arts, such as printing, &c. would be of unknown antiquity: and on the same supposition, there would be records long prior to the Mosaic; and likewise the sea and land, in all parts of the globe, might be expected to maintain the same relative situations now as formerly but none of these is the fact: therefore the world is not eternal." Again, "if the world existed from eternity, there would be records prior to the Mosaic; and if it were produced by chance, it would not bear marks of design: there are no records prior to the Mosaic; and the world does bear marks of design: therefore it neither existed from eternity, nor is the work of chance." These are commonly called Dilemmas, but hardly differ from simple conditional Syllogisms, two or more being expressed together. Nor is the case different if you have one antecedent with several consequents, which consequents you disjunctively deny; for that comes to the same thing as wholly denying them; since if they be not all true, the one antecedent must equally fall to the ground; and the Syllogism will be equally simple: e. g. "if we are at peace with France by virtue of the treaty of Paris, we must acknowledge the sovereignty of Buonaparte; and also we must

* A.D. 1815.

acknowledge that of Louis: but we cannot do both of these; therefore we are not at peace,' &c.; which is evidently a simple Destructive. The true Dilemma is, " a conditional Syllogism with several antecedents in the major, and a disjunctive minor;" hence,

Dilemma.

3d. That is most properly called a destructive Destructive Dilemma, which has (like the constructive ones) a disjunctive minor Premiss; i. e. when you have several Antecedents with each a different Consequent; which Consequents (instead of wholly denying them, as in the case lately mentioned) you disjunctively deny; and thence, in the Conclusion, deny disjunctively the Antecedents: e. g. 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. "If this man were wise, he would not speak irreverently of Scripture in jest; and if he were good he would not do so in earnest; but he does it, either in jest, or earnest; therefore he is either not wise or not good."

a Dilemma.

Every Dilemma may be reduced into two or Resolution of more simple Conditional Syllogisms: e. g. "If Æschines joined, &c. he is inconsistent; he did join, &c. therefore he is inconsistent ;" and

* The name Dilemma implies precisely two antecedents; and hence it is common to speak of "the horns of a dilemma;" but it is evident there may be either two or

more.

again, "if Æschines did not join, &c. he is unpatriotic; he did not, &c. therefore he is unpatriotic." Now an opponent might deny either of the minor Premises in the above Syllogisms, but he could not deny both; and therefore he must admit one or the other of the Conclusions: for, when a Dilemma is employed, it is supposed that some one of the Antecedents must be true (or, in the destructive kind, some one of the Consequents false), but that we cannot tell which of them is so; and this is the reason why the argument is stated in the form of a Dilemma.

Sometimes it may happen that both antecedents may be true, and that we may be aware of this; and yet there may be an advantage in stating (either separately or conjointly) both arguments, even when each proves the same conclusion, so as not to derive any additional confirmation from the other; still, I say, it may sometimes be advisable to state both, because, of two propositions equally true, one man may deny or be ignorant of the one, while he admits the other, and another man, vice versa.

From what has been said, it may easily be seen that all Dilemmas are in fact conditional syllogisms; and that Disjunctive Syllogisms may also be reduced to the form of Conditionals: but as it has been remarked, that

all Reasoning whatever may ultimately be brought to the one test of Aristotle's "Dictum,” it remains to show how a Conditional Syllogism may be thrown into such a form, that that test will at once apply to it; and this is called the

Reduction of Hypotheticals.*

§ 6.

For this purpose we must consider every Conditional Proposition as a universal affirmative categorical Proposition, of which the

* Aldrich has stated, through a mistake, that Aristotle utterly despised Hypothetical Syllogisms, and thence made no mention of them; but he did indicate his intention to treat of them in some part of his work, which either was not completed by him according to his design, or else (in common with many of his writings) has not come down

to us.

.

Aldrich observes, that no hypothetical argument is valid which cannot be reduced to a categorical form; and this is evidently agreeable to what has been said at the beginning of Chap. iii.; but then he has unfortunately omitted to teach us how to reduce Hypotheticals to this form ; except in the case where the Antecedent and Consequent chance to have each the same subject; in which case, he tells us to take the minor Premiss and Conclusion as an Enthymeme, and fill that up categorically; e. g. “If Cæsar was a tyrant, he deserved death: he was a tyrant; therefore he deserved death;" which may easily be reduced to a categorical form, by taking as a major Premiss, "all tyrants deserve death." But when (as is often the case) the Antecedent and Consequent have not each the same

Terms are entire Propositions, viz. the antecedent answering to the Subject, and the consequent to the Predicate; e. g. to say, "if Louis is a good king, France is likely to prosper," is equivalent to saying, "the case of Louis being a good king, is a case of France being likely to prosper:" and if it be granted, as a minor Premiss to the Conditional Syllogism, that "Louis is a good king," that is equivalent to saying, "the present case is the case of Louis being a good king;" from which you will draw a conclusion in Barbara, (viz. "the present case is a case of France being likely to prosper,") exactly

subject, (as in the very example he gives, "if A is B, C is D,") he gives no rule for reducing such a Syllogism as has a Premiss of this kind; and indeed leads us to suppose that it is to be rejected as invalid, though he has just before demonstrated its validity. And this is likely to have been one among the various causes which occasion many learners to regard the whole system of Logic as a string of idle reveries, having nothing true, substantial, or practically useful in it; but of the same character with the dreams of Alchymy, Demonology, and judicial Astrology. Such a mistake is surely the less inexcusable in a learner, when his master first demonstrates the validity of a certain argument, and then tells him that after all it is good for nothing; (prorsus repudiandum.) In the late editions of Aldrich's Logic, all that he says of the reduction of Hypotheticals is omitted; which certainly would have been an improvement, if a more correct one had been substituted; but as it is, there is a complete hiatus in the system.