A philosopher with positivistic or naturalistic leanings should posit transfinite cardinals of only those sizes required by prevailing scientific theories.

However, a philosopher who has positivistic or naturalistic leanings might argue that one should posit transfinite cardinals of only those sizes required by prevailing scientific theories. Arguably, the prevailing theory of the space-time continuum in physics is committed to the existence of infinite sets which have the cardinality of the set of space-time points contained within such a continuum (which is at least \(\aleph_1\)). If an argument of that sort is correct, this scientific theory is, in addition, committed to the existence of the power set of the foregoing set of space-time points ...