|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. |
Introduction/Abstract Objects/Abstraction/Wright: Thesis: Sets as well as directions and numbers are to be introduced by abstraction.
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").
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.
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