|Mathematical Entities: mathematical entities are research objects of mathematics, which cannot be regarded as material objects. Nevertheless, there are discussions about the status of their existence. Whereas Platonism assumes its (permanent) existence as intellectual objects or universals, this permanence is denied, e.g. by intuitionism, which assumes that mathematical entities exist only at the moment of their construction.<_____________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. |
Paul Benacerraf on Mathematical Entities - Dictionary of Arguments
Stalnaker I 41
Mathematics/Benacerraf/Stalnaker: (Benacerraf, 1973)(1): Benacerraf sees a tension between the need for a plausible representation of what mathematical statements say and a representation of the way we know that such statements are true.
Suppose we demand a causal connection to things that we claim to know. Then it is not clear how this is supposed to work in the case of numbers that are acasual.
>Causality, >Knowledge, >Causal theory of knowledge, cf. >Theoretical terms, >Theoretical entities, >Reference.
1. 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.
Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984
Ways a World may be Oxford New York 2003