Semantics: Warm-Up Kareem Khalifa Philosophy Department Middlebury College.

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Semantics: Warm-Up Kareem Khalifa Philosophy Department Middlebury College

Overview I.Logic, linguistics, & semantics II.Propositional semantics: basics III.Semantic validity IV.Proof-theoretic validity & tableaux V.Conditionals VI.Predicates

I. Logic, linguistics, & semantics A.Logic vs. linguistics B.Downplaying the distinction C.Emphasizing the distinction

II. Propositional semantics: basics A.Object &meta-language B.Syntax of object language C.Two notions of validity D.Soundness & completeness

III. Semantic validity A.Definition B.Valuation rules

IV. Proof-theoretic validity: tableaux A.Mechanics B.Definition

V. Conditionals A.Paradoxes B.Pragmatic Solution C.Subjunctive Solution D.Tougher examples E.Argument for “  ”

VI. Predicates A.Predicate logic (teaser) B.Representing predicates

Recap Logical tools can be of use to linguists Semantic theories are couched in meta-language; object languages are models of linguistic data Semantic validity leans on truth-preservation Proof-theoretic validity focuses on rules for making moves in the object language Material implication is messy. Predicates should be represented precisely.