and in all provinces of philosophical thinking, is essential; but the dialectic method has not been able to do away with the necessity of the Kantian distinction. Schleiermacher' explains the distinction between the analytic and synthetic judgments to be a fleeting and relative one. The same judgment can be analytic and synthetic, according as what is said in the predicate has or has not yet been included in the notion of the subject. But the distinction holds in reference to any single subject standing by itself. The incomplete judgment (which contains only the subject and predicate) is more analytic, the complete (which contains the object also) is more synthetic, the absolute judgment (whose predicate is the world) is again analytic. It must be urged, however, against Schleiermacher that the distinction of the analytic and synthetic character of the judgment is not connected with its completeness or incompleteness. Delboeuf says the advance of science consists in this, that synthetical judgments change to analytic, i.e. predicates subjoined empirically into those which exhibit necessity. This thought, in itself quite correct, is not so in relation to Kant's distinction. The meaning which Delboeuf gives to the expression is essentially different from the Kantian terminology, according to which an apodictic connection, which rests on a known causal relation, is synthetic. [J. S. Mill's distinction of propositions into verbal and real; those which assert of a thing under a particular name, only what is asserted in the fact of calling it by that name,' and those which predicate some attribute not connoted by that name;' corresponds very nearly to Kant's distinction between analytic and synthetic propositions.3] § 84. CONVERSION is that change of form, by means of which the parts of a judgment change their place in reference to its relation. 1 Dial. §§ 155, 308-9; Beilage, E. lxxviii. 5. 2 Prolég. philos. de la Géom. p. 46 ff. and Log. p. 103. 3 Cf. Logic, i. 119 ff. In the categorical judgment the subject becomes predicate and the predicate subject; and in the hypothetical judgment, the conditioning proposition becomes the conditioned, and the conditioned the conditioning. The conversion of the categorical judgment is internally correct, only when the notion of the predicate can itself become substantive, i.e. when the sum total of the objects, to which what is designated by the predicate-notion belongs, are all of the same kind, or are a class or genus (in the sense of § 58). For in this case, these objects only can be comprehended under a substantive notion, which can become a subject-notion (according to § 68), while the earlier subject-notion, from its connection with the auxiliary notion of existence, may refer to a relation of inherence, and so take the predicative form (cf. § 68). The internal correctness of the hypothetical judgment, generally, lies under no limitation, because it denotes only a causal nexus, whether in the direction of from cause to effect, from effect to cause, or from effect to effect. When relations of time come into consideration, the first presupposition is the most natural, and therefore the consequent, because the antecedent in Conversion is frequently to be expressed in the form of a final judgment (If it be-then must, &c.). The question of the internal correctness of Conversion was not discussed by Aristotle. The Aristotelian principle, that the elements of thought generally correspond to actual existence, and that the subject and predicate especially, which find expression in the ovoμa and pñua, must correspond to the thing, and to the action or quality, forms the basis for such a discussion; but Aristotle did not apply it to Conversion. 3 The possibility of making the predicate substantive' is a tacit presupposition, but is not further discussed. The post-Aristotelian and the modern formal Logic have still more neglected metaphysical relations referred to. Schleiermacher 2 has hinted at it, and Trendelenburg has remarked that in Conversion "The Accident is raised to be Substance,' (or rather) that the substance in which it inheres becomes the object thought of instead of the attribute inhering; but it does not follow from this, that Conversion, if we except the case of the universal negative judgment, is a mere artifice of formal Logic,' and can lead to no sure result. Logic, as a doctrine of knowledge, can and ought to investigate what and how much follows by conversion from a single given judgment, presupposed to be 1 Anal. Prior. i. 2. 2 Dial. § 325. 3 Log. Unters. 2nd ed. ii. 303; 3rd ed. ii. 336. The stand-point of logical treatment is completely mistaken, and numerous mistakes are inevitable in particular cases, when this investigation is supposed to be undertaken in order to teach and make possible an arbitrary thinking, according to artificial rules and formulae,' or to reduce thinking to a mechanical schema, in order to proceed arbitrarily according to this schema, so that we require to think according to the schema only, and not according to the notions.' * One might as well reproach the mathematico-mechanical procedure with being one-sided and arbitrary, if it investigates what follows simply from certain simple presuppositions, and looks at these apart from other data, from which they can never be actually separated. If, for example, the path and position of a projectile be computed solely on the ground of gravitation and inertia, without taking into consideration the influence of the resistance of the air, the concrete intuition will apparently determine the result more strictly and more accurately than the computation. But if mathematical mechanics did not use this abstract procedure the laws of motion could not be known, and the science would be ruined. It is true that there is commonly more than merely one judgment given to us, and that we ought to know more about the relation of the spheres of its subject and predicate from other sides than that only which the judgment, considered purely in itself, shows. If the given judgment be: All men are * J. Hoppe, Die gesammte Logik, Paderborn, 1868. internally correct. It must also show on what this internal correctness depends. The conversion of the disjunctive judgment, whether categorical or hypothetical, does not require special rules any more than the conversion of the copulative or any other co-ordinated judgment. Its rules come directly from the laws of the Conversion of simple judgments. The hypothetical judgment is also the type for the cognate kinds of judgments. § 85. By Conversion there follows I. From the Universal affirmative categorical judg- The particular affirmative: At least once or B The proof lies in the comparison of the spheres. mortal, or: All men are sensible-intellectual dwellers on earth, we know in other ways that there are also other mortal beings, but that there are no other sensible-intellectual inhabitants of earth. He who keeps to the example, and adds the other knowledge got in another way, can, without the trouble of abstraction, attain a completer result than the judgment which results according to the rules of Logic from a single given judgment, and so can very easily, on the ground of supposed notional' procedure, triumph over the logician, who troubles himself and others with his abstract schemata. But this procedure does not abolish a false logic for the sake of a better; it destroys the possibility of a methodically progressive logical knowledge of the laws of thought. It is only after the investigation, What follows from one datum? is finished-that the scientific theory of thinking requires to subjoin the consideration of other data. The given Categorical judgment: All S are P, presupposes (§71) the relations of the two spheres, which are signified by the Schema a, 1. SP a, 2. S P i.e. the action or quality, which the predicate-notion P denotes, is (a, 2) found in all the objects which the subject-notion S denotes, while it remains uncertain whether it is also found in others (a, 1) or is not so found (a, 2). Under the first present position it may only be said of part of the objects to which the action or quality denoted by the former predicate-notion P belongs, that they are S, under the second it may be said of all of them. It cannot be decided, from the given judgment alone: All S are P, when other data are excluded, which of the two presuppositions holds good in any case. But this decision is not required. The inference: At least some P are S, is true on both presuppositions. And this is what was to be proved. In the same way the hypothetical judgment: Whenever A is, B is, presupposes two relations of spheres, whose Schema is i.e. the relation denoted by в is found everywhere where A is; while it remains uncertain whether it is found in |