Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/819

 LOGIC 795 sphere of apperception. According to this view the whole pro vince of knowledge is excluded from logic, and it is assumed that knowledge is somehow given, mechanically, without the co-opera tion of processes, if not identical with, yet strongly resembling, those recognized as logical. Herbart does not succeed in vindicating an independent place for a purely formal logic. The Kantian Logic. 27. The critical method, which has so influenced general philo sophy that all later speculation refers more or less directly to it, has at the same time profoundly modified all later conceptions of the sphere and method of logic. From the Kantian philosophy there spring directly the three most important modern doctrines of logical theory, that which, with many variations in detail, regards logic as a purely formal science, the science of the laws of thought or of the laws under which thought as such operates, and of the forms into which thought as such develops; that which, likewise with many variations, unites logical doctrines with a more general theory of knowledge; and finally that which identifies both logic in the narrower sense and theory of knowledge with an all-comprehensive rnetaphysic. It is matter of history that the critical system was developed mainly from the basis of the Leibuitzian logical and metaphysical theories, and it is likewise matter of history that Kant, even in the speculative work which was to so large an extent antagonistic to these theories, remained under the influence of some of their cardinal positions. 1 In particular the view of logical thought as purely dis cursive, analytic in. character, a view never by Kant harmonized with his general system, is a relic, most significant for the develop ment of his logic, from the Wolffian reproduction of Leibnitz s philosophy. This historic basis is not to be lost sight of in attempt ing to acquire a clear idea of the special place and function assigned by Kant to logical theory. But a brief reference to the general result of the critical philo sophy will suffice to introduce the more special treatment of the Kantian logic. Knowledge, or real cognition, which is analysed in the Kritik in reference to its origin and validity, appears, when subjectively regarded, as a compound of intuition and thought, of sense and understanding. The isolated data of sense experience do not in themselves form parts of cognition, but are only cognized when related to the unity of the conscious subject, when the sub ject, as it may be put, has consciousness of them. This reflex act, resembling in some respects Leibnitz s apperception, or process of uniting in consciousness, is an act sui generis, not to be mechani cally conceived or explained. Only through its means do repre sentations become cognitions. The forms in which the synthetic act of understanding is carried out are, as opposed to the intuitive data on which they are exercised, discursive or logical in character. Essentially they are judgments : all acts of understanding are judg ments, and, as judgments, they imply a general element with which the particular of sense is combined, and in the light of which the particular becomes intelligible. In ultimate analysis it appears that no particular, whatever be its empirical character, can become an intelligible fact, save when determined through some specific act of understanding, through combination with some specific notion or general element. Combination of particular and general is thus the very essence of understanding, the mark of knowledge as such. In every item of cognition the same elements may be discerned as necessarily present. The consideration of the ultimate modes of intellectualization, of the series of acts by which understanding subsumes the particular, draws the particular into the unity of cognition, may be called in a large sense logic. If the considera tion be specially directed to the mode in which, by means of this combination, knowledge arises, and therefore include discussion of the wide problem regarding the relation between understamiingand objectivity in general (the matter of knowledge taken generally), the special title transcendental logic may be used. But if, concentrat ing attention solely on the kind of opei-ation implied in under standing, we endeavour to lay out fully the modes in which under standing proceeds in the construction of knowledge, making nbstraction of all inquiries regarding the origin, worth, significance of knowledge itself, the consideration is of a more general charac ter, and may receive the title of general logic. 2 The understanding, then, like everything else, works according to laws, the laws of its own nature. If we abstract from all that may characterize the matter considered, and take into account solely the laws according to which understanding must act, we may con struct a purely formal doctrine, a theory which is rational both in matter and in form, for the matter consists of the laws of reason, and the form is prescribed by the very nature of reason, a demon strative theory, for nothing can enter therein which cannot be shown to have its ground in reason, a completed theory, for although the matter of thought is infinite and infinitely varied, the modes in which the understanding must operate if unity of 1 See article K.VXT. vol. xiii. pp. 849, 852. 