@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024},
author = {Bigelow,John},
subject = {Lambda Calculus},
note = {I 98
Rules/composition/composition rules/syntax/Bigelow/Pargetter: one can also go the other way and want to simplify the rules. That is what the
λ-categorical language/Lambda calculus/Lambda notation/Lambda abstraction/Bigelow/Pargetter does: (see also Cresswell I and II, as well as Montague).
>Lambda-Abstraction/Cresswell, >R. Montague.
For example: Negation: surprisingly, one can assign a referent to it and keep it thus out of the rules:
I 99
Vs: we then have another referential layer in the theory.
Example
Negation: we can assign a set theoretical symbol that represents the value "true" or "false".
((s) Truth value/Frege/(s): assigns a referent to the negation, a "thing": "the false".
>Truth values, >Existence, >Objects, >Reference, >Sets, >Set theory.
Bigelow/Pargetter: then we have a judgement function that assigns the semantic value (or referent) V(a) to a symbol a.
>Valuation.
1: be "true".
0: be "false".
Def semantic value: (the negation V(a)) is then the function ω~, so that
ω ~ (1) = 0 ω ~ (0) = 1
is appropriate for compound expressions (internal/external negation, conjunction, etc.)
>Semantic value, >Outer negation, >Negation, >Conjunction.
I 100
Lambda categorical language/λ/Lambda/Rules/Bigelow/Pargetter: such languages have extremely few composition rules.
We have more referring symbols for this.
>Rules, >Symbols.
Realism: would describe this as ontologically honest.
Semantics/Bigelow/Pargetter: but the realist does not have to commit himself to one semantics instead of another.
>Realism.
The semantics does not decide upon ontology.
>Semantics, >Ontology.},
note = { Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990
},
file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=746735}
url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=746735}
}