à posteriori with the division of judgments into synthetic and analytic (cf. § 83), Kant finds three kinds of judgments— 1. Analytic judgments, or explanatory judgments, which, as such, are all judgments à priori; 2. Synthetic judgments à posteriori, or enlarging judgments, which are founded on experience; 3. Synthetic judgments à priori, which found themselves on the pure forms of intuition or the pure notions of the understanding, and ideas of reason. But those judgments which Kant calls synthetic judgments à priori are not, in fact, formed independently of experience, but are made in this way, that we complete the sense-perception by the presupposition of a causal interdependence (cf. § 140). Kant teaches rightly--That an element arising from within, and in this sense à priori, is added to the sensible or à posteriori, but wrongly-1. That the à priori element is independent of internal experience; and 2. That it does not belong to things in themselves.

The Kantian use of the expressions à priori and à posteriori, which at present prevails, has done more damage than good. Kant's mysterious fiction of a knowledge à priori,' which he took to be absolutely independent of experience, and his use of the term 'à priori,' often confounded with the old meaning of the term, has produced numberless obscurities and paralogisms, from which the Kantian and almost the whole post-Kantian Philosophy suffers. A return to Aristotle's meaning were better.

Schleiermacher teaches that the pure à priority of the Hegelian Dialectic and the pure à posteriority of Empiricism are alike one-sided and untenable. He says,''The judgments (together with the system of notions) which constitute science are developed in every individual identically, in proportion to the activity of his intellectual function, because of the relation between organic function and the outer world, which exists in all men.' Schleiermacher, accordingly, traces all scientific judgments to the co-operation of an inner and an outer factor, which are equally necessary for the formation of any judgment in the sense given above.

1 Dial. §§ 189–192.

PART FIFTH.

INFERENCE IN ITS REFERENCE TO THE OBJECTIVE CONFORMABILITY TO LAW.

74. INFERENCE (ratio, ratiocinatio, ratiocinium, discursus, σvλ20youós) in the widest sense is the derivation of a judgment from any given elements. Derivation from a single notion or from a single judgment is IMMEDIATE INFERENCE or (immediate) consequence (consequentia immediata). Derivation from at least two judgments is MEDIATE INFERENCE, or inference in the stricter sense (consequentia mediata).

As the conception represents the individual existence and what is to be distinguished in it, and the notion represents the essence, so the judgment and inference represent the relations of single existences. The judgment has to do with the primary and nearest relations; the simple judgment with a fundamental relation; and the complex judgment with a placing side by side of several relations. Inference has to do with such a repetition of similar or dissimilar relations as give rise to a new reference. The possibility of the formation of inference, and of its objective validity (as will be proved afterwards), rests upon the presupposition of a real interdependence of things conformably to law. This is to be said of mediate inference only, however, for immediate inference is a mere transformation of the subjective form of thought and expression (though not of the expression alone).

♦

'To derive from ' means to accept because of something else, so that the acceptation of the validity of the one depends upon the acceptation of the validity of the other, i.e. is received therefore and in so far, because and in as far as the other is received.

The immediateness' in the so-called 'immediate inference' is relative. It implies that this kind of inference does not require, as mediate inference does, the addition of a second datum to the first, but at once and of itself yields the derived judgment, which is nevertheless another judgment and not merely another verbal expression. There is no Immediateness, in the full sense, that no activity of thought is required to reach the derived judgment; but since the term is traditional, and holds good in a relative sense, it is not advisable to change it. When a change in terminology is not absolutely essential, it does harm, produces unintelligibility, and gives occasion to

error.

In Plato, συλλογίζεσθαι and συλλογισμός do not occur in the sense of later logical terminology. They have a wider and more indefinite meaning-to draw a result from several data, taking them all into consideration; and, more commonly-to ascertain the universal from the particular.'

