Philosophy Dictionary of ArgumentsHome
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| Finiteness: Finiteness is the property of having a limited number of elements or members. It is the opposite of infinity. See also Infinity, Sets, Classes, Element relation, Numbers, Real numbers._____________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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A. Heyting on Finiteness - Dictionary of Arguments
I 66 Finiteness/Heyting: what the finitist denies in intuitionism is the notion that mathematics has something to do with the infinite. >Infinity, >Mathematics. Intuitionism: of course, its extreme finiteness guarantees maximum security. Every student, however, understands the natural numbers and can see that they go on infinitely. >Induction, >Numbers. Letter: that a person understands it, is suggested to him or her. Intuitionism: this is not an objection, because communication with language can always be regarded as a suggestion. >Understanding. Euclid also knew what he was talking about when he proved that the set of prime numbers is infinite. >Euclide, >Primes._____________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. |
Heyting I Arend Heyting "Disputation", in: Intuitionism, Amsterdam 1956 German Edition: Streitgespräch In Kursbuch 8/1967, H. M. Enzensberger, Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |
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> Counter arguments against Heyting
> Counter arguments in relation to Finiteness
Ed. Martin Schulz, access date 2024-04-19