 | Spring Term
2002 PHIL 750: Advanced Symbolic Logic
Lecture/seminar
MW 12:30--2:18 p.m.
18 Lazenby Hall
Aims of this course
This course studies various limitative results in the foundations of
logic and mathematics. The first major aim is to impart the technical
mastery involved in proving these results. The second major aim is to
examine their foundational and philosophical implications and
significance, for such issues as: whether one can attain certainty in
the foundations of mathematics; the limits of expressive and deductive
power of any language for abstract thought; and the possible
transcendence of minds over machines.
Topics
Topics will include the undecidability of
first-order logic and arithmetic; the incompleteness of first-order
arithmetic; the unprovability of the consistency of arithmetic; the
non-axiomatizability of second-order logic; and Skolem's paradox. The
main metamathematical preliminaries, concerning recursive functions,
Church's Thesis, and the representability in arithmetic of recursive
functions, will be carefully explained, as will the central
proof-technique of diagonalization.
Textbook: Neil Tennant, Natural Logic, Edinburgh University Press, 2nd
edn., 1990.
Downloadable Handouts:
Other texts for extra material on certain topics:
- S. C. Kleene, Introduction to Metamathematics.
- J. Barwise, ed., Handbook of Mathematical Logic.
- G. Boolos and R. Jeffrey, Computability and Logic.
- M. Detlefsen, Hilbert's Program.
- A. R. Anderson, ed., Minds and Machines.
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NEIL W. TENNANT