Aristotle defines:2 συλλογισμὸς δέ ἐστι λόγος, ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει τῷ ταῦτα Elvat. This definition is not meant by Aristotle to include immediate inference. It comprehends the two kinds into which mediate inference divides-inference from the universal to the particular, and inference from the particular to the universal. In this sense, Aristotle distinguishes between ó dià Toû μéσov συλλογισμός and ὁ διὰ τῆς ἐπαγωγῆς, οι ὁ ἐξ ἐπαγωγῆς συλλοyouós.3 Syllogism, in the strict sense, is inference from the universal to the particular. Aristotle says, in this sense, Tpóπον τινὰ ἀντίκειται ἡ ἐπαγωγὴ τῷ συλλογισμῷ·—ἅπαντα πιστ τεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς.

Wolff, in agreement with Aristotle, and, like him, referring 1 Theaet. 186 D; cf. Phileb. 41 c. 2 Anal. Pri. i. 1, 24 в, 18. 3 Ibid. ii. 23. 4 Ibid.

to mediate inference only, defines it: est ratiocinatio operatio mentis, qua ex duabus propositionibus terminum communem habentibus formatur tertia, combinando terminos in utraque diversos; syllogismus est oratio, qua ratiocinium (seu discursus) distincte proponitur.

Kant defines inference to be the derivation of one judgment from another. This happens either without an intermediate judgment (iudicium intermedium), or with the help of such. On this is based the division of immediate and mediate inference. Kant calls the former inferences of the understanding, and the latter inferences of the reason.

Hegel3 sees in inference the re-establishment of the notion in the judgment, the unity and truth of the notion and judgment, the simple identity into which the formal distinctions of the judgment have returned, the end and aim towards which the judgment in its various kinds advances gradually, the universal which by means of particularity has coalesced with individuality.

He thinks inference the essential basis of all truth, the intellectual and all intellectual, the return upon itself of the mean of the moments of the notion of the actual. Hegel here also identifies the logical and metaphysical relation, or the form of knowledge and existence.

Schleiermacher' defines inference to be the derivation of one judgment from another by means of a middle premise. He does not recognise inference to be an independent third form, co-ordinate with notion and judgment, and denies that it has a real correlate of its own. He therefore does not believe that it has any scientific value for the production of knowledge; but thinks its worth didactic only, for the transmission of knowledge already existing. We believe this view to be erroneous, and will seek to show (§ 101) the real correlative of inference, and its significance as a form of knowledge.

[J. S. Mill defines inference to be the setting out from known truths to arrive at others really distinct. He refuses the name to the so-called immediate inferences,' because in

Log. §§ 50, 332.

2 Kritik der r. Vern. p. 360; Log. § 41 ff. 3 Log. ii. 118 ff; Encycl. § 181. Dial. p. 268. 5 [Log. i. 185.]

them the progression from one truth to another is only apparent, not real, the logical consequent being a mere repetition of the logical antecedent. He divides inference into three kinds, from generals to particulars, from particulars to generals, and from particulars to particulars. The third kind, though not generally recognised by logicians, is not only valid, but is the foundation of both of the others. It is the inference of every-day life, and in its finer forms corresponds to the Ooμòs of Aristotle, which plays such an important part in the formation of our judgments in matters of taste and morality— the delicate imperceptible ingathering of instances gradually settling and concreting into opinions. It is the recognition and discussion of this third kind of inference in all its manifold forms, but more especially in its formation of religious beliefs, which gives so much logical value to J. H. Newman's Grammar of Assent, 2nd ed., Lond. 1870.]

§ 75. The PRINCIPLES OF INFERENCE are the axioms of identity and correspondence, of contradictory disjunction (or of Contradiction and Excluded Third) and of sufficient reason. The derivation of a judgment from a notion rests on the first, the derivation of a judgment from a judgment on the first and second, and the derivation of a judgment from several judgments on the first, second, and third.

Logic considers these principles as rules of our thinking (which is also an act of knowing). It leaves to psychology to discuss in how far these laws are, or are not, so simple and evident in their application that they cannot be altered in clear thinking, and in this sense attain the character of natural laws for our thinking.

Aristotle does not place these axioms at the head of Logic, but discusses them, in so far as he enunciates them in scientific form at all, partly and occasionally as laws of the formation of inferences, and partly and more particularly in the Meta