Psychology Dictionary of Arguments

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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.
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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.

 
Author Concept Summary/Quotes Sources

Peter Geach on Expansion - Dictionary of Arguments

I 241f
Theory/Extension/Geach: For example, we add a predicate to system 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 extend to the tokens, not the types. That is, "Exy" is no longer: "x is identical to y" but "x is a token of the same form as the token y".
"F": not anymore "__ contains two occurrences of "e"", but "__ contains two tokens ..."
but not anymore: "twice the letter e".
E.g. truth conditions for whole sentences:
in T: there are two non-identical types ..."
in T1:" there are two non-uniform tokens ...".
>Truth conditions
, >Type/Token.

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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. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Gea I
P.T. Geach
Logic Matters Oxford 1972


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