Philosophy Lexicon of Arguments

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.
Author Item Excerpt Meta data
Geach, Peter T.
Books on Amazon
Expansion I 241f
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 ... ".

Gea I
P.T. Geach
Logic Matters Oxford 1972

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Ed. Martin Schulz, access date 2017-03-28