Sunday, May 14, 2017

Friday, May 12, 2017

This is the sheet of inference rules and definitions that you will have available during the final. Note the continued absence of proof methods, including mathematical induction. As always, the more you plan to rely on this sheet, the less well you are likely to do.

This is the model that will be used for the semantic portion of the exam. Study it carefully before the exam. Minor changes are possible. Check back Sunday evening just in case. If I have made any changes, there will be a post saying so and I will highlight the changes.

Remember the exam time is 12:45-2:45!

Thursday, May 11, 2017

Here are the essay questions for the final exam.
Clarification regarding final exam. As stated below, you will not be required to do proofs or semantic evaluations in multi-valued logic or Meinongian free logic, but you may be required to display an understanding of these systems in the essay questions.

These questions should be posted by this evening.

Monday, May 8, 2017

Here is your last homework question. It is based on the last set of slides posted to week 13 of the schedule. These slides are sufficient to answer the question, but they will not be complete until tomorrow afternoon.

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, sowing that there are mathematical truths that we will never be able to prove.

Thursday, May 4, 2017

See previous post for Monday's assignment.

Our final is Monday May 15th from 12:45 to 2:45.

The final exam will consist of the following:

Proofs: (2 pts. each)

A natural deduction proof of each of the following types:

  • Propositional logic
  • Predicate logic
  • Predicate logic with identity and functions
  • Predicate logic with identity, functions, membership and basic set theoretic concepts.
  • Leibnizian modal logic
A rigorous English language proof of each of the following types:
  • Set theory (as in HW 18)
  • Weak induction (as in HW 19)
At least half of the proofs will be drawn directly from homework sets. All will be designed to test your basic comprehension of these methods.

Semantics: (7 pts. total)
  • Evaluation of formulas in all of the above categories, as in HW's 3, 8 and 15. Models used will be similar, though not necessarily identical. 
  • Determining properties of functions, with explanations that makes explicit reference to definitions of these properties (as in HW 17.)
Short essay questions: (2 pts each)
  • A few days before the final I will post 5 short essay questions of a somewhat philosophical nature.  They will focus on the material covered since the last test. Each will require some technical competence to answer as well. Three of these questions will be chosen randomly at the beginning of class.  (Everyone gets the same three questions.) You will have two options:
    1. Answer two of the questions;
    2. Answer all three questions and select one problem from the proof section for which it is to be substituted. If you exercise this option, you must make this selection explicitly; i.e., you may not answer both and get credit for the one you do best. 

You will specifically not be required to do proofs or refutation trees in Meinongian free logic or multi-valued logic (finite or infinite). 

The rules for the final are the same as for the previous two tests. Your information sheet will be updated to include predicate logic definitions of essential set-theoretic concepts.  

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?  

Wednesday, May 3, 2017

Solutions to HW 19 are posted on the schedule page. A few more problems have been added with solutions as well.

I will post the assignment for Monday tomorrow as well as news about the final.

Please note that you have received course evaluations for this course in your Saclink. There is a significant inducement to complete them in the syllabus:

Course evaluations
There are two points of extra credit available for doing course evaluations at the end of the semester. This works as follows: The percentage of students in the class who complete the course evaluation will be multiplied by 2. The product will be added to every students point total. For example, if 80% of students do the evaluations then 1.6 points will be added to every students final grade. 

Tuesday, May 2, 2017

I just noticed that I left out a crucial stipulation in problem 5 which made it unprovable. I fixed it, underlining the part I left out.  I'm sorry about that.

Monday, May 1, 2017

Here are the solutions to the first two problems from today's homework. Please review these and the slides online. Turn in problems 3-5 from the same assignment on Wednesday.