Philosophy Lexicon of Arguments

Lambda Calculus, philosophy: The lambda calculus provides a way to avoid problems related to paradoxes, since, unlike the quantification of predicate logic, it does not make any existence assumptions. Where the quantification (Ex)(Fx) is translated colloquially as "There is an x with the property F" (in short "Something is F"), the translation of the corresponding form in the Lambda calculus is "An x, so that...". See also 2nd order logic.
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I 90
Lambda operator / Meixner: "A (b1, ... bn)" is true if and only if b1, bN .. EXEM lo1 ... oN [A (O1 ... oN] - here stands "A (b1,. ..bN)" for any seentence with N different names - lO1 ... ON [A (O1 ... oN]: represents the name of an N-ary (predicative) universal - O1 the placeholder replaces the O1 b1 name wherever it occurs in A (b1, ... bn) - LO1 ... oN .: this prefix indicates that lo1 ... ON [A (O1 ... on] is not a complete expression. but just a name: lO1 ... oN binds all vacancies in [A (O1 ... oN] - the name "LO 1 [O1 is a human being."] corresponds to the characteristic of being human.

Mei I
U. Meixner
Einf├╝hrung in die Ontologie Darmstadt 2004

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Ed. Martin Schulz, access date 2017-05-24