##
Philosophy 3349 |

Spring, 2002

## Book |

Christopher C. Leary, *A Friendly Introduction to Mathematical Logic*
(Prentice-Hall, 2000). Don't be misled by the title: this is not an introduction
to symbolic logic per se, but rather an introduction to metalogic. It includes
proofs of soundness and completeness theorems for first-order logic, the
compactness theorem, the upward and downward Löwenheim-Skolem theorems, and
culminates in proofs of Gödel's incompleteness theorems. However, compared with
other texts in the area, this one *is* fairly friendly.

We will also make use of a variety of other materials, including handouts and online materials on the philosophical implications of Gödel's results, and material on alternatives to, and extensions of, classical first-order logic. Especially valuable resources are the Routledge Encyclopedia of Philosophy (available in the library either in hard copy or in a CD-ROM version) and the Stanford Encyclopedia of Philosophy.

## Office Hours |

MW, 10:30 - 11:30, 2:00 -3:00; TR, 2:30 - 3:30.

I am usually in my office during office hours, but occasionally a meeting or another commitment prevents this. If you just drop by during office hours, you will probably find me in; if you want to see me at another time, or if you want to be certain I'll be in, we can set up an appointment.

## Requirements |

There will be a mid-term examination and a final examination. There will be regular shorter assignments -- sometimes homework problems, sometimes short papers. Every member of the class will be expected to give at least two in-class presentations on topics germane to the course: an extension to, or revision of, first-order logic or a metalogical result. There will also be a final project for the course. Percentages: Mid-term, 20%; Final, 20%; presentations and class participation, 20%; Short Assignments, 20%; Final Project, 20%. (Easy to remember!)

## Very Rough Schedule |

## structures and languages

## deductions

proof of soundness

proof of the deduction theorem## completeness and compactness

proof of completeness theorem

proof of compactness theorem

proofs of upward and downward Skolem-Lowenheim theorems## incompleteness - groundwork

recursive sets and functions

Gödel numbering

NUM and SUB functions## incompleteness - proofs

proofs of Gödel's first and second incompleteness theorems

## significance of the incompleteness results

relation between incompleteness and uncomputability

Penrose: incompleteness shows AI impossible (handout from Penrose)

criticisms of Penrose (Chalmers essay)

Putnam on realism (handout)

criticisms of Putnam (recentJournal of Philosophyarticle)

## equivalent systems

axiomatic systems, natural deduction systems, sequent introduction systems

equivalent sets of axioms, rules, etc.## extensions

modal logic (handout from Forbes)

deontic logic

others?## alternatives

intuitionistic logic (handout from Forbes)

nonmonotonic logics?

dialethic logic?

Last update: January 13, 2002 |