Psychology Dictionary of ArgumentsHome
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| Description Levels: Levels result from dividing a domain into sub-domains, for which different rules for making statements are valid. Thus, e.g. other statements are made about sets than about their elements. See also metalanguage, object language, theories, metatheory, metalogic, metasemantics, meta-ethics, meta-level, paradoxes, order, 2nd order logic, higher order logic, HOL, completeness._____________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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Hartry Field on Description Levels - Dictionary of Arguments
II 345 Indefiniteness 2nd order: it is unclear whether an undecidable sentence has a particular truth value. >Platonism. II 354 Logic/second order logic/Field/(s): excludes non-standard models better than theory 1st order. - 2nd order has no impredicative comprehension scheme. >Second order logic, >Comprehension, >Unintended models, >Models, >Model theory. --- III 33 Theory of the 1st order/Field: E.g. the theory of the space-time points. - (s) E.g.a theory which only uses functions but does not quantify over them. >Quantification. Theory 2nd order/Field: E.g. theory of real numbers, because it quantifies over functions. - Quantities of higher order: are used for the definition of continuity and differentiability. III 37 Theory of 1st order/2nd order/Hilbert/Field: Variables 1st order: for points, lines, surfaces. 2nd order: Quantities of ... Solution/Field: quantification 2nd order in Hilbert's geometry as quantification over regions. Only axiom 2nd order: Dedekind's continuity axiom. III 95 f Logic 2nd order/Field: E.g. Quantifiers like "there are only finitely many". - Also not: E.g. "There are less Fs than Gs". >Quantifiers. III 98 Extension of the logic: preserves us from a huge range of additionally assumed entities. - E.g., what obeys the theory of gravity. QuineVs: we should rather accept abstract entities than to expand the logic. (Quine in this case pro Platonism). III 96 Platonism 1st order/Field: accepts abstract entities, but no logic 2nd order. Problem: but it needs this (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 |
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> Counter arguments against Field
> Counter arguments in relation to Description Levels
