Logic Bivalence and Denotation

3xPx 3y Vx(Px abbreviates applied argument atomic statements Basis Step complete model contradiction counterexample defined definite description denotation disjunct domain E!b & Pb English statements entail exactly example existential quantification exists expressed finite free logic free tableau hence identity induction hypothesis Inductive Step infinite interpretation function intuitive John is tall Lemma list of statements logic of singular logic of statements logical falsity logical truth logically false logically superfalse logically supertrue metalogical modal logic n-tuples natural number negated or unnegated notion occurs negated occurs unnegated official idiom P(IxPx Pa & Pb paraphrased Pegasus possible worlds precise presuppositions Principle of Bivalence proof prove Reagan Section singular terms occurring standard logic statement letters statements containing structure supertruth supervalid supervaluations suppose tableau procedure terminates terms and predicates truthtable truthvalue gaps truthvalueless universal quantification university will survive valid valuation variables verifies VX Px Vx(x VxPx VxQx Y₁