|12A||Introduction to Logic||Mancosu||TuTh 9:30-11||TBA|
The course will introduce the students to the syntax and semantics of propositional and first-order logic. Both systems of logic will be motivated by the attempt to explicate the informal notion of a valid argument. Intuitively, an argument is valid when the conclusion ‘follows’ from the premises. In order to give an account of this notion we will introduce a deductive system (a natural deduction system), which explicate the intuitive notion of ‘follow’ in terms of derivational rules in a calculus. This will be done in stages, first for propositional reasoning (only connectives such as ‘and’, ‘or’, ‘if… then…’ and later for the full first-order calculus (including expressions such as ‘for all…’ and ‘there exists…’. In addition, we will also develop techniques to show when a claim does not follow from the premises of an argument. This is done by developing the semantics for the propositional and the predicate calculus. We will introduce truth-tables for the propositional connectives and ‘interpretations’ for sentences of first-order logic. At the end of the course, if time allows, we will also cover some metatheoretical issues, such as soundness and completeness of the propositional calculus.
Textbook: J. Barwise, J. Etchemendy, Language, Proof and Logic, latest edition. (The book comes with a CD. Do not buy the book used! If you do, you will not be able to submit your exercises on line, which you will be required to.)
Previously taught: FL20, SU20D, SU20C, SU20A, SP20, FL19, SU19D, SU19C, SU19A, SP19, FL18, SU18D, SU18C, SP18, FL17, SU17D, SU17A, SP17, FL16, SU16D, SU16A, SP16, FL15, SU15D, SU15A, SP15, FL14, SU14D, SU14A, SP14, FL13, SU13D, SU13A, SP13, FL12, SU12D, SU12A, SP12, FL11, SU11D, SU11A, SP11, FL10, SU10D, SU10A, SP10, FL09, SU09D, SU09A, SP09, FL08, SU08D, SU08A, SP08, FL07, SU07A, SP07, FL06, SU06A, SP06, FL05, SU05D, SP05, FL04, SU04D, SU04A, SP04, FL03.