Abstract

This is a complement of 'Cantor's set theory and his philosophy', compiled in my collected papers, Borderland between Mathematics and Philosophy (1998, in Japanese). Cantor (1845-1918) was a mathematician with a strong tendency to philosophy, which tendency appeared as early as 1867 (Dissertation), and finally exerted latent influences upon the formation of transfinite set theory. For a purely mathematical purpose, this theory as well as its formation process can be explained without any reflection on his philosophical writings. However, in this case, we shall miss the complete figure of his conception. In fact, he expressed an opinion on Time and Space, opposed to Kant, on the basis of his Continuum, and gave an interpretation of-Spinoza's 'Deus' (in Ethica) through his transfinite ordinals (1883). He attempted, too, to establish a sort of Pythagorean Natural Philosophy, but in vain, in which was applied the Continuum Hypothesis (1885). This Natural Philosophy, fantastic as it was, can be traced back via several marks in his papers up to 1867. On the other hand, to speak frankly, Cantor's philosophical reasonings are far from systematic, and sometimes remain casual remarks.