I 8
Platonism/Field: his only argument is the applicability of mathematics.
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Mathematics/Field, >
Mathematical entities.
I 14
FieldVsPlatonism: Platonism has to answer the fictionalist in his language - it cannot rely on it's "initial plausibility".
I 152
Def Priority Thesis/PT/Crispin Wright: Thesis: the priority of the syntactic over the ontological categories.
Platonism/Wright: that allows Frege to be a Platonist.
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Numbers/Frege, >
Gottlob Frege.
Def Gödelian Platonism/Crispin Wright: in addition: the thesis that mathematical knowledge must be explained by a quasi-perceptual relation.
FregeVsGödel.
WrightVsGödel: we do not need that.
I 153
Def weak Priority Thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term.
l 159
Equivalence/Platonism/Nominalism/Field: Question: In which sense is a Platonist statement (e.g. "direction 1 = direction 2") and a nominalistic statement equivalent (c1 is parallel to c2)?
Problem: if there are no directions, the second cannot be a sequence of the first.
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Nominalism.
I 186
Def Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations.
Def Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact.
l 189
Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers.
I 192
Heavy Duty Platonism/Field: assumes size relationships between objects and numbers.
FieldVs: instead only between objects.
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II 332
Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable.
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Field theory.
II 334
Quinish Platonism/Field: as a basic concept a certain concept of quantity, from which all other mathematical objects are constructed. So natural numbers and real numbers would actually be sets.
III 31
Number/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ( "What line?") - What should be zero point - What should be 1?
III 90
Platonistic/Field: are terms such as e.g. gradient, Laplace Equation, etc.
III 96
1st order Platonism/Field: accepts abstract entities, but no 2nd order logic - Problem: but he needs these (because of the power quantifiers).