Hilbert’s Hotel as Purely Possible and as an Actuality

Authors: Gilead A*

DOI: 10.23880/phij-16000S1-005

Special Issue 1: Practical Uses of Philosophy

Abstract

It was George Gamow who publicized the world of the fascinating thought-experiment that he called “Hilbert’s Hotel,” whose author was the eminent mathematician David Hilbert and which Gamow interestingly associated with the Big Bang cosmology and the expansion of the universe. The number of the rooms in Hilbert’s Hotel is infinite and they are always fully occupied. Nevertheless, this fantastic hotel can receive any number of new guests at any time and can find a vacant room for each of them. According to Gamow and some interpreters, Hilbert’s Hotel demonstrates how an actual infinite is possible and that it is not an absurd idea. In contrast, others have interpreted Hilbert’s thought-experiment as meant to show the contrary, namely, that an actual infinity is impossible and simply an absurd idea. In this paper, I explain how Hilbert’s Hotel can be purely possible and actual as well.

Keywords: Actual infinite(ies); Mathematical possibilities; Mathematical objects or entities; Possibilism; individual pure possibilities; Panenmentalism; the Big Bang; New inflation cosmology; David Hilbert; George Gamow; Frederick Hoyle; Baruch Spinoza

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