## Philosophy Lexicon of Arguments | |||

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Structures, philosophy: structures are properties of an object, a set, or a domain of objects which determine the constitution and possible formability of this object, this set, or this domain. The properties defining the structure may be derived from the objects, e.g. magnetic forces or electric charge or can be imprinted on the objects such as e.g. the mathematical operations of multiplication or addition. See also order, system, relations._____________ 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 | Item | Summary | Meta data |
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Books on Amazon: Paul Benacerraf |
Field I 22 PlatonismVsNon-factualism/mathematics/Field: If we assume platonistically that the number 2 is a definite object, then the question whether the set {, {}} (also as a concrete object) is identical with it would be a question of fact. Field: if one admits the Platonism, perhaps, but I do not. Structure/Structuralism/Mathematics/Benacerraf: one can also see it "structuralist" that there are literally no numbers, but structures are the sequences. KitcherVs: (1974): if numbers are not acceptable entities, then also not the sequences. FieldVsVs: there is a variant with a solution: indeterminate reference or referential indeterminacy. Field: indeterminacy of the reference is an everyday fact! _____________ 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. |
Bena I P. Benacerraf Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984 Fie I H. Field Realism, Mathematics and Modality Oxford New York 1989 Fie II H. Field Truth and the Absence of Fact Oxford New York 2001 Fie III H. Field Science without numbers Princeton New Jersey 1980 |

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Ed. Martin Schulz, access date 2017-10-23