matter of the judgment, or in that about which I think. I express the state of mind produced by this necessity by must, as I might express a generalisation from experience by will, or an objective possibility by may or can; but all these are properly distinctions arising from the matter or application of the complex subject or predicate, which is really change having a cause, all bodies gravitating, this seed growing. These refer to degrees of my knowledge, founded no doubt on objective fact, but none the less capable of being stated in a plainly assertory form.

That the simple assertion is the essential and only necessary thing, is proved by the fact that it alone is sufficient to guarantee a necessity of inference. All A is B, all C is A, all C is B, is as valid as all A must be B, all C must be A, therefore all C must be B. Whatever be the relation of the terms, as to material connection, this does in no way affect the necessity of the inference.

(b) "There is no modal enunciation,” says Valla; "there is necessity and possibility in the conclusion, as there is truth in all parts of the argumentation. For all must be true whether you say it is necessary, or possible, or easy, or honourable, or anything else. In this respect the true is the same as the certain, for nothing is true that is not certain and confessed. But the truth of the two prior parts of the syllogism and argumentation is placed as certain and confessed; in the last, however-that is, in the conclusion-it is extorted, and therefore there is in it necessity or quasi necessity."-(Dialectica, L. ii. c. 39, f. 50a, ed. 1530.)

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CHAPTER XXI.

COMPOSITE JUDGMENTS—HYPOTHETICAL OR CONDITIONAL,
DISJUNCTIVE, DILEMMATIC.

$320. Looking to the special relation of the subject to the predicate of a judgment, as direct (or unconditional), or indirect (or conditional), we have, as has been already said, the various forms of judgment, known as Categorical, and Composite or Conditional. For we may assert directly, absolutely, or simply one thing of another—that an attribute belongs to the subject-or that something will be or happen, or needs to be thought, if only something else in the first place happens or is thought. We may say A is B, or if A is, then B is. If the sun is up, then it is day. A is either B or not-B. A is either B or C or D. The world is either eternal or not-eternal. The world is either the work of chance, or the work of intelligence. This intelligence is either a single act in a remote past, or it is a continuous act. We have thus the Hypothetical Judgment (called also Conjunct and Conjunctive) if is, there is; or the Disjunctive Judgment-this is either, or. To these should be added the Hypothetico-Disjunctive, also called Dilemmatic, being a combination of the two first-mentioned, as if A is B, it is either C or D.

(a) With Aristotle categorical (karnyopikós) means affirmative. In later usage, it is applied to a judgment of simple or absolute assertion or denial, as opposed to the hypothetical or disjunctive judgment.-(Cf. Hamilton, Logic, L. xiii.) Aristotle cannot be said to have recognised the distinction of categorical and conditional (conjunctive and disjunctive) judgments, at least as grounds of reasoning, so as to form hypothetical and disjunctive syllogisms. This distinction or addition to the Aristotelian view seems to be due to Theophrastus and Eudemus. It was among the Latins elaborated by Boethius.-(De Syllogisimo Hypothetico.)

(b) With regard to the use of Hypothetical and Conditional, it ought to be noted that the former is sometimes employed to mark the genus of Conditional and Disjunctive judgments, as by Aldrich and Whately. This usage ought not to be followed. Conditional is better suited to mark the genus of which hypothetical and disjunctive are species, though even this term is not unambiguous.-(Cf. Hamilton, Logic, L. xiii.)

§ 321. The Hypothetical or Conditional judgment is a statement of relation between an antecedent and a consequent, or reason and result. The form lies in the connection or consequence. If A is, B is; or B is on the supposition or condition that A is. Should a stormy wind blow, that wall will fall. In this form of judgment, the condition or hypothesis is attached to the antecedent or subject.

§ 322. The hypothetical judgment thus differs from the categorical, inasmuch as the latter affirms an attribute existing in a subject, or a subject as belonging to a certain class; whereas the affirmation, mental or real, of the consequent in a hypothetical judgment, depends on the previous or contemporaneous affirmation of the subject. It is one thing to say-Lying is dishonourable; it is quite another to say-If this man lies, he dishonours himself. In the former case we affirm an attribute of a subject; in the latter we do not properly affirm, but state a supposition or sequence following the realisation of a definite hypothesis. This is simply a preparation for absolute affirmation. It is not wholly determinate.

