SET THEORY AND FURTHER LOGIC Last Updated 28/04/05 BACK TO LPSG CONTENTS The Paper Textbooks ... Modal Logic
1. The Paper This paper covers basic axiomatic set theory plus a subject within the ambit of formal logic but beyond the introductory logic of a standard first year course. In recent years that further subject has been modal logic (the logic of necessity and possibility). Another candidate for the further logic' component is intuitionistic logic, another would be probability theory. Students would of course be advised of any change in the further logic' component , and the paper in any changeover year would include questions on set theory and on both further logic' subjects. This paper has a sister paper, Mathematical Logic . The common parent was a paper, now defunct at the B.A. level, called Symbolic Logic. Once modal logic became part of the staple diet it was felt that there was too much ground for an undergraduate to cover in any depth in one paper; hence the split. The courses are taught in alternate years: if Mathematical Logic is taught one year, Set Theory and Further Logic is taught the next. But B.A. exam papers for both are set every year. What can set theory do for a philosophy student? Here is a four-part answer. (1) Set theory provides a bagful of conceptual tools useful in many areas of rigorous thought and teaches one to handle them with precision, e.g. partial ordering, equivalence relation, isomorphism, recursive definition and proof by (mathematical) induction. (2) It sharpens reflection on matters central to philosophy of thought and language, such as the nature of truth, satisfaction, predicate extensions and associated antinomies such as Russell's Paradox. (3) It is very important for philosophy of mathematics, for questions of ontology and the number systems. (4) It provides a proper understanding of infinity (and one of the deepest problems of mathematics, the continuum problem), and enables one to see through mystical twaddle wrapped in talk of the infinite.