Philosophy Dictionary of ArgumentsHome
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| Continuum hypothesis: The continuum hypothesis is a statement in mathematics that says that there is no set of real numbers whose cardinality is strictly between that of the integers and that of the real numbers. In other words, there are no sets of real numbers that are bigger than the set of integers but smaller than the set of real numbers. See also Continuum, Real numbers, Sets, Set theory._____________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 Continuum Hypothesis - Dictionary of Arguments
I 48 Continuum hypothesis/mathematics/physics/Field: analogy in physics formulated without set theory: e.g. for each subregion of a line there is either a graph depicting a 1/1-Correspondence to another line, or a 1/1-Correspondence to a discrete region of the type w but no reason to assume that the response in the physical case is the same as in the mathematical case. Cf. >Set theory._____________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 Continuum Hypothesis
Ed. Martin Schulz, access date 2024-04-27