794 LOGIC
through which alone perceptions are raised into cognitions, through which alone reasoned knowledge is possible. It is the only explanation possible on the basis of psychological individualism; its value, and therefore the value of the systematic deductions from it, must depend on the accuracy and coherence of the psychological or metaphysical theory on which it is founded.
24. It was possible, however, to proceed by another route from the position taken up by Locke. If it be held that the elementary impressions, mechanically regarded as somehow arising in mind, are in themselves cognitions, then it is possible to view them as containing in themselves all possible cognition. In other words, we may confusedly identify the proposition that knowledge does not extend beyond the field of experience with the very different proposition that the only items of knowledge are the isolated impressions which appear to make up experience. If this identification be accepted (and the conception involved is precisely that underlying all consistent nominalism from Antisthenes downwards), then the only processes requiring to be taken into account are those whereby clearness and distinctness are introduced into our (possibly) vague perceptions. For these processes analysis is an adequate title. All knowledge, i.e., whatever is characterized by clearness, definiteness, consequence, is the analysis of what is given in isolated perceptions. Each perception is itself and is only itself; no judgment is possible save that of identity. In other words, if there be judgment at all, it can consist only in the assertion that the unanalysed perception is identical with that into which it is analysed, and as each perception and each analytic portion of a perception may be signified by an arbitrary sign (name or other hieroglyphic), judgment is essentially an affair of naming, a declaration that different names are identical or belong to the same perception. Reasoning is simply the transition from one identity to another, – a more developed result of analysis. Scientific or real knowledge is an accurately framed system of signs, i.e., a collocation of signs which expresses precisely the results of the analysis of complex perceptions. Logic, under this doctrine of knowledge, is merely a statement of the various modes in which analysis is carried out, of the ways in which names are applied, and of the forms in which names are combined. Such is the theory of logic presented by Condillac.[1]
Logic on the Basis of Metaphysical Psychology.
Leibnitz and Herbart.
25. One development from the psychology of Locke has thus appeared as an extreme formalism, which if carried out consistently must needs assume the aspect of a numerical or mechanical system of computation.[2] It is remarkable that a very similar result was reached by Leibnitz, a thinker who proceeded from a quite opposed psychological conception. The similarity is due to the presence in both theories of a certain abstract principle, intimately though not necessarily connected with the respective psychologies. In place of the single perception which in Condillac's logic is the element to be analysed, there appears in Leibnitz's view the single consciousness of the monad (see LEIBNITZ, p. 424); in both cases, however, knowledge is assumed to exist there implicitly and to stand in need only of evolution. The methods by which this evolution is to proceed form for Leibnitz the substance of a new and all-comprehensive science, "Scientia Generalis,"of which the older logic is but a part.
The characteristics of Scientia Generalis are at once deducible from the two general principles which in Leibnitz's view dominate all our thinking, – the law of sufficient reason and the law of non-contradiction. It must contain a complete account of the modes in which from data conclusions are drawn, and in which from given facts data are inferred, and since the only logical relations are those of identity and non-contradiction, the forms of inference from or to data must be the general modes of combination of simple elementary facts which are possible under the law of non-contradiction. The statement of the data of any logical problem, and the description of the processes involved in combining them or in arriving at them, are much assisted by, if not dependent on, the employment of a general characteristic or symbolic art.
The fundamental divisions then of Scientia Generalis, so far at least as its groundwork are concerned (for Leibnitz sometimes includes under the one head all possible applications of the theory), are (1) the synthetical or combinatorial art, the theory of the processes by which from given facts complex results may be obtained (of these processes, which make up general mathesis, syllogistic and mathematical demonstration are special varieties); (2) the analytic or regressive art, which starting from a complex fact endeavours to attain knowledge of the data from whose combination it arose.[3]
Of the nature of the second portion only a few brief indications are contained in the logical tracts and in detached utterances in the larger works of Leibnitz. When complex combinations are presented, or, in the most general form, when the investigation has to start from experience, from truths of fact, the work of analysis is endless; the regress to conditions is practically infinite. Determination of the necessary data cannot in such a case possess more than probable value, but the probabilities may be estimated according to the rules laid down in the progressive or synthetic art.[4] The logic of probability is thus recognized as an integral portion of the logical system.
