784 LOGIC
5. In order to make clear the reasons for this astonishing diversity of opinion regarding the province and method of logic, and so make some advance towards a solution of what may well be called the logical problem, it seems necessary to consider some of the leading conceptions of logic, with such reference to details as will suffice to show how difference of fundamental view determines the treatment of special logical problems. In this consideration the order must be historical rather than systematic. Not, indeed, that it is needful, nor is it proposed, to present an historical account of philosophy at large, or even of logic in particular; our purpose is merely to disentangle and bring clearly forward the nature of the principles respecting logical theory which have served as basis for the most characteristic logical systems. Such an inquiry will not only assist in explaining the divergencies of logical systems, but throw light upon the essence of logic itself.[1]
In this historico-critical survey, the first section must naturally be devoted to a consideration of the Aristotelian logic. The records of Oriental attempts at analysis of the procedure of thought may, for our present purpose, be disregarded.[2]
The Aristotelian Logic.
6. In a remarkable passage at the close of the tract called by us the Sophistical Refutations, Aristotle claims for himself distinct originality in the conception of subjecting to analysis the forms or types of argument. "The system I have expounded had not been partially, though imperfectly, elaborated by others; its very foundations had to be laid. ... The teachers of rhetoric inherited many principles that had long been ascertained; dialectic had absolutely no traditional doctrines. Our researches were long, tentative, and troublesome. If, then, starting from nothing, it bears a comparison with others that have been developed by division of labour in successive generations, candid criticism will be readier to commend it for the degree of completeness to which it has attained than to find fault with it for falling short of perfection."[3] Although the specific reference in this passage is to the analysis of dialectical argument contained in the Topica, the same claim might with justice have been made in regard to the more extensive analysis of the forms of reasoning in general which makes up the substance of the other books of the Organon. There had been, prior to Aristotle, much discussion of problems that would under any view be included under the head of logic, but no systematic attempt had been made to analyse knowledge as a whole in its formal aspect, to throw under general heads or classes the types of reasoning, whether dialectical or scientific, and to exhibit the general relations in which the elements of all reasoning stand to one another. After Aristotle, it became possible to refer all such discussions to a common head, and to view them as component parts of one systematic doctrine. In a peculiar sense, then, Aristotle may be described as the founder of logical science.
The precise nature of the inquiries falling within the scope of the Aristotelian logic may receive some preliminary explanation supplementary to that which can only be given by a careful study of the chief theorems of the system, if there be taken into account (a) the advances towards a theory of logical method contained in the speculations of earlier Greek thinkers, (b) the classification of philosophic discipline which underlies the body of Aristotle's writings, and (c) the general conception of the matter of logical analysis which may be deduced from any special or incidental treatment of the question in Aristotle. Of these in order.
7. (a) Logical discussions prior to Aristotle.
The inquiries which find a place in the Aristotelian logic are all, in a large sense, problems of the theory of knowledge. They arise, therefore, only in connexion with critical reflexion on the nature, grounds, and method of knowledge. The earliest forms of Greek speculation, turning rather upon explanation of natural fact, being in _essence attempts to reduce the multiplicity of known fact to unity of principle, contain, as a consequence, problems of a metaphysical character, which might involve problems of strictly logical character,_ but were logical only in potentiality. Of all these metaphysical questions the most important centre round the fundamental opposition between unity of principle and multiplicity of fact, between the one and the many, an opposition which under varied forms presents itself at every stage in the history of philosophic speculation. In the first period of Greek speculation, the problem presented itself in its simplest, most direct aspect, and, after a few rough attempts at a quasi-physical explanation of the genesis of many out of one, there come forward, as reasoned, ultimate solutions, the Eleatic doctrine that only unity has real being, the Heraclitic counter-doctrine that only in change, in the many, is truth to be found, and the Pythagorean notion of number, harmony, as containing in abstracto the union of the opposites, one and many. No one of these philosophic treatments can be said