 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 – which is needed to accommodate continuous and discontinuous linear paths. (This power set has the cardinality of the set of mathematical functions from reals to reals.) But scientific theories do not appear to require the existence of any set larger than that power set. So, a philosopher who has positivistic inclinations might tentatively conclude that the cardinal number of this power set (which is at least \(\aleph_2\)) is in fact the largest cardinal. In a related vein, W. V. O. Quine dismisses “excessive” magnitudes, for instance, “\(\beth_\omega\) and inaccessible numbers,” as mere fancies of “recreational mathematics” bereft of of ontological import (Quine 1986, p. 400; cf. Quine 1960, Ch. 7). If a reader is unfamiliar with Quine’s illustrations of scientifically gratuitous magnitudes, please note that \(\beth_0 = \aleph_0\), \(\omega\) (omega) is \(\aleph_0\)’s [infinite] ordinal counterpart, i.e., \(\aleph_0\) is the \(\omega\)-th cardinal number, and \(\beth_\omega\) is the \(\omega\)-th iteration of the power set of \(\beth\)0; inaccessible numbers (roughly speaking) are (putative) uncountable large cardinals which cannot be derived via summations of, or power set operations on, smaller cardinals. Quine judges that such magnitudes exceed the theoretical demands of the empirical sciences because admitting them would not contribute to the simplication of our scientific computations and generalizations. Even so, there is a view of the cumulative set-theoretical hierarchy to which Quine seems (reluctantly) willing to accede, at least in part because it provides a “convenient cut-off” limiting the extent of that hierarchy. According to this view, all sets are constructible (in a sense defined by Kurt Gödel) from more elementary sets, a position significantly more restrictive than is needed to avoid the known set-theoretical paradoxes. But, arguably, when examining omnipotence, given its robust theological and metaphysical dimensions, a less positivistic or naturalistic, more expansive, criterion of ontological commitment is appropriate. After all, it would be natural to assume that the Supreme Being has the power to create any number of possible worlds governed by different laws of nature. Given that assumption, it appears that an omnipotent agent’s power would not be circumscribed by theoretical scientific laws governing the actual world.