

Course ID:  PHIL(LING) 4510/6510. 3 hours. 
Course Title:  Deductive Systems 
Course Description:  Symbolicmathematical logic, examining the propositional and predicate calculi, with emphasis on problems in translation and formalization and topics in the philosophy of logic and mathematics. 
Oasis Title:  Deductive Systems 
Prerequisite:  PHIL 2500 or PHIL 2500H or PHIL 2500E or permission of department 
Semester Course Offered:  Offered fall semester every year. 
Grading System:  AF (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
truthfunctional logic and construct proofs of prooftheoretic 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 prooftheoretic 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. Truthfunctional 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 