Philosophy Dictionary of ArgumentsHome
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| Mathematics: Mathematics is the study of patterns and relationships. It encompasses arithmetic, algebra, calculus, geometry, trigonometry, topology, and others. Mathematics is used in science, engineering, business, and finance. See also Physics, Logic._____________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. | |||
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Charles Chihara on Mathematics - Dictionary of Arguments
Field III 44 f Mathematics / Chihara: Thesis: numbers are only linguistic entities - not abstract entities. >Numbers, >Mathematical entities, >Abstract objects. FieldVsChihara: 1st then there may only be predicative predicates (i.e. no bound variables of a higher order than ^ x). >Predicativeness, >Levels/order, >Second Order Logic. 2nd Chihara must also take account of never expressed tokens 3rd Chihara does not show the use of extrinsic, causally irrelevant entities. >Causality, >Extrinsic, >Use, >Relevance, Cf. >Electron example._____________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 |
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> Counter arguments against Chihara
> Counter arguments in relation to Mathematics
Ed. Martin Schulz, access date 2024-04-19