## 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!

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

## Thursday, May 11, 2017

These questions should be posted by this evening.

## Monday, May 8, 2017

Clearly identifythreesignificant 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:

A natural deduction proof of each of the following types:

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

- 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:

- Answer two of the questions;
- 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.

**Clarifications:**

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

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

*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 theproofsof these results resemble each other?

## Wednesday, May 3, 2017

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

## Monday, May 1, 2017

## Thursday, April 27, 2017

## Wednesday, April 26, 2017

## Tuesday, April 25, 2017

## Thursday, April 20, 2017

## Wednesday, April 19, 2017

## Tuesday, April 18, 2017

## Monday, April 17, 2017

## Sunday, April 16, 2017

See multiple posts below for information regarding Monday's test.

## Saturday, April 15, 2017

## Friday, April 14, 2017

Please see previous post for general description of Monday's test. Here is a sneak peek of the models that will be used for problems 1 and 3 respectively.

The test on Monday will have roughly the same format as the first test. It will involve 5 problems worth 5 points each as follows:

Sunday night I will put the models up here for 1 and 3 so that you don't have to spend time assimilating them on Monday.

1. The semantics of modal logic, in which you evaluate formulas with respect to a model.There will be no set theory on the test. As before, it is closed book, but I will provide a sheet containing relevant material (inference rules and equivalences) from the first test as well as the inference rules for modal logic and free logic. It will not contain valuation rules for the truth values of formulas on any system.

2. A proof in modal logic. It will be very similar to one of the homework problems.

3. The semantics of free logic, in which you evaluate formulas with respect to a model.

4. A proof in free logic. It will be very similar to one of the homework problems.

5. The semantics of multi-valued logic (both finite and infinite), in which you will evaluate the truth values of a list of propositions relative to specific truth value assignments. For finite multi-valued logic you should know both Bochvar's and Kleene's approach, which I will refer to on the test as Policy 1 and Policy 2 respectively (just as in the notes.)

Sunday night I will put the models up here for 1 and 3 so that you don't have to spend time assimilating them on Monday.

## Wednesday, April 12, 2017

## Monday, April 10, 2017

## Thursday, April 6, 2017

## Wednesday, April 5, 2017

## Monday, April 3, 2017

## Thursday, March 30, 2017

Monday's homework is in the previous post. This is Wednesday's homework, on infinite valued logic. Turn in solutions to the even numbered problems. Show your work.

For Monday, please be sure you have familiarized yourself with the slides on finite multi-valued logic. Your turn-in homework for Monday is as follows:

Modus ponensis a classically valid inference pattern. Its classical truth table shows that there is no case in which the premises are true and the conclusion is untrue. (Note the use of the word 'untrue' here rather than 'false.' In classical logic, the only value that is untrue is false, but that is not the case in multi-valued logic.)

Task: Draw complete truth tables formodus ponensfor both Bochvar's and Kleene's versions of three-valued logic (in the slides, policy 1 and policy 2 respectively.) Then answer the following questions:

1. Do either of these systems preserve the validity ofmodus ponensas defined above?

2. What does your answer suggest about the relative desirability of these systems?

## Wednesday, March 29, 2017

## Tuesday, March 28, 2017

Also, I posted full solution to Monday's homework on the schedule page. This contains the answers to a few problems I skipped because I wasn't completely sure how they should be evaluated. I have confirmed these solution and they are highlighted in blue. The rationales are straightforward and you should familiarize yourself with them. Ask questions Wednesday if you don't understand them.

## Tuesday, March 21, 2017

## Wednesday, March 15, 2017

I will assign homework on the semantics of free logic by Wednesday next week, due Monday the 27th when we return from spring break. Also, I have decided to push the next text back. It is now scheduled for April 17th.

## Monday, March 13, 2017

Wednesday we will work the remaining problems from today's homework. Please turn in numbers 9 and 11. The second half of the period we will begin talking about Meinongian free logic.

## Friday, March 10, 2017

## Thursday, March 9, 2017

## Monday, March 6, 2017

## Friday, March 3, 2017

See below for Monday homework.

Grades for test 1 have been posted to SacCT. These reflect a curve of 2 points, which produced a mean score of 17.5 = 70%. Your returned copy will only show your original score. Be sure to check my addition and also that your score in SacCT is 2 points higher than the score on your test.

Now is a good time to review the syllabus and refresh your memory on the impact of this test and ways to recover if you have done poorly. Note that the deadline on one of those ways, participating in the Nammour Symposium Student Contest, is fast approaching. Check the department Facebook link for the most recent announcements.

Grades for test 1 have been posted to SacCT. These reflect a curve of 2 points, which produced a mean score of 17.5 = 70%. Your returned copy will only show your original score. Be sure to check my addition and also that your score in SacCT is 2 points higher than the score on your test.

Now is a good time to review the syllabus and refresh your memory on the impact of this test and ways to recover if you have done poorly. Note that the deadline on one of those ways, participating in the Nammour Symposium Student Contest, is fast approaching. Check the department Facebook link for the most recent announcements.

