|Interpretation: A) Making statements about other statements, whereby new vocabulary may be introduced. If no new vocabulary is introduced, new information can be obtained by changing the syntactic grouping.|
B) In logic, interpretation is the insertion of values (objects) instead of the constants or free variables.
_____________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.
Books on Amazon:
|Field I 22
Interpretation/Benacerraf: (1965) 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. - Field ditto.
Indeterminacy of reference/Field: is not a problem, but commonplace.
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.
BenacerraffVsPlatonism: locus classicus - VsBenacerraf: based on an outdated causal theory of knowledge.
Field I 25
BenacerrafVsPlatonism: (1973): if without localization and interaction we cannot know whether they exist. VsBenacerraf: indispensability argument._____________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.
Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980