Philosophy Lexicon of Arguments

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Abstraction: Subsumption of objects by non-consideration of certain properties. See also equivalence relation, concretion, concreta, indiscernibility.

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.

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Books on Amazon

I 158
Introduction/Abstract Objects/Abstraction/Wright: Thesis: Sets as well as directions and numbers are to be introduced by abstraction.
I 157
Field: Example simple abstraction: is suitable for us saying that our talk of directions refers to parallelism. - But that does not quite work accordingly for numbers as it does for non-numeric talk (and "non-set theory").
III 24
Homomorphism/Field: (structure-preserving representation) is the bridge to find abstract counterparts to concrete statements ((s) observation statements) - Semantic Ascent/Abstract Counterparts: we would always obtain the results without them. - ((s) otherwise they would be something else.) - Field: we save a lot of time with this.

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.

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

H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2018-02-20