies, I have been going on the plan of taking each fallacy in connexion with its special safeguard, and in accordance with that plan propose to deal here with the two great types of fallacy in deductive argument. Both of them were recognised and named by Aristotle: but before explaining them it is worth while to indicate Aristotle's plan as a whole.

Some of his Argumentative Tricks were really peculiar to Yes-and-No Dialectic in its most sportive forms: but his leading types, both Inductive and Deductive, are permanent, and his plan as a whole has historical interest. Young readers would miss them from Logic: they appeal to the average argumentative boy.

He divides Fallacies broadly into Verbal Fallacies ([Greek: para ten lexin], _in dictione_), and Non-Verbal Fallacies ([Greek: exo tes lexeos], _extra dictionem_).

The first class are mere Verbal Quibbles, and hardly deserve serious treatment, still less minute subdivision. The world was young when time was spent upon them. Aristotle names six varieties, but they all turn on ambiguity of word or structure, and some of them, being dependent on Greek syntax, cannot easily be paralleled in another tongue.

(1) Ambiguity of word ([Greek: homonymia]). As if one were to argue: "All cold can be expelled by heat: John's illness is a cold: therefore it can be expelled by heat". Or: "Some afflictions are cheering, for afflictions are sometimes light, and light is always cheering".

The serious confusion of ambiguous words is met by Definition, as explained at length in pt. ii. c i.

(2) _Ambiguity of structure_ ([Greek: amphibolia]).

"What he was beaten with was what I saw him beaten with: what I saw him beaten with was my eye: therefore, what he was beaten with was my eye."

"How do you do?" "Do? Do what?" "I mean, how do you feel?" "How do I feel? With my fingers, of course; but I can see very well." "No, no; I mean, how do you find yourself?" "Then why did you not say so? I never exactly noticed, but I will tell you next time I lose myself."

(3) _Illicit conjunction_ ([Greek: synthesis]).

Socrates is good. Socrates is a musician. Therefore Socrates is a good musician.

(4) _Illicit disjunction_ ([Greek: diairesis]).

Socrates is a good musician. Therefore he is a good man.