Download PHILOSOPHY 326 / MATHEMATICS 307 SYMBOLIC LOGIC This

PHILOSOPHY 326 / MATHEMATICS 307
SYMBOLIC LOGIC
This course is a second course in symbolic logic. Philosophy
114, Introduction to Symbolic Logic, is a prerequisite for Philosophy
326 (or Mathematics 307). It is assumed that all students will have a
thorough grasp of the fundamentals of the two-valued logic of
propositions – including the fundamental vocabulary of formal
deductive logic, the basic two-valued truth functions, truth tables,
decision procedures for determining truth functional validity and
logical equivalence, and (most importantly) proficiency in constructing
proofs in a system of natural deduction for the logic of propositions.
This course does not have a fixed and predetermined syllabus.
There is core content which will be covered in class, and a number of
options for additional content. The specific content of the course, the
type and frequency of examinations, will be negotiated by the
instructor and students.
• The main part of this course will concentrate on the elementary
logic of quantified propositions, also known as predicate logic or
the first-order predicate calculus. The course covers the
monadic predicate logic, a decision procedure for the monadic
predicate logic, natural deduction for the predicate logic,
multiple quantification, relations and identity.
In addition to the core content of the predicate calculus all of
the following are possible additional topics.
• Aristotelian logic, focusing on its presentation as an axiomatic
system and its analytic limitations.
• Additions to the two-valued logic of propositions to include
basic elements of modal logic.
• An axiomatic presentation of the two-valued logic of
propositions with emphasis on the characteristics of axiomatic
systems, including the concepts of consistency, independence,
and deductive completeness.
• Normal form techniques.
• Mathematical induction and its use in symbolic logic.
If you have any questions, please feel free to contact me.
[email protected]
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