SECTION II.-OF THE PRODUCTS OF THOUGHT. III.-DOCTRINE OF REASONINGS. SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO B. CONDITIONAL. -HYPOTHETICAL AND HYPOTHETICO- 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 Par. LXV. reasoning whose form is determined by the law tical sylloof Reason and Consequent. It is, therefore, re- general gulated 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 it is merely VOL. I. Y LECT. 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; 1, MODUS PONENS: α 2, MODUS TOLLENS: Explication. B 1) MODUS PONENS-Si poteris possum; sed tu potes; ergo ego possum. 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. Hypothetical syllogism in general. Contains 1°, "Likeevery other species of simple syllogism LECT the Hypothetical is made up of three propositions,a sumption, a subsumption, and a conclusion. There must, in the first place, be an hypothetical proposition holding the place of a general rule, and from this pro- three propoposition the other parts of the syllogism must be sitions. deduced. 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." is competent kind of -the mo and modus "But as the sumption in an hypothetical syllogism In a hypothetical sylcontains two relative clauses, an antecedent and a con- logism there sequent,-it, therefore, appears double; and as either a twofold of its two members may be taken in the subsumption, reasoning, there is, consequently, competent a twofold kind of dus ponens reasoning. For we can either, in the first place, con-tollens. clude 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 the XVIII. LECT. Constructive Hypothetical, but more properly the 2o, Its peculiar prin law of Reason and Consequent. Modus Tollens-If Socrates be virtuous, he merits esteem; So much for the character of the Hypothetical Syllogism in general. I now proceed to consider its peculiar principle. 2°, "If the essential nature of an Hypothetical ciple, the Syllogism consist in this, that the subsumption affirms or denies one or other of the two parts of a thought, standing to each other in the relation of the thing conditioning and the thing conditioned, it will be the law of an hypothetical syllogism, that,-If the condition or antecedent be affirmed, so also must be the conditioned or consequent, and that if the conditioned or consequent be denied, so likewise must be the condition or antecedent. But this is manifestly nothing else than the law of Sufficient Reason or of a Krug, Logik, § 81, Anm. 1, p. 254. Compare Esser, Logik, § 90, p. 172.-ED. B [Nomenclature of Theophrastus, Eudemus, and other Peripatetics, in regard to Hypothetical Syllogism, in contrast with that of the Stoics. Πράγματα, νοήματα, φωναί (Peripatetic), are called by the Stoics respectively, TUYxávovтa, èкpopiká, λEKτά. Here, If it be day is called το ἡγούμevov, both by Peripatetics and by Stoics; the sun is on the earth, is called Tò éπóμevov by Peripatetics, Tò Anyor by Stoics. The whole, If it be day, the sun is on the earth, is called Tò συνημμένον by Peripatetics, τὸ τροπι κόν by Stoics : But it is day, is μετάAnis to Peripatetics, póσλnyis to Stoics. Therefore the sun is on the earth is ovμnépаoμa to Peripatetics, Take this Hypothetical Syllogism:- popά to Stoics. See Philoponus, In Anal. Prior., L. i. c. 23, f. 60 a, If it be day, the sun is on the earth; ed. Venet. 1536. Brandis, Scholia, p. Therefore, the sun is on the earth. α XVIII. How Reason and Consequent." The principle of this LECT syllogism is thus variously enounced,-Posita conditione, ponitur conditionatum; sublato conditionato, enounced. tollitur conditio. Or otherwise,-A ratione ad rationatum, a negatione rationati ad negationem rationis, valet consequentia. The one alternative of either rule being regulative of the modus ponens, the other of the modus tollens.B cannot con the truth of antecedent, falsehood of dent to the "But here it may be asked, why, as we conclude Why we from the truth of the antecedent to the truth of the clude from consequent (a ratione ad rationatum), and from the the conse falsehood of the consequent to the falsehood of the quote antecedent (a negatione rationati ad negationem ra- and from the tionis), can we not conversely conclude from the truth the anteceof the consequent to the truth of the antecedent, and falsehood of from the falsehood of the antecedent to the falsehood the conseof the consequent? In answer to this question, it is manifest that this could be validly done, only on the following supposition-viz., if every consequent had only one possible antecedent; and if, from an antecedent false as considered absolutely and in itself, it were impossible to have consequents true as facts. "Thus, in the first place, it is incompetent to conclude, that because B exists, that is, because the consequent member of the sumption, considered as an absolute proposition, is true, therefore the supposed reason A exists, that is, therefore the alleged antecedent member must be true; for B may have other reasons besides A, such as C or D. In like manner, in the second place, we should not be warranted to infer, that because the supposed reason A is unreal, and the antecedent member false, therefore the result B is also unreal, and the consequent member false; for the ED. a Esser, Logik, § 91, p. 174.— B See Kant, Logik, §§ 75, 76. Krug, quent. |