Of the first art, the logical calculus in particular, a somewhat clearer and fuller outline is given.[5] The logical calculus implies (1) the statement of data in their simplest form, (2) the assignment of the general laws under which combination of these data is possible, (3) the complete exposition of the forms of combination, (4) the employment of a definite set of symbols, both of data and of modes of combination, subject to symbolic laws arising from the laws under which combination is possible. In the Fundamenta Calculi Ratiocinatoris and the Non-inelegans Specimen Demonstrandi, something is effected towards filling up the first, second, and fourth of these rubrics, but in no case is the treatment exhaustive. The simple data, called characters or formulæ, are symbolized by letters, relations of data by a somewhat complicated and varying system of algebraic signs; for the calculus, or set of operations exercised upon relations given so as to produce new formulæ, no comprehensive system of symbols is adopted. Formulæ, relations, and operations take the place of notions, judgments, and syllogism. The general laws of combination of data are stated without much precision. Leibnitz recognizes the law of substitution, notes also what have been called the laws of reduplication and commutativeness, but, in actual realization of his method, employs indifferently the relation of containing and contained or the relation of identical substitution (æquipollence). No attempt is made to develop a complete scheme of possible modes of combination.[6]
At the root of Leibnitz's universal calculus, as of Condillac's method of analysis, and generally of nominalist logic, there lies a peculiar acceptation of the abstract law of identity. That a thing is what it is, – that knowledge of a thing is a single, indivisible, mechanical fact, susceptible only of explication or of expanded statement, – this is the principle dominating logical theories which in other respects may differ widely. Insistance upon this aspect of knowledge or of the object known is the ground for assigning to thought a function purely analytic, which is the very keynote of nominalism. It is not hard to see, however, that so to view the law of identity is to abstract from all the conditions of actual thinking and knowing, and to throw into the assumed simple fact all the complexity which is afterwards to be discovered in it by analysis. The knowledge of a thing is not to be explained in this abstract or mechanical fashion. Truth does not consist in the empty recognition that a is a, and in the repetition of this unimportant fact, but in the knowledge of the nature of a, a knowledge which essentially consists in relating a to its intellectual conditions, in assigning to it a place in the intelligible world. The identity of the thing with itself is a mere aspect of the complex process whereby the thing is cognized. It hardly requires to be pointed out that the minor forms of the same fundamental view, the various attempts to express the essence of a judgment as the assertion of identity, are open to the same objection. They take an abstract view of the judgment, and regard as the essential fact that which is but an accessory or adjunct or consequence. Difference, to put it in the briefest fashion, is no less essential to a judgment than identity.[7]
26. The view of logic put forward by Herbart, from a metaphysico-psychological basis resembling that of Leibnitz, agrees in so many respects with that of Leibnitz, although containing no reference to the idea of a logical calculus, that it may be placed under the same head. Logic, according to Herbart, is a purely formal doctrine; it has to do only with the modes by which clearness, distinctness, and system are introduced among our ideas. Logical forms, then, the notion, judgment, and syllogism, are not to be regarded as having any metaphysical reference; they are not even to be explained psychologically; they stand on their own footing as explanatory processes exercised about the representations which under their own natural laws fill up consciousness, coming and going within the
2 Such as is hinted at by Hobbes, and as is carried out in the various works of Professor Jevons.
- ↑ See Langue de Calcul; Art de Penser; and Logique. Cf. Laromiguiere Leçons de Philos. i. pp. 5-43; and Robert, Les théories logiques de Condillac, 1869.
- ↑ 2
- ↑ Leibnitz sometimes includes these two under the head of "Ars Inveniendi," and places alongside of this, as first part of Scientia Generalis, "Ars Judicandi," a division resembling that appearing in Bacon; but the "Ars Judicandi" may be thrown out of account.
- ↑ Op. Ph., pp. 397, 398; cf. generally pp. 84, 93, 343.
- ↑ See specially Op. Ph., pp. 92-114; also the tract "De Arte Combinatoria," Op. Ph., pp. 6-45.
- ↑ It is interesting to note that Leibnitz signalizes the distinction between the logical and mathematical senses of a whole, and between the distributive and the collective meaning of quantity; that he emphasizes the function of the particular judgment as the negation of its opposed universal; and that he approximates to some modern modes of formulating the judgment (a is b, e.g., he would express as a = ab, or ab is; no a is b, as ab is not).
- ↑ Much of the confusion which reigns supreme in many modern works on logic is doubtless attributable to a confusion between the nature of the judgment and the result of a judgment. The result of a judgment is always an increased richness of the subject notion; the subject unqualified and the subject qualified by the predicate are doubtless identical; but it would be absurd to say, therefore, that the function of the judgment is the assertion of this identity.
