Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


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Sc. Camps
Theses I
Theses II

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Field I 22
Interpretation/Benacerraf: (1965)(1) Thesis: Identification of mathematical objects with others is arbitrary - E.g. numbers with quantities. - E.g. real numbers with Dedekind cuts, Cauchy sequences, etc. - There is no fact that decides which is the right one.
>Equations, >Equality, >Identification, >Real numbers, >Numbers, >Mathematics,
>Mathematical entities.
Field ditto.
I 22
Indeterminacy of reference/Field: is not a problem, but commonplace.
>Reference, >Indeterminacy.
I 25
For Benacerraf it is about identity, not about reference - otherwise he might falsely be refuted with primitive reference: "Numbers" refers to numbers but not to quantities - But that is irrelevant.
Cf. >Reference/Field.
I 25
BenacerraffVsPlatonism: locus classicus - VsBenacerraf: based on an outdated causal theory of knowledge.
>Platonism, >Causal theory of knowledge.
Field I 25
BenacerrafVsPlatonism: (1973)(2): if without localization and interaction we cannot know whether they exist. VsBenacerraf: indispensability argument.

1. Benacerraf, P. What Numbers Could Not Be, The Philosophical Review 74, 1965, S. 47–73.
2. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679.

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