Thursday, May 4, 2017

For our last week we will be looking at some of the important results concerning the limitations of logic and set theory. Slides for Monday, already posted, cover Russell's Paradox, the nature of the ordinals and the Burali Forti Paradox. This draws from the book The Infinite, by A.W. Moore which is available as an etext through our library. Wednesday we will cover Gödel's incompleteness results. Slides for that will be up this weekend, and they will draw mostly from Moore's book as well.

Monday's turn-in homework is the following question:
State the specific contradictions implied by (a) Russell's Paradox and (b) The Burali-Forti Paradox. In what interesting sense do the proofs of these results resemble each other?  

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