Semantics: Warm-Up

Kareem KhalifaPhilosophy Department

Middlebury College

OverviewI. Logic, linguistics, &

semanticsII. Propositional semantics:

basicsIII. Semantic validity

IV. Proof-theoretic validity & tableaux

V. ConditionalsVI. Predicates

I. Logic, linguistics, & semantics

A. Logic vs. linguisticsB. Downplaying the distinctionC. Emphasizing the distinction

II. Propositional semantics: basics

A. Object &meta-languageB. Syntax of object languageC. Two notions of validityD. Soundness & completeness

μετά

III. Semantic validity

A. DefinitionB. Valuation rules

IV. Proof-theoretic validity: tableaux

A. MechanicsB. Definition

V. Conditionals

A. ParadoxesB. Pragmatic SolutionC. Subjunctive SolutionD. Tougher examplesE. 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.