Lexicon of Arguments

 Philosophical and Scientific Issues in Dispute
 
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Field I 22
PlatonismVsNon-factualism/mathematics/Field: If we assume platonistically that the number 2 is a definite object, then the question whether the set {, {}} (also as a concrete object) is identical with it would be a question of fact.
>Mathematical entities, >Sets, >Numbers, >Interpretation/Benacerraf.
Field: if one admits the Platonism, perhaps, but I do not.
>Platonism.
Structure/Structuralism/Mathematics/Benacerraf: one can also see it "structuralist" that there are literally no numbers, but structures are the ω-sequences.
KitcherVs: (1984)(1): if numbers are not acceptable entities, then also not the ω-sequences.
FieldVsVs: there is a variant with a solution: indeterminate reference or referential indeterminacy.
Field: indeterminacy of the reference is an everyday fact!
>Indeterminacy, >Belief/Benacerraf.


1. Kitcher, P. (1984). The nature of mathematical knowledge. Oxford University Press, Oxford.

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