Logic A 3800-ISP-L1A

This course is an introduction to formal logic and formal methods in philosophy. The course covers the following topics: Formal methods of evaluating arguments: Sentential (propositional) logic, Categorical logic, Predicate (quantificational) logic.
The course covers the following topics:
Formal methods of evaluating arguments:
Sentential logic: validity and the formal analysis of arguments; truth-functional connectives: conjunction, disjunction, conditional, biconditional, negation; first steps in symbolization; truth-tables; comparison of natural-language and logical connectives; tautologies, contradictions and contingent statements; symbolizing entire arguments; testing for validity with semantic tableaux; testing for validity by exhaustive search, testing for validity by constructing interpretations; expressive completeness; non-truth-functional connectives.
Natural deduction in sentential logic: the concept of proof; rules for conjunction, disjunction, negation, conditional and biconditional; sequent and theorem introduction.
Semantic and deductive consequence; soundness and completeness.
Categorical logic: categorical propositions; the four basic categorical forms; contradictories; existential commitment; validity for arguments containing categorical propositions; immediate inferences; syllogisms; Venn diagrams for syllogisms; the classical square of opposition.
Predicate (quantificational) logic:
Monadic predicate logic: the quantifiers (existential and universal); symbolizations, semantics for the quantifiers, constructing counterexamples; deductive consequence (rules for quantifiers).
First-order logic with identity: n-place predicates; identity; definite descriptions; ambiguity; demonstrating invalidity; proofs; rules for identity; semantic consequence, deductive consequence and decidability; some limitations of first-order logic.