to contain specifically logical elements, but they raise questions of a logical kind, and, especially in the records of the Eleatic views, one can trace a close approximation to the critical reflexion which marks the transition to a new order of ideas. Results which in these systems are stated with metaphysical reference only, reappear with new aspect among the sophists and the Socratic schools. The transition stage, indeed, partly aided by the atomic separation of objective fact from subjective sense experience, is mainly the effect of the sophistic and Socratic teaching. Socrates and the sophists have this in common that both treat the fundamental problem of philosophy as it had been handed down with special reference to the subjective experience of the individual. In the teaching of the sophists generally is to be discerned the opposition between subjective reflexion and objective fact; in that of Protagoras and Gorgias in particular there appear as problems of the theory of knowledge difficulties for the older metaphysic of Heraclitus and the Eleatics respectively. The Heraclitic principle of change is the general foundation for the doctrine that the momentary perception is the only fact of cognition, and upon it may be based the conclusions that all truth is relative to the individual state of the individual subject, and that judgment, as a mode of expressing truth, is a contradiction in itself. Thus the extreme Heracliteans, as Cratylus, rejected the proposition, or combination of words, as expressing a unity and permanence not to be found in things, and reduced speech to the symbolism of pointing with the finger. Less developed but not less clear is the connexion between the brief sceptical theses of Gorgias and the Eleatic doctrine of unity . As knowledge was impossible on the Heraclitean view, since it implied a synthesis not discoverable amidst incessant change, so for Gorgias knowledge was impossible, since in the synthesis was involved an element of difference, multiplicity, not reconcilable with the all-embracing unity of things. It is evident from the treatment of such views in Plato and in Aristotle, how many of the illustrations used in support of the general thesis depended for their apparent strength on neglect of some of the elementary conditions of thought, and how inevitably reflexion upon these difficulties led to the construction of a theory of thought. The first outlines of such a theory are to be found in the Socratic principle of the notion (or concept, as we may call it, for the notion as viewed by Socrates is certainly the concrete class notion, the simple result of generalization and abstraction), and to Socrates is assigned by Aristotle the first statement of two important logical processes – induction, or the collection of particulars from which by critical comparison a generalized result might be drawn, and definition, or the explicit statement of the general elements disclosed by critical comparison of instances.[4] In the Socratic teaching, so far as records go, no explicit reference was made to the problems in connexion with which those processes are of greatest significance, but in the lesser Socratic schools on the one hand, and in Plato on the other, we find the new principle either brought to bear upon the old difficulties, or developed into a comprehensive method.
The Socratic concept contains in itself the union of one and many, but it is in nature subjective; it is a mode of knowledge. If, then, it be regarded as only subjective, the old difficulties reappear. How is it possible to reconcile, even in thought, an opposition so fundamental as that between unity and plurality? Must there not be a like irreconcilable opposition between the subjective counterparts of these objective relations, between the individual notion, the atom of knowledge, and the proposition or definition? How, indeed, can there be a combination in thought of that which is in essence uncombinable? Whether we take Aristippus, who draws mainly for theory of knowledge on the Heraclitic-Protagorean sources, or Antisthenes, who leans towards the Eleatic, or the Megarics, who also, in accordance with the Eleatic thoughts, devoted chief attention to the polemical aspect of the theory, we find a set of problems appearing, the solution of which imperatively called for a theory of knowledge as the combination of one and many. Perhaps the most interesting of these early thinkers, so far as the history of logic is concerned, is Antisthenes, whose extreme nominalism presents the most curious analogies to some recent logical work.[5] According to Antisthenes, the world of cog-
- ↑ For a notice of works on the history of logic, see note A p 802.
- ↑ For a notice of some of the more developed systems of Oriental logic, see note B p. 802.
- ↑ The above translation, which is somewhat free, is taken from Mr Poste's edition of the Sophistici Elenchi, p. 95.
- ↑ Metaph., 1078b, 27-29.
- ↑ On Antisthenes, see the third part of the Theætetus, which appears, beyond doubt, to refer to him (comp. Peipers, Untersuchungen über das System Plato's, 1874, pp. 124-48), and Aristotle, Metaphysics, 1024b, 32; 1043b, 24; Topica, 104b, 21.
