@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} }