Logic as Logics

Four kinds of logic are found throughout the history of Western philosophy : I. formal logic, 2. transcendental logic, 3. dialectical logic, 4. analogical logic. The formal logic established by Aristotle is based upon the law of identity. According to Parmenides, from whom this law is originally derived, there are only two ways how to start philosophising, viz., ‘being is being ' or ‘not-being is not being' --an explicit declaration of the law of identity. Being undoubtedly the surest and the most evident of all the propositions, it is, however, at the same time simply self-evident saying almost nothing, nothing indeed but a mere truism. This is the reason why Kant maintained that genuine judgements should be synthetic instead of being merely analytic ; what his transcendental logic requires is : ‘A is B', and not : ‘A is A, '; he remarks that the law of identity--so also that of contradiction--is a principle essential to our thinking but is not sufficient by itself for constituting any knowledge worthy of the name. From this point of view the transcendental logic may be looked upon as an amelioration of formal logic. Another law indispensable in the formal logic was that of contradiction, the discovery of which is ascribed to Zeno, the disciple of Parmenides. It is no other than the law of identity itself, only in a different aspect. From Zeno's view-point the third, i. e. the dialectical, logic would be nothing but the violation of the principle of his logic ; for, while in his logic the law of contradiction excluded contradictions, postulating their non-entity, the dialectical logic does include contradictions. Its formula reads : ‘A=non-A'. Such a formula, unallowable in the traditional logic, constitutes here its very essence. Hegel's logic is thus a construction exactly reverse to that of Zeno. In the fourth place we reach the logic of analogy, notable in significance in spite of its serious neglect on the part of the human intellect. Having originated in the philosophies of Plato and Aristotle, it was explicitly carried out by Thomas Aquinas. This logic consists in the reversal of what was required in the formal logic by the law of excluding the middle, which law, allowing nothing midway between two truths, postulated that one proposition must be either true or false and that there could be none which would be neither true nor false. It is when the so-called probable or possible assertion comes into question, that the analogical logic has its rôle to play. This may be formulated : ‘A : C = C : B'. Here A and B are not connected directly ; a middle term is introduced, which connects these two terms. I have not, however, entered into discussions in full concerning the nature and significance of this particular logic ; the theme has been of late carefully dealt with by J. Anderson in his work “Bond of Being”. The aim of this paper was rather to exhibit the said four logics in comparison, examining each in its specific character as a logic ; only, stress has been laid on how the logic of analogy should be necessitated by the dialectical logic itself ; the key to the understanding of this point will be found, as I believe, in what is called the infinite judgement