A Study in the Philosophy of Science by Evert W. Beth (Eds.)

By Evert W. Beth (Eds.)

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According to Lukasiewicz, the Stoics defended a linguistic interpretation of logic. This seems not to be correct. The Stoics made a clear and apposite distinction between (i) the sound of a word, (ij) its meaning, (iij) the external object which it denotes, and (iv) the subjective image connected with it. 63 ) Logic deals only with meanings. v") enabled the Stoics to adopt, in their logical studies, a formalistic point of view and to ignore complications of a linguistic or psychological nature which they rightly considered as irrelevant in this connection; the usual reproach that they mixed up logic and grammar is, therefore, utterly devoid of justification and can be made only by scholars who do not sufficiently distinguish between logic and psychology, or who are unaware of 24 THE PREHISTORY OF RESEARCH INTO FOUNDATIONS the importance of sentential logic or of its independence with regard to predicate logic.

Vol. 177, 1940), that there are no grounds to attribute, with H. HlI8se-H. Scholz, Die Grundlagenkrisis der griechischen Mathematik (KantBtudicn vol. 33, 1922), a system of infinitesimal calculus a la Cavalieri to Zeno's opponents; we must rather ascribe to them an atomistic conception of the continuum comparable to the views of Giordano Bruno; cf. H. Lasswitz, Geschichte der Atomistik, Hamburg-Leipzig 1890. 88) All these texts are reproduced, of course, in Diels-Kranz, Die Fragmente der Vorsokratiker (cf.

7) Let F (x, y) be the phrase: x takes its exchange-value [rom. y; then 1 will be the Wertsubstanz in the sense of Marx. The application of the Principles of the Absolute is what Plato 38) calls 'progressing to the anhypotheton' and what Aristotle 39) calls 'induction'. Belief in the Principle of the Absolute is the basis for several of the traditional proofs for the existence of God. Kant 40) refers to the Principle of the Absolute as the 'Prinzip der Vernunft'. In his opinion, the principle has no conclusive force (nevertheless he applied it when he introduced the categorical imperative).

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