Course Description
Symbolic-mathematical logic, examining the propositional and predicate calculi, with emphasis on problems in translation and formalization and topics in the philosophy of logic and mathematics.
Additional Requirements for Graduate Students:
More difficult problems assigned, possibly an in-class presentation, and higher standards for all assigned work.
Athena Title
Deductive Systems
Prerequisite
PHIL 2500 or PHIL 2500H or PHIL 2500E or permission of department
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
Students are expected to be able to do the following: a) construct semantic proofs, including proofs by mathematical induction, deploying the concepts of truth- functional logic; b) construct derivations in a natural deduction system for truth-functional logic and construct proofs of proof-theoretic results for such systems; c) symbolize complex sentences of English using predicate logic with identity; d) construct proofs of basic semantic metatheorems for models of predicate logic with identity; e) construct derivations in a natural deduction system for predicate logic with identity and construct proofs of proof-theoretic results for such systems; f) construct proofs of basic results for the advanced topic chosen by the instructor.
Topical Outline
Topics may include: I. Sentential Logic A. Truth-functional validity and related concepts B. Mathematical induction C. Expressive completeness D. Proof theory for sentential logic II. Predicate Logic A. Advanced symbolization in predicate logic with identity B. Models for predicate logic with identity C. Proof theory for predicate logic with identity. III. Advanced topics (any advanced topic in logic, such as one of the following) A. Modal logic B. Philosophy of logic C. Philosophy of mathematics
Syllabus