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

By Evert W. Beth (Eds.)

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In my opinion, this current interpretation is basically correct; but one might wish to connect a more definite picture with these rather enigmatic statements, and this indeed possible if we use the first-order predicate calculus with identity, as follows. In this system, the sentence: there are exactly three red roses, can be expressed as follows: (Ex)(Ey)(Ez)[a(x) & b(x) & a(y) & b(y) & a(z) & b(z) & y=/=z & z=/=x & &x=/=y & (t){[a(t) &b(t)]-+ [t=xvt=yvt=z]}] if a is taken to stand for red, and b for rose.

The author rightly stresses the divergences between MeliBBus and Zeno (p. 113) and clearly points out that Aristotle, in his discussion of the Stadion paradox, 'has entirely missed the point of the argument' (p, 89). But, in my opinion, his defence of the conventional view 'that Parmenides had declared all plurality and motion to be in some way or other illusory', and 'that Zeno's arguments were intended to give support to Parmenides' thesis' (p. 65) against the interpretations set forth by P. Tannery and G.

Nevertheless, they seldom go farther back in the history of thought than to Kant's criticism, the relative importance of which in this connection is thereby greatly exaggerated. In my opinion, we must go back at least to Aristotle if we want to grasp the ultimate roots of the doctrinal divergences which have arisen from the results of modern research into the foundations of mathematics. Indeed, it was Aristotle who, inspired by Plato's philosophy, systematically set forth a theory of science which for centuries to come directed and actually dominated scientific and philosophical thought.

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