# Philosophy Lexicon of Arguments

Platonism: Platonism in the narrower sense is the thesis in modern philosophy that some ideas and mental objects, especially ideas, are attributed reality. Various authors are Platonists with respect to e.g. numbers, mathematical entities, or universals. In contrast, e.g. intuitionism of mathematics assumes that numbers are not objects. This distinction has a significant effect on the logical formalisability of statements of mathematics. See also nominalism, mathematical entities, theoretical entities, completeness, evidence, fictions.

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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Item Summary Meta data
I 8
Platonism/Field: his only argument is the applicability of mathematics.
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I 14
FieldVsPlatonism: has to answer the fictionalist in his language - cannot rely on his "initial plausibility".
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I 152
Definition Priority thesis/PT/Wright: Thesis: the priority of the syntactic over the ontological categories. - Platonism/Wright: that allows Frege to be a Platonist. - Definition Gödelian Platonism/Wright: in addition: the thesis that mathematical knowledge must be explained by a quasi-perceptual relation - FregeVsGödel - WrightVsGödel: we do not need that.
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I 153
Definition weak Priority thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term.
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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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I 186
Definition 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. - Definition Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact.
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l 189
Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers.
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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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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.
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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?
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III 90
Platonistic/Field: are terms such as e.g. gradient, Laplace Equation, etc.
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III 96
1st order Platonism/Field: accepts abstract entities, but no 2nd order logic - Problem: but he needs these (because of power quantifiers).

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2018-06-22