Philosophy Dictionary of ArgumentsHome
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| Interpretation: A) Making statements about other statements, whereby new vocabulary may be introduced. If no new vocabulary is introduced, new information can be obtained by changing the syntactic grouping. B) In logic, interpretation is the insertion of values (objects) instead of the constants or free variables. _____________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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P. Benacerraf on Interpretation - Dictionary of Arguments
Field I 22 Interpretation/Benacerraf: (1965)(1) Thesis: Identification of mathematical objects with others is arbitrary - E.g. numbers with quantities. - E.g. real numbers with Dedekind cuts, Cauchy sequences, etc. - There is no fact that decides which is the right one. >Equations, >Equality, >Identification, >Real numbers, >Numbers, >Mathematics, >Mathematical entities. Field ditto. I 22 Indeterminacy of reference/Field: is not a problem, but commonplace. >Reference, >Indeterminacy. I 25 For Benacerraf it is about identity, not about reference - otherwise he might falsely be refuted with primitive reference: "Numbers" refers to numbers but not to quantities - But that is irrelevant. Cf. >Reference/Field. I 25 BenacerraffVsPlatonism: locus classicus - VsBenacerraf: based on an outdated causal theory of knowledge. >Platonism, >Causal theory of knowledge. Field I 25 BenacerrafVsPlatonism: (1973)(2): if without localization and interaction we cannot know whether they exist. VsBenacerraf: indispensability argument. 1. Benacerraf, P. What Numbers Could Not Be, The Philosophical Review 74, 1965, S. 47–73. 2. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679._____________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. |
Bena I P. Benacerraf Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984 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 |
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> Counter arguments against Benacerraf
> Counter arguments in relation to Interpretation
Ed. Martin Schulz, access date 2024-04-18