Abstract
Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator.
Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them.
STATEMENT OF MODAL PLATONISM. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@.
Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown:
MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T.
The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.
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Friedman, J.I. Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities. J Philos Logic 34, 227–273 (2005). https://doi.org/10.1007/s10992-005-0557-4
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DOI: https://doi.org/10.1007/s10992-005-0557-4