Psychology Dictionary of Arguments

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Platonism: Platonism in the narrower sense is the thesis in modern philosophy that some ideas and mental objects, especially ideas, are attributed reality. Various authors are Platonists with respect to e.g. numbers, mathematical entities, or universals. In contrast, e.g. intuitionism of mathematics assumes that numbers are not objects. This distinction has a significant effect on the logical formalisability of statements of mathematics. See also nominalism, mathematical entities, theoretical entities, completeness, evidence, fictions.
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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.

 
Author Concept Summary/Quotes Sources

Robert Stalnaker on Platonism - Dictionary of Arguments

I 43
Def Liberal Platonism/LP/terminology/Stalnaker: (early thesis): if the practice is legitimate (inferences, etc.) then we really make assertions and the semantics really tells us what the statements say.
Reference/liberal Platonism: a causal connection as a condition of reference is then superfluous.
>Reference
.
Problem: the existence of numbers cannot be constituted by a practice.
>Numbers.
I 45
Liberal Platonism/Stalnaker: Solution: the commitment to numbers is constituted by the endorsement of the practice.
>Practise.
I 48
Liberal Platonism: in contrast to the modal realism it is still verificationistic.
>Verificationism, >Realism.
I 54
Platonism/Mathematics/Stalnaker: Mathematical Platonism suggests an image according to which mathematical propositions are contingent.
>Mathematical entities, >Hartry Field.
Ontological commitment/Mathematics/Platonism/Stalnaker: Since the Platonist claims at the end that realm of mathematical entities exists necessarily, he has not made any ontological commitment at all.
>Ontological commitment.
Liberal Platonism/Stalnaker: Liberal Platonism says that since ontological commitment is not a commitment to exclude a possibility, one does not need an external relation (causal connection).
If true mathematical propositions are necessarily true, one does not need facts to make the propositions true.
>Truthmakers, >Nonfactualism.
Knowledge/Consequences/Stalnaker: Nevertheless, it could still be that one does not know all true consequences of necessary sentences.
>Omniscience.
Solution/Stalnaker: Here we should introduce the concepts of proof, calculation, construction, etc.
>Proofs, >Mathematics.

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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.

Stalnaker I
R. Stalnaker
Ways a World may be Oxford New York 2003


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