|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.|
|Geach, Peter T.
Books on Amazon
Theory/Extension/Geach: For example, we add a predicate to T that allows us to distinguish between different tokens: T1. In the extended system T1, each complete sentence has the same truth conditions as in T, but the subordinate expressions (subsets) are completely changed: the quantifiers now suffice for the tokens, not the types. That is, "Exy" is no longer: "x is identical to y" but "x is a uniform token as the token y".
- "F": no anymore "__ contains two occurrences of "e"", but "__ contains two tokens ..." but not anymore: "twice the letter e" - (s) so not only the trivial: truth conditions for compound sentences (conditional) are shown in the table "((s)Vs: anyway not: because the table does not say what the case is) - E.g. truth conditions for whole sentences: in T: there are two non-identical types .. "in T1:" there are two non-uniform tokens ... ".
Logic Matters Oxford 1972