has been carried out by Hamilton on the basis of assertions of Aristotle,' and according to partial precedents in the Logique ou l'Art de penser,' and in Beneke. Cf. § 120. For the use of these Schemata as aids in the demonstration of the theorems which have to do with inference, cf. § 85 and § 105 ff.; cf. also § 53. § 72. Two judgments, of which the one precisely affirms the very thing which the other denies, are coNTRADICTORY to each other, or are contradictorily opposed (iudicia repugnantia sive contradictorie opposita). Contradiction is the affirmation and denial of the same thing. Judgments are opposed to each other diumetrically, or as CONTRARIES (contrarie opposita), which, in reference to affirmation and negation, are as different as possible from each other, and, as it were, stand furthest apart. Judgments should be called SUBCONTRARIES, the one of which particularly affirms what the other, agreeing with it in other respects, particularly denies. Judgments are SUBALTERN (iudicia subalterna), the one of which, affirmatively or negatively, refers a predicate to the whole sphere of the subject-notion, while the other refers the same predicate in the same way to an indefinite part of the same sphere. The former is called the subalternant (iudicium subalternans), the latter the subalternate judgment (iudicium subalternatum). ai Aristotle defnes‘—ἔστω ἀντίφασις τοῦτο· κατάφασις καὶ ἀπόφασις αἱ ἀντικείμεναι. He distinguishes contradictory opposition (ἀντιφατικῶς ἀντικεῖσθαι· ἡ ἀντικειμένη ἀπόφανσις) from 1 De Interp. c. vii. 2 Par. 1664. 3 Cf. upon this Trendelenburg, Log. Unters. 2nd ed. ii. 304-307, and Appendix B. 4 De Interp. c. vi. contrary (ἐναντίως ἀντικεῖσθαι· ἡ ἐναντία ἀπόφανσις). Judgments with the same content of the forms a and o (S a P and So P) stand to each other in the relation of contradictory opposition, and so do judgments of the forms e and i (Se P and SiP). Judgments of the form a and e (S a P and Se P) stand in the relation of diametrical or contrary opposition. The relation between the forms of judgment i and o (Si P and So P) Aristotle calls only apparently analogous,' Kaτà τηv λέξιν ἀντικεῖσθαι μόνον. Later logicians call such judgments πρоτáσειs Vπεvaνrías, iudicia subcontraria. Aristotle arranged the four forms of judgment, πᾶς ἐστιν ἄνθρωπος δίκαιος (a), οὐ πᾶς ἐστιν ἄνθρωπος δίκαιος (Ο), πᾶς ἐστιν ἄνθρωπος οὐ δίκαιος (Θ), οὐ πᾶς ἐστιν ἄνθρωπος οὐ δίκαιος (i), according to the annexed scheme : ὑπεναντίας, The judgments a and e, which stand furthest apart from each other, according to their mutual relations, and in the same way the judgments i and o, are thus set at the opposite ends of the diagonal or διάμετρος. In this scheme all the above-mentioned relations of judgments are thus arranged:opposit. contradict. a Modern Logicians represent these relations in the following scheme (which is found in Boëthius, and, with some difference 1 Anal. Pr. ii. 15. 2 De Interp. x. 19 в, 32–36. of terminology, but with the same position of the forms of judgment, in Apuleius) :— This is less convenient because contraries do not lie at the opposite ends of the diameter, but in another view is better. § 73. The matter or content of our judgments is obtained immediately through external and internal perception, mediately by inference. In the act of judgment the forms, which are designated by the Categories of relation, are imposed upon this matter. We recog nise these forms: (a) First and immediately in ourselves by means of internal perception. For example, the relation of what inheres to what subsists is recognised in the relation of the individual perception or individual feeling or volition to the totality of our existence or to our ego, the relation of causality to dependence in the relation of our will to its expression, &c. (b) In the personal and impersonal essences without us, on the ground of its analogy to our own internal existence. The notional apprehension of these forms, in their separation from the content, with which they are combined, comes afterwards, by means of abstraction. The objective validity of these forms is warranted by the same moments, and lies under the same limitations and gradations, as the truth of internal perception and its analogues (§ 41 ff.), as the truth of the conception of individuals (§ 46), and as the notional knowledge of the essential (§ 57). Kant believed these forms to be à priori, or originally inherent in the human understanding (Stammbegriffe des Verstandes). Before his time knowledge à priori meant, agreeably to the Aristotelian idea, knowledge from causes which are the prius natura (πрóтɛρov þúσɛɩ), and knowledge à posteriori, knowledge from effects which are the posterius natura (vσтερov þúσε), and therefore knowledge from immediate experience and by testimony (for this knowledge is a kind of knowledge from effects). Leibniz identifies connaître à priori and par les causes. He calls 2 ratio à priori that reason which is the cause not merely of our knowledge, but of the truth of things themselves. He distinguishes prouver à priori par des démonstrations' (which, of course, is sufficient only when 'démonstrations' mean syllogistic deductions from known real reasons), and à posteriori par les expériences.' He recognises the Axiom of Identity and Contradiction (the element à priori) to be the only principe primitif' for all knowledge co-ordinate with experience (the à posteriori element); 3 but later adds the Principle of Sufficient Reason." The same use of the terms is also found in Leibniz, applied to mathematics, in a very instructive passage of his Epistola ad Jacobum Thomasium,5 in Leibniz's edition of the work of Nizolius, De veris principiis et vera ratione philosophandi: Si rem cogitemus curatius, apparebit demonstrare eam (sc. geometriam) ex causis. Demonstrat enim figuram 1 Theod. i. § 44, e.g. 2 Nouv. Ess. ii. 17. 6 3 Réflexions sur l'Essai de Locke, 1696. 5 Published in 1669. 1 ex motu, e.g. ex motu puncti oritur linea, ex motu lineae superficies, ex motu superficiei corpus. Ex motu rectae super recta oritur rectilineum. Ex motu rectae circa punctum immotum oritur circulus, &c. Constructiones figurarum sunt motus; iam ex constructionibus affectiones de figuris demonstrantur. Ergo ex motu, et per consequens à priori et ex causa.' Wolff says, very insufficiently: utimur in veritate proprio Marte eruenda vel solo sensu; vel ex aliis cognitis ratiocinando elicimus nondum cognita: in priori casu dicimur veritatem eruere à posteriori, in posteriori autem à priori. He adds that experience has to do with the individual only, but yet supplies us with the principles from which those individual cognitions, which are not to be reached by immedi ate experience, must be derived à priori. Only by such a 'connubium rationis et experientiae' can the trifling Scholastic formulae be avoided, and be taught 'non ex proprio ingenio conficta, sed naturae rerum consentanea.' Kant holds that knowledge which has been reached by a general rule, if this rule be itself derived from empirical sources, is only relatively to be considered knowledge à priori. He, for his part, will not understand such knowledge to be à priori which is independent of this or of that experience, but only knowledge which is absolutely independent of all experience. Opposed to it is every kind of empirical knowledge, or knowledge possible only à posteriori, i.e. by experience.' Kant has narrowed the notion à posteriori in its relation to the Aristotelian knowledge from effects, or from the votepov þúσel (but has done so in accordance with the use prevailing in Leibniz and Wolff). He understands by it, knowledge from one kind of effects (viz. from those which affect our senses). He has given an entirely new meaning (which has since come to be the prevailing one) to the expression à priori (partly determined by Wolff and Baumgarten, and partly on the other side by Hume). He denotes by it, not the opposite of knowledge from effects, but the opposite of knowledge from experience. By combining the distinction of knowledge à priori and 1 Log. § 663. 2 Kritik der reinen Vern., Einl. i. |