2 It does not seem necessary to advert more in detail to the divisions and sub divisions of logic drairn out in the Kritik, pp. 80-93 (Hixrtenstein s cd., 1868). cognition is to result, are finite and capable of exhaustive statement, and a theory developed from its own basis, standing in no need of psychology or metaphysics, but deducible from the mere idea of understanding as that which introduces unity into representations, whether given (empirical) or a priori (pure). Were this the only determination of the province of logic given by Kant, the question which at once arises as to the possibility of any such independent doctrine would receive an easy solution. For it is evident that logic, as a theory of the form of thought, could consist only of a portion of the more general doctrine, by whatever title that be known, in which the nature of understanding as synthetic activity is unfolded. The distinction on which Kant lays stress between matter and form, a distinction employed by all subsequent writers of his school, is ambiguous and misleading. If by matter be meant the particular characteristics of the things thought about, in which sense we might speak of judgments of physical, chemical, grammatical matter, and so on, then to say that logic does not take this into account is perfectly inept. If logic be a philosophic discipline at all, a theory in any way concerned with thinking, it is at once evident that it can in no way deal with the specialities of any particular science. But this distinction between matter and form is by no means identical with another, lying in the background, and too frequently confused with the first, the distinction of understanding as a faculty per se with its own laws, deducible from its mere notion, and understanding as the concrete real act of thinking. What Kaut calls the mere idea of under standing, and what in other writers of his school appears as a definition of thought, is really nothing but a reference to what has presented itself in the wider inquiries of the Kritik as the com plex nature of the synthetic activity of understanding. Kant him self never attempts to deduce from the notion of understanding the varied characteristics of logical forms, and his followers, e.g., Hamilton, when they are consistent, start from concepts as ex pressing the bare notion of thought, and regard all other forms of thought as combinations of concepts. But Kant does introduce another element into his treatment of the province of logic, one not original to him, but of the utmost import ance for later developments from his point of view. He inquires- what kind of relations among the elements of thought can form the matter of logical treatment, and defines these as two in number (1) formal consequence, (2) non-con tradictoriness. By formal con sequence we are to understand the relation between a conclusion and its premisses, no inquiry being raised as to the truth or validity of the premisses. By non-contradictorinesswe are to understand that, logically, notions, judgments, or reasonings can be subjected to treat ment only in regard to the absence of explicit contradiction among the factors entering into them. Thought, which introduces unity and system into experience, must certainly introduce formal con sequence and preserve analytic truth or correctness. Formal logic, then, treats only of these formal qualities of all products of thought. 3 The detailed treatment of logic, so far as that can be gathered from the very brief summary (Locjik, IVcrke, iii. 269-340), shows with the utmost clearness how impossible it was for Kant to deduce the forms and relations of thought from the mere notion of under standing, even when coupled with the principles of formal con sistency and consequence. Assuming that understanding is the discursive faculty, the faculty of cognizing the many particulars through the one concept or notion, Kant deals first with concepts (Begriffe) as general or discursive representations. He is careful to avoid an error into which many of his followers have fallen, that of regarding Begrift e in a mechanical fashion as a specific kind of Vorstellung, distinguished only by containing a few of the marks making up the single intuitions. He rightly notes that cognition proceeds by subsuming the particulars under the common ele ment contained in them, and that the generality of the concept thus rests upon the relation in which it stands, as reflective ground of cognition, to the particulars. The characteristics of concepts, as possessing extent and content, are treated briefly, after the fashion familiar in the more detailed logics of his school. It is, however, when the doctrine of judgment is reached that the difficulties of his position appear with greatest distinctness. Judgment is de fined &quot; as the representation of unity in the consciousness of distinct representations, or the representation of the relation of&quot; 3 Two at least of the followers of Kant have worked out the system of logic from this point of view, the one, Twesten, in his Logik, insbesondi-re die Ana- tytik (1825), the other, the late Professor Mansel, in his Prolegomena f.oyica. JIansel recognizing the distinction between the two modes of determining formal logic, adopts the second, and is therefore led, in consistency, to define logic, not as the science of the laws and forms of thought, but as the science treating of formal thought, or of the formal element in the forms of thought. In other words, he recognizes that the statement of the forms of thought must be intro duced into logic ab extra, from psychology or what not, and that logic, accepting these, has to consider the formal element (non-contradictoriness) in them. It is well to have the doctrine brought tints to its ultimate issue, for it is thence apparent that there is no independent science called logic, but simply one compre hensive precept, which may be called logical, viz., avoid contradietoriness in thought. Illustrations of the ways in which contnulictoriness manifests itsilf ir&amp;gt;ay lie offered, and a useful logical praxis may thus be afforded, but these do- not make up a science or theory.