XVII. to say nothing, as the first clause is only a special LECT. application of the rule common to all syllogisms that the conclusion can contain nothing more than the premises, and must, therefore, follow the weaker part; and the second is self-evident, as only a special application of the principle of Excluded Middle, for, on this law, if one contradictory be affirmed in the subsumption, the other must be denied in the conclusion, and if one contradictory be denied in the subsumption, the other must be affirmed in the conclusion. junctive of Compre Extension. The Disjunctive, like every other species of syllo- The Disgism, may be either a reasoning in the quantity of Syllogism Comprehension, or a reasoning in the quantity of Ex-hension and tension. The contrast, however, of these two quantities is not manifested in the same signal manner in the disjunctive as in the categorical deductive syllogism, more especially of the first figure. In the categorical deductive syllogism, the reasonings in the two counter quantities are obtrusively distinguished by a complete conversion, not only of the internal significance, but of the external appearance of the syllogism. For not only do the relative terms change places in the relation of whole and part, but the consecution of the antecedents is reversed; the minor premise in the one syllogism becoming the major premise in the other. This, however, is not the case in disjunctive syllogisms. Here the same proposition is, in both quantities, always the major premise; and the whole change that takes place in converting a disjunctive syllogism of the one quantity into a disjunctive syllogism of the other, is in the silent reversal of the copula from one of its meanings to another. This, however, as it determines no apparent difference in single propositions, and as the disjunctive sumption remains XVII. LECT. always the same proposition, out of which the subsumption and the conclusion are evolved, in the one quantity as in the other, the reversal of the sumption, from extension to comprehension, or from comprehension to extension, occasions neither a real nor Examples. an apparent change in the syllogism. Take, for example, the disjunctive syllogism : - Plato is either learned or unlearned ; But Plato is learned; Therefore, Plato is not unlearned. Now let us explicate this into an intensive and into an extensive syllogism. As an Intensive Syllogism it will stand : Plato comprehends either the attribute learned or the attribute unlearned; But Plato comprehends the attribute learned; Therefore, &c. As an Extensive Syllogism it will stand :— Plato is contained either under the class learned, or under the class unlearned; But Plato is contained under the class learned; Therefore, &c. From this it appears, that, though the difference of reasoning in the several quantities of comprehension and extension obtains in disjunctive, as in all other syllogisms, it does not, in the disjunctive syllogism, determine the same remarkable change in the external construction and consecution of the parts, which it does in categorical syllogisms. LECTURE XVIII. STOICHEIOLOGY. SECT. II.-OF THE PRODUCTS OF THOUGHT. III. DOCTRINE OF REASONINGS. SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO B. CONDITIONAL.-HYPOTHETICAL AND HYPOTHETICO DISJUNCTIVE. XVIII. HAVING now considered Categorical and Disjunctive LECT Syllogisms, the next class of Reasonings afforded by the difference of Internal or Essential Form is the Hypothetical; and the general nature of these syllogisms is expressed in the following paragraph :— 2. Hypothe gism,-its character. ¶ LXV. An Hypothetical Syllogism is a rea- Par. LXV. soning whose form is determined by the law of tical sylloReason and Consequent. It is, therefore, regu- general lated by the two principles of which that law is the complement, the one,-With the reason, the consequent is affirmed; the other,-With the consequent, the reason is denied: and these two principles severally afford the condition of its Affirmative or Constructive, and of its Negative or Destructive, form (Modus ponens et Modus tollens). The sumption or general rule in such a syllogism is necessarily an hypothetical proposition (If A is, then B is). In such a proposition VOL. I. Y LECT. it is merely enounced that the prior member (A) and the posterior member (B) stand to each other in the relation of reason and consequent, if existing, but without it being determined whether they really exist or not. Such determination must follow in the subsumption and conclusion; and that, either by the absolute affirmation of the antecedent in the subsumption, and the illative affirmation of the consequent in the conclusion (the modus ponens); or by the absolute negation of the consequent in the subsumption, and the illative negation of the antecedent in the conclusion (the modus tollens)." The general form of an hypothetical syllogism is, therefore, the following:Common Sumption-If A is, then B is; Explication. B 1) MODUS PONENS-Si poteris possum; sed tu potes; ergo ego possum. a [For use of terms ponens and tollens, see Boethius, De Syllogismo Hypothetico, Opera, p. 611; Wolf, Phil. Rat., § 406-410. Mark Duncan uses the terms “a positione ad positionem," and "a remotione ad remotionem."] [Institutiones Logica, L. iv. c. 6, § 4, p. 240. Cf. p. 243, Salmurii, 1812.-ED.] 8 [On the Hypothetical Syllogism in general, see Ammonius, In de Interp., Procem., f. 3, Venetiis, 1546; Philopouus, In Anal. Prior., i. c. 23, f. 60, Venet., 1536; Magentinus, In Anal. Prior., f. 16 b; Alex. Aphrodisiensis, In Anal. Prior., ff. 87, 88, 109, 130, Ald., 1520; In Topica, f. 65, Ald., 1513; Anonymous Author, On Syllogisms, f. 44, ed. 1536; Scheibler, Opera Logica, pars iv. p. 548; Bolzano, Wissenschaftslehre, Logik, ii. p. 560; Waitz, Organon, In An. Prior., i. c. 23.] These lines are the Author's own.-ED. XVIII. logism in Contains 1°, "Like every other species of simple syllogism LECT the Hypothetical is made up of three propositions, a sumption, a subsumption, and a conclusion. There 1 Hypomust, in the first place, be an hypothetical proposition general. holding the place of a general rule, and from this pro- three propoposition the other parts of the syllogism must be de-sitions. duced. This first proposition, therefore, contains a sumption. But as this proposition contains a relative and correlative member,-one member, the relative clause, enouncing a thing as conditioning; the other, the correlative clause, enouncing a thing as conditioned; and as the whole proposition enounces merely the dependency between these relatives, and judges nothing in regard to their existence considered apart and in themselves, this enouncement must be made in a second proposition, which shall take out of the sumption one or other of its relatives, and categorically enounce its existence or its non-existence. This second proposition contains, therefore, a subsumption ; and, through this subsumption, a judgment is likewise determined, in a third proposition, with regard to the other relative. This last proposition, therefore, contains the conclusion proper of the syllogism. kind of the mo and modus "But as the sumption in an hypothetical syllogism In an hypothetical sylcontains two relative clauses, an antecedent and a logism there is competent consequent,-it, therefore, appears double; and as a twofold either of its two members may be taken in the sub- reasoning, sumption, there is, consequently, competent a twofold dus ponens kind of reasoning. For we can either, in the first place, tollens. conclude from the truth of the antecedent to the truth of the consequent; or, in the second place, conclude from the falsehood of the consequent to the falsehood of the antecedent. The former of these modes of hypothetical inference constitutes what is sometimes called |