PHILOSOPHY 514
MATHEMATICAL LOGIC II
Spring 2006
Kevin C. Klement
MATHEMATICAL LOGIC II
Spring 2006
Kevin C. Klement
Course description: Introduction to and comparative study of various logical foundations of mathematics, including classical set-theoretical foundations (ZF, NBG), Quine’s “New Foundations” and related systems, higher-order logic and type theory, and others, as well as related logical meta-theory and philosophical issues concerning mathematical and logical entities.
Prerequisite: Phil 310 (Intermediate Logic) or equivalent, or consent of instructor
Course Handouts and other materials:
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- Course Syllabus
- Take-Home Exam 1 (due March 17th)
- Take-Home Exam 2 (due April 28th)
- Final Exam 3 (due May 26th)
- Primary Handouts (=Lecture Notes)
- First-Order Logic Review 1 (pp. 1-5) (Feb. 3)
- First-Order Logic Review 2 (pp. 6-7) (Feb. 6)
- First-Order Logic Review 3 (pp. 8-9) (Feb. 8-13)
- Naive Set Theory / Frege's Project 1 (pp. 10-11) (Feb. 15)
- Naive Set Theory / Frege's Project 2 (pp. 12-14) (Feb. 17-21)
- Naive Set Theory / Frege's Project 3 (pp. 15-16) (Feb. 22)
- Textbook Type-Theory 1 (pp. 17-18) (Feb. 24)
- Textbook Type-Theory 2 (pp. 19-20) (Feb. 27 - Mar. 1)
- Higher-Order Type-Theories 1 (pp. 21-22) (Mar. 3-6)
- Higher-Order Type-Theories 2 (pp. 23-24) (Mar. 6-8)
- Higher-Order Type-Theories 3 (pp. 25-27) (Mar. 10-13)
- ZF Set Theory 1 (pp. 28-31) (Mar. 15-17)
- ZF Set Theory 2 (pp. 32-33) (Mar. 27-29)
- ZF Set Theory 3 (pp. 34-37) (Mar. 31 - Apr. 7)
- NBG/MKM Set Theories (pp. 38-39) (Apr. 10-14)
- Set Theories with Urelements (p. 40) (Apr. 14-19)
- Relative Consistency Proofs (pp. 41-42) (Apr. 19-21)
- Quine's Systems NF/ML 1 (pp. 43-46) (Apr. 24-28)
- Quine's Systems NF/ML 2 (pp. 47-48) (Apr. 28 - May 1)
- Quine's Systems NF/ML 3 (pp. 48-49) (May 3)
- Cocchiarella's λ-HST* and Variants 1 (pp. 50-51) (May 3-5)
- Cocchiarella's λ-HST* and Variants 2 (pp. 52-54) (May 5-10)
- Hume's Law, Frege's Theorem and Frege Arithmetic (pp. 50-60) (May 10-15)
- Boolos's (New V) and Others (p. 61) (May 17)
Email Kevin at klement@philos.umass.edu
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