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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] Home: 775-787-3949