 The unease many have about multiverse proposals are only reinforced by the liberal appeals to “infinities” in discussion of the  idea.[55]  Many have argued, for example, that we must formulate an account of anthropic reasoning that applies to a truly infinite, rather than merely very large, universe. Claims that we occupy one of infinitely many possible pocket universes, filled with an infinity of other observers, rest on an enormous and speculative extrapolation. Such claims fail to take seriously the concept of infinity, which is not merely a large number. Hilbert (1925 [1983]) emphasized that while infinity is required to complete mathematics, it does not occur anywhere in the accessible physical universe. One response is to require that infinities in cosmology should have a restricted use. It may be useful to introduce infinity as part of an explanatory account of some aspect of cosmology, as is common practice in mathematical models that introduce various idealizations. Yet this infinity should be eliminable, such that the explanation of the phenomena remains valid when the idealization is  removed.[56]  Even for those who regard this demand as too stringent, there certainly needs to be more care in clarifying and justifying claims regarding infinities.