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.

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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 Item Summary Meta data

 
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!


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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.

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