By Henriette de Swart
1. what's meaning?; 2. Desiderata for a idea of that means; three. Connectives, fact, and fact stipulations; four. Predication and quantification; five. Scope and anaphora; 6. Limits of first-order predicate good judgment; 7. Generalized quantifier concept; eight. Worlds and occasions; Appendix
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Extra resources for Introduction to natural language semantics
What I do want to do is to make a case for the Second-order quantifiers as logical operators, in exactly the same way that the first-order quantifiers as well as negation, conditional, conjunction, and disjunction are logical operators. The cogency of this claim will depend of course on how we think of the logical operators. I also want to show that the grounds for their qualifying as logical operators can be settled affirmatively, without having to settle the ontological issues A. , Rm. com © Springer International Publishing Switzerland 2015 A.
P1 ; : : : ; pn / of propositional sort. p/ for p D t, to express that p is true. x1 ; : : : ; xk // ! p D q: The last of these is of course just Extensionality for predicates. Models M1 of S are given by any non-empty universe of individuals U as the range of the individual variables, and the set ft; f g (with t ¤ f ) as the range of the propositional variables. Furthermore each assignment to a k-ary predicate variable in M1 determines a propositional function P from U k to ft; f g as its extension, via the interpretation of the application function Appk .
3 Implicit Definitions 33 guaranteed by the truth of the two versions of the theory from which it logically follows. Consequently, whatever necessity the biconditional might have is derivative from whatever necessity the theory may have. It does not have it on its own. There have been several different proofs of Beth’s definability theorem, for a broad range of theories. The theories under consideration could be physical, mathematical, or logical. We shall be concerned here with just the logical theories, both first and second-order and we will not be concerned with Beth’s famous theorem that connects the concepts of implicit with explicit definition.