|This is a file in the archives of the Stanford Encyclopedia of Philosophy.|
1. Let I be an interpretation function with respect to a model, so that I(a) is the individual I assigns to the individual constant a, I(Fn) is the n-place relation that I assigns to n-place predicate Fn. Then for all n-place predicates Fn and individuals constants c1, ..., cn, the sentence Fnc1...cn is true in the interpretation just in case < I(c1), ..., I(cn)> ext(I(Fn)). We would relativize this clause to variable assignments in the usual way to define satisfaction conditions for atomic sentences.
2. More generally, if is a formula with free occurrences of exactly the variables v1, ..., vn, then [v1,..., vn ] is an n-place complex predicate (normal quotation marks are used here as stand-ins for quasi-quotation). In more complicated applications we could allow to contain no free variables (in which case [ ] denotes the proposition that-) or more free variables than are bound by the -operator (to allow expressions like [x Fxyz], which we could quantify into, as with y([x Fxyz]).
3. A standard sort of comprehension schema holds that for each open formula , Xnx1...xn(Xnx1...xn if and only if ).
First published: September 23, 1999
Content last modified: September 23, 1999