Psychology Dictionary of ArgumentsHome | |||
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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._____________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 | Concept | Summary/Quotes | Sources |
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Hartry Field on Platonism - Dictionary of Arguments
I 8 Platonism/Field: his only argument is the applicability of mathematics. >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. >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. >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. --- II 332 Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable. >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)._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 |