This is the turn-in homework for Monday:

In the semantics of Leibnizian modal logic, the following proposition is a necessary truth.

□(P → Q) → (□P → □Q)It says that "If it is necessarily the case that if P then Q, then if it is necessarily the case that P, then it is necessarily the case that Q."

Use Leibniz's notion of possible worlds to explain in English why this should be a necessary truth.

## Wednesday, March 1, 2017

## Tuesday, February 28, 2017

## Monday, February 27, 2017

See previous posts for anything you may have missed.

## Thursday, February 23, 2017

## Wednesday, February 22, 2017

On Monday we'll finish working on the most recent homework in preparation for the test on Wednesday. I'll post the complete solutions to the previous homework by

For Monday do problem 15 from the most recent homework. I have actually changed it slightly to make it less complicated, so if you downloaded or printed it out already, get the new version.

For Monday do problem 15 from the most recent homework. I have actually changed it slightly to make it less complicated, so if you downloaded or printed it out already, get the new version.

Here is a link to the homework tally as of the end of last week. Scores are indexed to last four numbers of student id. This link will also be on the top of the schedule page.

## Tuesday, February 21, 2017

Here are the solutions to the first 6 problems of Homework 6. We did the first three in class. Study these solutions and bring any questions you have. We'll do a few more on this sheet and then get started on Homework 7 assigned below.

## Monday, February 20, 2017

On Wednesday my office hours will be from 8:45-10:45 rather than the usual 9-11.

Also, note that our first test is on March 1, a week from Wednesday. It is an in class test for which you will only require a few good pencils and a good eraser. Do not do it in pen. The test is closed book and you will have the entire period to do it. All of the problems will be drawn directly from the solved homework problems, with the exception of #3 below. There will be five problems as follows:

1. A refutation tree in propositional logic.

2. A refutation tree in predicate logic.

3. 10 predicate logic formulas to be evaluated as true or false in a model.

4. A natural deduction proof in propositional logic.

5. A natural deduction proof in predicate logic (possibly including identity and functions.)

## Wednesday, February 15, 2017

## Tuesday, February 14, 2017

## Monday, February 13, 2017

I am unable to hold my usual office hours on Wednesday, but I will hold them directly after class from 2:45-4:25.

## Thursday, February 9, 2017

Next week is natural deduction in predicate logic. On Monday we'll focus on natural deduction in propositional logic. Make sure you reacquaint yourself with important rules of inference, especially disjunction elimination, conditional elimination and negation elimination. These are all covered in the PHIL 60 modules indicated on our schedule page, and the rules are all summarized in the course tools section on the bottom of the PHIL 60 schedule page.

This is the homework for Monday. Turn in only problem number 10. We'll review as many as we can and move on to deduction in predicate logic on Wednesday.

## Wednesday, February 8, 2017

## Monday, February 6, 2017

Wednesday's assignment is in the previous post.

## Saturday, February 4, 2017

This is the homework for Wednesday. Turn in #6 and #10 in class on Wednesday.

## Thursday, February 2, 2017

This is your practice homework, which we will review on Monday. Your turn in homework is to write down two different predicate logic formulas substantially different from any that occur in the practice homework and which pertain to the same model. Do not create new names or predicates. Evaluate these as true or false in the model and provide reasoning.

The relevant review material for this exercise is to be found in Module 10 on the Philosophy 60 schedule page.

## Monday, January 30, 2017

For your turn-in assignment do the following.

Translate the following into predicate logic.

- A king is dead.

Now translate this to the best of your ability.

- The king is dead.

Explain the difference between these two sentences and explain how your translation captures that difference.

## Friday, January 27, 2017

*Logics*into the readings folder on Blackboard. This functions as a clickable table of contents and makes it easier to use. I think you probably need to be using Adobe Reader. You will not see it right when you open the document. You need to click on the bookmark icon in the sidebar on the left. It's the one right above the paper clip.

Please see the previous post for your Monday assignment.

## Thursday, January 26, 2017

Note that in class we will not specifically cover natural deduction in propositional logic, since all the natural deduction rules are subsumed within natural deduction in predicate logic. However, most of you will still want to review this material, since this is where the book and my lectures introduces the rules employed there.

Also, I know that the pdf of the book

*Logics*, which is currently available in Blackboard, is more than a bit irritating to use because it is so long and it does not contain clickable bookmarks. I am fixing that, and should have one bookmarked to chapters and subsections available by tomorrow.

Please feel free to email me with any questions you have before class. I will get back to you promptly or at least let you know when to expect a response.

## Monday, January 23, 2017

## Monday, January 16, 2017

This is where you are going to come on a daily basis to find out what's going on in class. The syllabus is currently available, though subject to minor revisions. I'll be working to get the schedule done this week. If you are anxious to brush up on your elementary logic skills early, then you can go to the schedule page of my Philosophy 60 course. We'll begin the course by reviewing propositional and predicate logic using the material developed there.

See you in class!

Subscribe to:
Posts (Atom)