Mathematics · Avançado · Nível 3

Symbolic logic

The language of propositional logic: formulas and their main connectives, symbolising English, truth tables, tautology and contradiction, logical equivalence, normal forms and complete sets of connectives. Validity as the absence of a countermodel, the named argument forms and the fallacies they are confused with, consistent sets and what follows from them. Natural deduction: the basic rules, disjunction and the chain rule, strategy, conditional proof and reductio. Predicate logic: predicates and quantifiers, mixed quantifiers and the order they come in, negation, interpretations and truth in a structure, and identity with the counting claims it makes possible. And the metatheory: what soundness and completeness say about the relation between a derivation and an entailment, which questions have a decision procedure, and what the incompleteness theorems state about a formal system that meets their conditions.

Ages 18+ 24 lessons about 8.5 hours in all

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