sities of what is called human thought or experience,-an expression which is made to stand for accurate thinking and discrimination of points that differ. All modal expressions are, in fact, syncategorematic, and wholly external to the true nature of the proposition, of which even they form part.

§ 319. But what is necessity? On what ground is a proposition necessary? Is there more than one kind of necessity? These questions require to be answered in regard to the first form of modality. What branch of philosophy is to give the answers? Clearly that which deals with the nature, origin, guarantee of human knowledge. But this is obviously, at least, a very different science, or series of sciences, from that which deals with the nature and relations of concepts in every matter, judgments of every kind, and propositions in every form of reasoning.

As to the possible, that which may or may not issue,what is to be our test of this? Clearly something in the character of the matter or cause, something, therefore, to be determined by observation and induction. The possible may depend on a law or rule of doubtful application, on a converging series of causes, whose total result we cannot beforehand predict with certainty. Is it seriously maintained that an inquiry into principles which would help us to regulate knowledge or anticipation of this sort, is to be classed with the laws which regulate actual and possible conception, judgment, and reasoning? We should thus require to have recourse not only to the whole rules of Induction, but to those of the estimate of Proof. And if the conclusiveness of our inference from the proposition were to depend on its character as contingent, this would be paralysed in a thousand cases, and never be absolutely strict in any. At any rate, we should be driven to a set of inquiries wholly foreign to the precise and useful rules of consistent and connected thinking, with the prospect only of indefinite delay. To reproach the Science of Formal or Deductive Logic for not taking into account the modality of propositions, is utterly beside the point and futile, just as much so as to say that Geometry does not tell you of the particular spaces it can measure, or Arithmetic the properties of the things, pears, apples, or cherries, which it can help you to number.

(α) Aristotle said, πᾶσα πρότασίς ἐστιν ἢ τοῦ ὑπάρχειν ἢ τοῦ ἐξ ἀνάγκης

ὑπάρχειν ἢ τοῦ ἐνδέχεσθαι ὑπάρχειν. — (An. Pr., i. 2.)

From this hint

logicians have worked out modal judgments; and though it may be said that Aristotle's statement refers to the relations of existence or actuality, this may readily further be taken as the ground of the various degrees of certainty regarded as represented by modal judg.

ments.

According to Ueberweg, the notion of affirmation is "the consciousness of the agreement of the combination of conceptions with actual existence; the notion of negation, "the consciousness of the want of agreement of the combination of conceptions with actual existence." According to modality, "the judgment is problematic, assertory, or apodictic. Its problematic character lies in the uncertainty of coming to a decision upon the agreement of the combination of conceptions with actual existence. Its assertory character lies in the immediate certainty (based on one's own or another's perception); and its apodictic character in the mediately acquired (based on demonstration, dwódciğis) certainty of coming to such decision.”—(Logic, p. 206.) From what I have already said, it is, I think, clear that no one science, call it Logic or anything else, could possibly deal with all the grounds on which such judgments ought to be made, even as with a view simply to specify the conditions, laws, and methods of determining matter of fact, what only may be, what cannot be, what must be. This would be the most heterogeneous science conceivable, or a series of logics of the most varying order. One's own perception is the basis in some cases; "authentic witness" in others; inference, necessary inference, from another judgment. How can these be discussed from a single point of view? Or how can they be discussed at all, apart from the whole range of Mental Philosophy?

Aúvaobai (to be capable), in the Aristotelic use, may be taken as meaning possibility in the sense of the existence of the cause, and thus of its possible operation, as a matter of fact. The seed is capable of developing into the plant; the plant is capable of flowering; èvdéxeoðaι may be taken as meaning the absence of hindering or hostile circumstances, in other words, causes that might frustrate the possible (natural) effect, as frost in respect to the seed in the earth. Hindering circumstances may further be represented by the absence of concauses, as apart from moisture, air, suitable soil, &c., the seed will not develop into what is potentially in it. These concauses, sometimes called conditions, are truly parts or elements of the cause, which is generally the sum of concauses.-(On this point cf. Waitz, Org., i. 376, and Ueberweg, Logic, p. 208 et seq.) Supposing the sum of concauses or the cause to be present, and there being no counteracting cause, the effect will follow with necessity, that is, hypothetical necessity, or uniformly without exception. There is, however, even here no true logical or even metaphysical necessity.

In an Assertory Judgment, the certainty is said to depend on the correspondence between the judgment and our observation or generalisation of facts, as bodies gravitate. All the planets move with the sun in space. Some A is B. This refers to what is known as a matter of fact. But there is really no true distinction in respect of generalisations from

experience between assertory and problematic judgments. The assertory judgment all bodies gravitate is not a matter of past experience, it is not even a matter of fact. It is a matter partly of fact and partly of objective possibility, or probability, and therefore of belief. Some bodies have been found to gravitate; all bodies will or may gravitate. This latter proposition is not strictly assertory; it is a problematic proposition, with the highest degree of subjective certainty. It is a description of the state of my knowledge or assurance regarding fact, rather than of fact itself. It is my belief that all bodies will or can gravitate, is the true form of the universal assertory judgment, and it is simply a modification of the problematic.

It,

Then the Problematic Judgment has no proper place by itself. too, describes a state of my knowledge or a limited degree of assurance regarding fact. It is the case or I know that this event can happen, either because I know the sum of its concauses exist, or more slightly still, because I do not know anything that can prevent it happening. This seed can or may grow into a tree,—this person may commit suicide; either because there is nothing to hinder the one, or it is in the power of the person to do what I suppose possible. But this indicates merely a state of limited certainty or expectancy on my part. The subject of the judgment, if it can be so called, is not primarily, as in the assertory judgment, the seed or the person spoken of, but the state of my mind is such that I believe that the seed can grow, or the person destroy himself. The problematic judgment is simply the statement of a hypothesis which is not itself a judgment but a conception. As far as the problematic judgment is one, it is simply assertory. The problem is merely a stage on the way to judgment proper, in which quite different terms will appear, for we shall then be able to say, the seed has become a tree,-not, it is my belief that it may.

The Apodictic Judgment has no better title to be considered as a separate form. It, too, refers to the degree of certainty or assurance, and is properly expressed in the assertory form-it is the case, or I know or believe that A must follow B. In the first place, must here is ambiguous. It may refer to a mere physical sequence, in which must simply represents unexceptional uniformity, as, all bodies must gravitate; or to a sequence, metaphysical or other, in which must is strictly taken as representing a relation the reverse of which is inconceivable, as, this change has a cause; 5+ 5 = 10; all the angles of a triangle are equal to two right angles; nothing is less than something; one is not none. In the former case there is no necessity, that is, absolute necessity, in the sequence. There is simply the high, very high, certainty which attends a sound generalisation from experience; and this in its universality is always only problematical, only relative to grounds of belief, the actual facts not having, from the nature of the case, happened.

In the latter case, the judgment is simply assertory of a state of my knowledge or belief, or of a condition of my knowledge. A change has a cause, and I know it must have a cause, for the reason that I cannot think it otherwise; 2 + 2 = 4, for the reason I cannot conceive the sum any more or less. The objective necessity lies properly in the

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.)

270

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 (kaтηYоρikós) 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.)