## 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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Books on Amazon |
I 8 Platonism/Field: his only argument is the applicability of mathematics. --- I 14 FieldVsPlatonism: has to answer the fictionalist in his language - cannot rely on his "initial plausibility". --- 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. --- I 153 Definition 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. --- 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. --- 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. --- II 332 Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable. --- 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 power quantifiers). |
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 2017-05-28