The Characters of the Aristotelian Logic

THE CHARACTERS OF THE ARISTOTELIAN LOGIC CLASSICAL logic involves a doctrine as well as a technique. Both are intimately associated because the processes of thought organize themselves ultimately on the strength of their correspondence with the deeper fabric of reality. To be sure, the mind can well go beyond the presentations of consciousness, and build logical patterns of its own which may or may not have a counterpart in new experiences. Yet, the fact remains that, in the last resort, the potential must be justified in terms of the actual, and this may be considered as the basic motivation of the Aristotelian logic. On the other hand, modern logic, as expounded by scientific positivism especially, endeavors to explain the real in terms of the possible. From this angle, which stresses exclusively the formal aspect of science, it is natural that Aristotle's logic should appear as a restricted portion of the vast field which is now known as mathematical logic; and the more so, as it is casually maintained that Aristotle built his logic with his biological and linguistic intuitions at the expense of any mathematical inspiration. These considerations, however, have value only as consequences of the nominalistic principles which have been arbitrarily monopolizing the evaluation of modern logic. A truer alternative is offered by a combined interpretation of Aristotle's logical technique and ontological doctrine. Hence, the purpose of this essay is to show the real characters of the Aristotelian logic, to emphasize the mathematical aspect of its general background , and to estimate its importance with regard to the recent developments of the science of thought. THOMAS GREENWOOD I. THE ORIGIN oF LoGIC The idea of necessity, which Plato tried unsuccessfully to impose in his own way on the universe of being, was rediscovered by Aristotle in the concrete world and in the realm of thought separately. In endeavoring to systematize the conditions of this parallelism between being and thought, which the Eleatics had already noticed, Aristotle opened the way to the establishment of logic as a science. In this respect, he well deserves the compliment he paid himself for having created a new science, when he said, without disparagement of others, that the subjects treated in the Topics had never before received any scientific discussion.1 One can hardly say that a ready-made ~cience of logic came out of Aristotle's mind, as many elements of his system are found in earlier writers. But it is also unfair to consider Aristotle as a mere compiler or systematizer of what had been worked out before in this :field.2 In fact, no complete logical system is to be found in any of his predecessors, although their discussions about mathematics and language have distinct logical implications and prove that they were actively interested in the formal problem of the structure of deductive science. Plato was aware, of course, of the postulational character of mathematics, which he could not call real knowledge so long as its assumptions were left unexamined.8 But, though he considered the possibility and the necessity of a higher and more rigorous science, he was able only to describe the aims of dialectic, without establishing it as an independent science. Thinking and reasoning correctly are so natural to the mind, that it seemed scarcely necessary to exteriorize into cold rules the behavior of what we all enjoy as a natural gift. Hence Plato went no further than proposing the gradual mathematization of knowledge as the ultimate practical rule for the rationalization of things 4 and of our knowledge of reality. ' Sophistic:al Refutations, 183b 34 • Cf. Enriques, The Historic Development of Logic, p. 4. • Republic, VII, 533 C. • The reduction of pure mathematics to absolute deduction remained but an THE CHARACTERS OF THE ARISTOTELIAN LOGIC 223 It is true, however, that Plato gave in his writings important hints of the later logic, but there is no justification in supplying a science of pure thought by inferences from his own methods, or by a combination of his incidental logical references. As Zeller says, " though we cannot but recognize in Plato essential elements of the Aristotelian logic, it would be a mistake to force these out of their...