Why No Possible World is Mathematical
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The notion of possible mathematical world is discussed. The problem is analyzed from the point of view of two classical realistic stances in the philosophy of mathematics (Quine's realism and Gödel's Platonism), and from the point of view of Balaguer's full-blooded Platonism. Balauger's stance seems to be compatible with the use of the notion of a possible mathematical world (a universe), but as a matter of fact it is not. If one adopts such a notion, several profound philosophical problems arise, concerning e.g. the criterion of identity, the problem of the 'borders of mathematicity', the problem of singling out the actual world from a possible one. In conclusion the author claims that the notion of possible world is not clear enough to be used in ontological discussions concerning mathematics.
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