Lexicon of Arguments

 

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Rules/composition/composition rules/syntax/Bigelow/Pargetter: you can also go the other way and want to simplify the rules. That is what makes the
λ-categorical language/Lambda/Lambda Calculus/Lambda Notation/Lambda Abstraction/Bigelow/Pargetter: ((see also Cresswell I and II. and Montague).
>Lambda abstraction, >Lambda calculus, >M.J. Cresswell, >R. Montague.
For example: Negation: you can surprisingly assign a referent to it and keep it out of the rules.
>Reference, >Negation, >Rules.
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Vs: we then have another referential layer in the theory.
Example:
Negation: we can assign a set theoretical symbol to it that represents the value "true" or "false".
((s) Truth values/s): assigns a referent to the negation, a "thing": "the
False".
>Truth values, >Truth values/Frege.
Bigelow/Pargetter: then we have a judgement function that assigns the semantic value (or referent) V (a) to a symbol a.
1: be "true".
0: be "false". +
Def semantic value: (of the negation V (a)) is then the function ω ~, so that
ω ~ (1) = 0 ω ~ (0) = 1
correspondingly for compound expressions (internal/external negation, conjunction, etc.)
>Outer Negation.