|Expansion, philosophy: when expanding theories it comes to the question whether a consistent theory remains consistent when it is expanded. Maximum consistent theories are not expandable. See also axioms, maximum consistent, theories, consistency, maximum._____________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. |
Logic/Independence/Field: what does not go with a set of concepts (e.g. a distinction, a proof) does also not go with an extension of the concepts when the new concepts are merely derived from the old ones only.
Possibility/Field: modified concept of possibility: "is a possible extension of the actual world" (the real one). - Then there are models in which singular terms denote nothing. - The extension then provides a term for something that would not have a denotation in the non-extended model. - Then additional predicate "act" for the distinction.
Problem: this only works outside the modal contexts.
Solution: truth must define truth in a model relative to another model, which is a sub-model of the first.
Extension/Theory/Language/Predicate/Field: one cannot simply decide to introduce a new predicate for which the indeterminacy of all extensions does not apply.
Logic 2nd order/Field: E.g. quantifiers like "there are infinitely many". - ((s) Quantified over sets). - Also not: e.g. "there are fewer Fs than Gs".) - ((s) Fs and Gs only definable as sets or properties.).
Expansion of Logic: Preserves us from a vast area of additionally assumed entities. - E.g. "What obeys gravitation theory".
QuineVs: rather accept abstract entities than expand the logic. - (Quine in this case per Platonism)._____________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