§ 323. In the hypothetical judgment there are three elements-the Antecedent, the Consequent, the Connection or Sequence-as, If A is B, C is D. A being B is the antecedent, C is D is the consequent. If is, or if then, is the copula, and indicates the sequence. The effect of the copula is to bind up antecedent and consequent into one act of judgment. It is, in fact, a statement simply of connection. As Ammonius Hermieæ puts it: "Hypothetic enouncements are made up of categoric. For they express the consequence or opposition of one categoric proposition and another, uniting them with each other, by either the conjunctive or disjunctive particles, in order to show that they constitute together a single enouncement."

"1

1 On De Interpretatione, f. 3, 1546. Quoted by Hamilton, Logic ii., Appendix B, p. 389.

§ 324. The sequence, moreover, is a necessary one; for we are supposed to have in the antecedent a reason, full and adequate, otherwise there would be no reason at all for the consequent. This may be founded on material considerations of causality in the antecedent; but this is merely the ground, more or less valid, of the reason, or cause as a reason,—in a word, of the necessary form into which we suppose ourselves entitled to put the particular sequence. If the one thing is, the other thing is. This formula, however grounded in any partic ular sequence, is yet independent of the given sequence, and raises the connection to the form of a necessary one,-necessary in our thinking. Even if the reason or antecedent given were found to be insufficient to warrant the consequent, this would not affect the validity of the principle of connection, but only its material truth. At the same time, the principal value in practice of hypothetical judgment and reasoning is the material truth or actual sufficiency of connection between antecedent and consequent in any given case.

§ 325. The Hypothetical judgment may be regarded as in Extension, and as in Comprehension. In the former case, the formula will be,-If A is, B is; if man is, animal is. If all A is B, then C (a part of A) is D (a part of B). Or, If all man is animal, European (a part of man) is mortal (a part of animal). Here the supreme law or canon regulating the inference will be simply that of Identity. In this case Reason and Consequent will be completely identified with the formal law of the relation of whole and part.

In the latter case-in Comprehension-the formula will be-(a) If A is, B is; if the sun is up, it is day. (b) If A have for its mark B, then C (a mark of B) is a mark of A. If the moon presents always the same face to the earth, then, having no diurnal revolution on her axis (a mark of always presenting the same face to the earth) is a mark of the moon. The law which immediately governs this proposition, or rather the inference from it, is-A mark of the mark is a mark of the thing itself, or Prædicatum prædicati est prædicatum subjecti. Nota nota est nota rei ipsius.

The subject in this case is taken comprehensively, as that which has immediate and mediate marks or attributes. The strength or validity of the assertion lies in the connection, however materially grounded, between the immediate and the

mediate attributes. This may depend on inherence or causality, on coexistence or succession, and affects the actual truth of the judgment; but the form or supposition being given, we are able logically, independently of this, to educe the formal consequence.

§ 326. In the Disjunctive judgment, the essence or form lies in the opposition or contrast of the several members of the predicate, as A is either B or not-B; A is either B or C or D. The opposition among the disjunct members means that one is to be affirmed, and one only. There is just this much truth or assumption, that the subject is to be found in one or other of the members, and, if found in one, is not to be found in the other or others. In the former case, or strictest kind of disjunction, the logical form alone necessitates the exclusion; in the latter case, the whole of disjunction has been constituted through intuition; the members are given as exclusive on this ground; and hence the inclusion in one (or affirmation) implies the exclusion from the others. The world is either eternal or non-eternal, is an instance of the former-contradictory disjunction. A was born either in 1801, or 1802, or 1803; the burglar made his escape either by leaping from the window, or from the roof, or by sliding down the rone, are instances of the latter-contrary disjunction. Contrary alternatives are properly, in the end, forms of contradictory. A is either B or C or D, means really, A or not-A, B or not-B, C or not-C. The world is either eternal, or it is the work of chance or of intelligence. This, strictly taken, means the world is either eternal or non-eternal (that is, it had a beginning in time); it is either the work of chance or not,-i.e., it is the work of intelligence. As the work of intelligence, it may be of a single act or not; that is, it is plural or continuous. The disjunctive statement is thus also a preparation for determinate affirmation or negation, rather than affirmation itself.

§ 327. In the case of the disjunctive judgment, the copula is either-or; this brings together the alternatives in one act of conception. And this synthesis is the preliminary to the analysis or ultimate exclusion of the one from the other. All disjunction is affirmation and negation through affirmation, or it is affirmation through negation. For when we say A is B, then it is neither C nor D. It is neither spring nor summer ; therefore is is either autumn or winter.

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