necessary evolution or dialectic than this progress from the reflective judgment to the necessary? Certain forms of body are elastic, means, it seems, that elasticity belongs to all bodies, but more particularly to some! Hence the subject loses its character of individuality, becomes general, and thus the subject and the predicate may be substi tuted for each other! But when the generality enters expressly into the subject, as all bodies are elastic, it is no longer a fact which we express, but a necessity. Hence the transition from reflective to necessary judgments. A doctrine which is based on the identification of some and all, which confounds universality with necessity, and is supposed to be bolstered up by a hypothetical dictum,-what can be said of all the individuals belongs necessarily to the species,-may be fairly left without comment. § 359. In necessary judgments, the subject and predicate are so related that the one is the true essence or substance of the other, and reciprocally. Further, they are subordinated as individual to the species of which it forms part. Thus, the violet is a flower, this ring is of gold, gold is a metal. The copula is here marks not simple existence, or relation, but absolute necessity. To say that gold is dear, and gold is a metal, is to state two totally different judgments. Dear is an accident, and metal marks the essence. The form of proposition, gold is a metal, says implicitly that the quality of metal belongs not only to gold, but to silver, copper, iron, &c. Whence it follows that judgment. does not carry in itself the proof or reason of its truth or necessity. This reason is expressed in the second form of necessary judgment,-the Hypothetical or Conditional-as, if this thing is, this other thing must be also, or if A is, B is. Judgments of this class almost deny the existence of the two terms A and B, by showing that neither A nor B can exist alone by themselves, because A is not only A but B. Without losing the one, we recover the other in the Disjunctive form that is, the third and last form of the necessary judgments. Thus A (genus) is either B, or C, or D (species). These are the only species and all the species. But we need science to show us that the species actually enumerated complete the genus. We need, therefore, another form of judgment to show this. § 360. This leads to the highest of all,-the Ideal Judgments. These are conformed to the idea by which we judge that which is according to that which ought to be. Here the copula is has acquired all the energy which it ought to have. The first form of the Ideal Judgment is purely Assertory, as, this action is good, this house is beautiful. But as doubt is not resolved, this judgment is really problematic. The second form,-the Problematic Judgment,-is more advanced, since it is more explicit. It says, In this or that point of view this house is beautiful. But in this form there is still a doubt. Hence the need of another form—the Judgment Apodictic. This tends by itself to reject all uncertainty, repel all objection. This (which shows the individual thing) house (which marks the general) built in such and such a way (which indicates that which it has of the particular) is bad or beautiful (which formulates the apodictic judgment). Hence this (individual) is finally a genus, rendered manifest in particularising itself. The dialectical force disengages itself from the apodictic judgment, and passes into reasoning.1 These latter dogmata may very fairly be left without comment. 1 Die Subjective Logik, p. 89 et seqq. Cf. the summary given in La Logique Subjective, p. 40 et seqq. 288 CHAPTER XXIII. THE POSTULATE OF LOGIC-THE QUANTIFICATION OF THE § 361. Logic, as the science of the form of thought, necessarily demands that in the case of every given thought,-be it Concept, Judgment, or Reasoning, the thought should be strictly analysed and determined, so that all that is in the thought, and nothing but what is in the thought as a mental fact, should be expressly set forth in language or symbols. In this Logic asks nothing more than is required by every science which seeks its own perfection. Every science, in dealing with a matter or datum, seeks to know precisely and determinately what that datum is; and Logic as the science of the form of thought, requires to know exactly the thought, and its precise limitations, as in the mind. Hamilton has expressed this in what he calls the Postulate of Logic. "The only postulate of Logic which requires an articulate enouncement is the demand that, before dealing with a judgment or reasoning expressed in language, the import of its terms should be fully understood. In other words, Logic postulates to be allowed to state explicitly in language what is implicitly contained in the thought." This is essential to a scientific Logic. As a science of law and of the laws of thought, it must know precisely what it has got to regulate. The ambiguities and ellipses of language are