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Lambda abstraction/Cresswell: takes over the binding of the variable (instead of the existence quantifier). The idea is that every predicate has as many digits as possible which are also needed, so that their argument digits can be connected to one another that is the reason why, however it is only a one-digit predicate, we must form the two-digit predicate <λxy > - This two-digit predicate determines the class of all pairs in which b is a donkey - has: determines the class of all pairs in which a has b, and therefore a pair can only then exist in all three relations if a is a man who has b and b is a donkey.
Λ-abstraction/lambda abstraction/logical form/everyday translation/Cresswell: Example - "is an x such that x does not whistle" - can be regarded as a complex predicate - abstraction operator: its main task is the formation of complex predicates.
L-categorial language/syntactic categories/Cresswell: generic names/common nouns: are in category (0/1) - intransitive verbs: (0/1) - transitive verbs: (0/11) (Montague: (0/1(0/01) Adverbs: (0/1)/(0/1) - some adverbs: (0/0) (also sentence operators like "not" and operators for the formation of time.) - Adjectives: ((0/1 )/(0/1)) - prepositions: (((0/1)/(0/1))1) - meaning of a functor: is a certain kind of function.
Meaning of expressions in category (t/s1 ,,, sn): are functions whose arguments are derived from the meanings of s1, ... sn and their values from the meanings of t - meanings: are always intensions here (see above).
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984