exchanged while their relation remains unaltered, there may also be a change in the Relation itself. This occurs when an hypothetical is formed from a simple categorical judgment (which is always possible), or when several hypothetical are formed from a disjunctive categorical judgment, or when the converse of both cases happens. The possibility of this change of form rests on this:

1. The relation of inherence always includes a certain dependence of the predicate upon the subject, which may always be made conspicuous when it is treated by itself, and is expressed in an hypothetical judgment.

2. The disjunctive judgment is the comprehensive expression of several hypothetical judgments, and may be resolved into them as easily as these mutually-related hypothetical judgments may be reduced to a disjunctive judgment.

From the judgment: A is B, the judgment: If A is, в is, may be deduced. But the categorical judgment is not always correct, when the hypothetical is; for the latter does not proceed upon the hypothesis of the existence of A, but only on the fact that B stands in a relation of inherence together with A. From the judgment: Every A, which is B, is c, follows the judgment: If A is B, A is C; and the latter, which presupposes the existence of such a which are B, may be reduced. to the former. The judgment: A is either B or C, divides into the mutually connected hypothetical judgments: If A is B, it is not C, and If A is c, it is not B; If A is not B, it is c, and If A is not C, it is B. And the latter may be again reduced to the former.

The possibility of this Change of Relation does not prove1 that difference of Relation is only verbal, and has no logical or

1 As several modern logicians believe-viz. Herbart, Einleit. §§ 53, 60 Rem.; Beneke, Log. i. 163 ff.; Dressler, Denklehre, 199 ff.

metaphysical significance. If this view were correct, the change of form could be accomplished, without alteration of the material constituent parts of the judgment, equally well by changing the hypothetical judgment into a categorical as by changing the categorical into an hypothetical. But this is not the case. The transformation of the hypothetical judgment into a categorical is only admissible, in so far as a relation of inherence is connected with the relation of dependence, and the existence of the subject is ensured, as it is in the cases adduced above. It is not possible whenever the hypothetical judgment is given: If A is B, C is D; for the fact that A is в does not stand in the same relation to the fact that c is D, that a does to B or C does to D. The former is not the latter, nor can it be considered to be a kind of the latter. But the A is a B, and can be held to be a kind of B. There is not only a verbal, but a logico-metaphysical difference, which reveals itself indeed in language, the flexible garment or rather the organic body of thought, but belongs originally to thought itself. One fundamental relation exists between the parts of the hypothetical judgment, and another between those of the categorical. The two are essentially related and connected with each other,' but they are not to be thought identical. Cf. §§ 68, 85.

§ 95. Subalternation (Subalternatio) is the passing over from the whole sphere of the subject-notion to a part of it, and conversely from a part to the whole. By Subalternation follows:

1. From the truth of the universal categorical judgment (Sa Por Se P) the truth of the corresponding particular (Si P or So P), but not conversely the former from the latter.

1 Cf. Trendelenburg, Log. Unters. 2nd ed. i. 343; 3rd ed. 351: 'The settled product of causality is substance;' 2nd ed. i. 355; ii. 246; 3rd ed. i. 363; ii. 270.

2. From the falsehood of the particular the falsehood of the universal judgment, but not conversely the former from the latter.

The proof for the correctness of the first consequence lies in this, that the subalternate judgment repeats an assertion lying in the subalternant, and only asserts as true what is already recognised to be true. The second consequence is founded on this, that, if the universal judgment be true, then (according to 1) the particular is true, which contradicts the hypothesis. The converse consequences, however, are not universally valid, because the truth of the particular judgment may co-exist along with the falsehood of the universal, because it may happen that Some S are and others are not P.

The same laws hold good of hypothetical judgments (If A is, B always is-At least in some cases, if a is, b is also).

The consequence from the universal to the particular is called consequentia or conclusio ad subalternatam propositionem, that from the particular to the universal conclusio ad subalternantem.

The older logicians were accustomed to express the law of consequence, ad subalternatam propositionem, in the dictum de omni et nullo, in the following way: quidquid de omnibus valet, valet etiam de quibusdam et singulis; quidquid de nullo valet, nec de quibusdam vel singulis valet.'

§ 96. By (qualitative) AEQUIPOLLENCE (aequipollentia) modern Logic means the agreement in sense of two judgments of different Quality. This agreement becomes possible by the fact that the predicate notions stand in

the relation of contradictory opposition to each other. Consequence per aequipollentiam proceeds from the judgment: All S are P, to the judgment: No S is not-P, and vice versâ; from the judgment: No S is P, to the judgment: Every S is a Not-P, and vice versâ; from the judgment: Some S are P, to the judgment: Some S are not Not-P, and vice versâ; and lastly from the judgment: Some S are not P, to the judgment: Some S are Not-P, and vice versa.

The proof for the correctness of these consequences lies in the relation of the spheres, according to which every S, which does not fall within the sphere of P, is outside it, and must lie in the sphere of Not-P; and whatever falls within this cannot lie within the sphere of P.

Every sin contradicts the conscience; there is no sin which does not contradict the conscience. Nothing sinful is in harmony with the ethical consciousness; whatever is sinful is not in harmony with the ethical consciousness.

The earlier logicians' understand by ἰσοδυναμοῦσαι προTáσus, iudicia aequipollentia sive convenientia, every kind of equivalent judgments, i.e. those which with material identity are necessarily true or false together because of their form. (Cf. the expression avтioтpépe found in Aristotle.2)

Kant and some modern logicians with him will not allow the inferences of Aequipollency to be inferences proper, because there is no consequence, and the judgments remain unchanged even according to form. They are to be looked at only as substitutions of words which denote one and the same

notion. But since in Aequipollency the Quality of the judg

1 Cf. § 82.

2 De Interpret. c. xiii. p. 22 A, 16.

3 Log. ed. Jäsche, § 47, Rem.

ment passes over to its opposite, however trivial the change may be which here exists, it evidently concerns the form of the judgment itself, and not its mere verbal expression.

§ 97. Opposition (oppositio) exists between two judgments of different Quality and different sense with the same content.

By Opposition follows (cf. §§ 71 and 72) :—

1. From the truth of one judgment the falsehood of its contradictory opposite, since according to the axiom of contradiction (§ 77) judgments opposed contradictorily cannot both be true;

2. From the falsehood of a judgment the truth of its contradictory opposite, since according to the axiom of Excluded Third (§ 78) judgments opposed as contradictories cannot both be false;

3. From the truth of one judgment the falsehood of the contrary opposite (but not conversely from the falsehood of the one the truth of the other), according to the axiom that judgments opposed as contraries cannot both be true (though both may be false). Otherwise the assertions opposed as contradictories, which (according to § 95) are contained in them and may be deduced by Subalternation, must both be true, and the axiom of Contradiction does not admit this (but their common falsehood includes neither the truth nor the falsehood of assertions which are opposed to each other as contradictories);

4. From the falsehood of a judgment the truth of its subcontrary (but not conversely from the truth of the one to the falsehood of the other), according to the axiom, that subcontrary judgments cannot be both false