thus, first, to be cleared up. Neither purely empty terms, nor ambiguous terms, nor so-called indefinite judgments, nor enthymematic reasonings can be accepted by Logic as they occur. Logic demands that these be rigorously cleared. And, in this 1 Logic, ii. sect. 6, and ii., Appendix, p. 252 et seq. precision, there is revealed the true state or process of the thought. Whatever amount of elliptical expression may be permissible in ordinary or in rhetorical speech, Logic allows none. It is not necessary as a speaker or writer that one should use the explicit form of thought which logical analysis demands, but it is necessary that the logician should make articulate the state of any concept, judgment, or reasoning, or that it should be given to him in an articulate form. Logic will thus teach us how we really think, when we seem to think otherwise than we do. Contradiction, vagueness, want of consecution, in our thinking, can thus, and thus only, be scientifically exposed. Such a postulate is a simple necessity for logical purposes. Thus only can we extricate the meaning clothed or hid in words. A proposition, as expressed in language, may have various meanings, according to intention and emphasis. It may be involved, defective, redundant, obscure, and until it is stated directly, categorically, in the case of a purely affirmative or negative judgment, it is unfit to be dealt with logically. This postulate not only may, but must be made by logic; and it underlies the practice of every logical analyst. "It is the function of the logician, from the various formulas of speech (however involved), and from the scope of the oration or speaker, like a skilled anatomist to resolve or to dissect, member by member, what is said, that he may distinctly perceive (at least in his own mind) what is said of what, and how far, whether of the whole or of the part."1 As has been said, whatever helps to exclude error, and to simplify logic, is a real addition to the science. § 362. It is from an application of this postulate that Hamilton reaches his doctrine of a Quantified Predicate; and on it as a general principle this doctrine rests for its vindication. It is clear that the postulate must be admitted, in other words, ordinary language must be translated into exact terms; ellipses must be supplied. We must state in language what is efficient in thought; and before proceeding to deal logically with any proposition or reasoning, we must be allowed to determine and express what it means.2 The pos tulate is demanded by the ordinary logic not less than by that 1 Wallis, Logica, ii. 11. 2 Logic, ii., Appendix, p. 270. T of Hamilton. And if Hamilton's application of it in the analysis of judgment and reasoning show elements essential to those processes in our ordinary or actual thinking, it only carries out the Aristotelic analysis to a fuller and more scientific issue; and its pretensions to this must be tested by the accuracy of the analysis, and the necessity of the new forms in thought. § 363. The first application of the Postulate may be fairly taken in reference to the subject of Propositions. Here as everywhere we need explicitness in the data. Hamilton's classification of Propositions (Judgments) according to Quantity is new and important. The judgment is the proposition as thought; the proposition is the judgment as expressed in language. The judgment is (a) either of determinate (definite) quantity, according as we know and circumscribe the objects of which we speak; or (b) it is of indeterminate (indefinite) quantity, according as the sphere is not known and not circumscribed. Determinate or Definite Judgments relate either (a) to an undivided whole, and thus form a General and Universal Proposition, or (b) to a unity indivisible, and thus form an Individual or Singular Proposition. An Indeterminate (indefinite) judgment refers to some indefinite number less than the whole of a class, and thus forms a Particular Proposition. Thus, every X is Y; every mineral acid is a poison-is a Universal Proposition. Here we speak of the whole number of objects in the class. Catiline is ambitious - is an Individual Proposition. Here we speak of the whole, but it is a single object. Some men are virtuous-is a Particular Proposition. Here we speak of some indefinite number less than the whole. The quantity of a judgment is thus always either indefinite or definite. In judging, we must judge either of some, or of the whole, taken universally or individually. These are the only quantities of which we ought to hear in Logic; and the expression, the propositional form of the inner thought,— must, for purposes of exact logical analysis, adequately and thoroughly indicate the extent of the judgment. Hence what are called Indefinite Propositions—that is, propositions which do not indicate by their language the extent in which the subject is taken, whether indefinite or definite, cannot as such be dealt with logically. They should be called Preindesignate |