Monday, December 4, 2017

Here is a sample final and here are the solutions. The proof problems are drawn from actual homework problems or problems worked out in the notes, and this will be the case on the actual test as well. The other problems will be similar, but not identical. The essay questions listed are the ones that will be used for the final. You will have two hours to do this test.

Friday, December 1, 2017

For our last week we will be looking at some of the important results concerning the limitations of logic and set theory. Tuesday we will 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 e-text through our library, though the accompanying slides should be adequate. Thursday we will cover Gödel's incompleteness results. Slides on this draw mostly from Chapter 12 of the same book.

Tuesday 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?

Thursday's turn-in homework is the following question:

Clearly identify three significant errors in the following.
Church's theorem shows that predicate logic is incomplete. This means that there will never come a time when we can be sure that it is finished. Gödel proved the same thing about math, showing that there are mathematical truths that we will never be able to prove.

Tuesday, November 28, 2017

(I posted this to the wrong class over Thanksgiving, hence everyone who comes to class will get credit for today Tuesday)

Tuesday we will focus on the last half of Lecture slides 2.4 (beginning with the first slide with the heading: Cardinality of sets. We will work as many problems on this sheet as we have time for.

Thursday we will move on to mathematical induction, focusing on the lecture slides and section 4.1 of the text.  Turn in problems 1 & 3 from this sheet.

Sunday, November 19, 2017

Grades for Test 2 have been posted. Grades reflect a 3.5 point curve. Number on your test should be 3.5 points lower than the number recorded in BB. Please double check after you test is returned, and check my addition on your points as well.

Friday, November 17, 2017

The test solution is posted here and at the top of the schedule page.
Here is the homework for Tuesday.  It covers Set Theory 2.3 and the first half of 2.4. Turn in the even numbered problems.

I will post the answers to the exam shortly.  I expect to have them graded by Tuesday.

Wednesday, November 15, 2017

I just noticed that I had failed to publish the solutions to the free logic semantics homework. I just did that, and the homework numbers have changed as a result. See below for other test-relevant posts.