Just a reminder that the final is today from 12:45-2:45.

## Thursday, December 14, 2017

## Monday, December 4, 2017

__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

*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 theproofsof these results resemble each other?

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

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

## Tuesday, November 28, 2017

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

## Friday, November 17, 2017

## Wednesday, November 15, 2017

## Tuesday, November 14, 2017

## Monday, November 13, 2017

Be sure to study the models so you you don't have to waste time figuring out how to interpret them during the test. The ones on the test will have all of the same features, though the specifics may vary slightly.

## Friday, November 10, 2017

The obvious next move is to do a "E on line 3. But the question is what do you eliminate to? The important thing to see is that you are not restricted simply to name letters, like a, b and c. You already know this, because, e.g., you can eliminate to functions like f(a) or g(a,b). So this applies to sets as well. For example, if I know that "xFx, then I know that

__every single thing__has the property F. So, e.g., since__sets__are now things for us, I could us "E to infer that F{a,b}. Think, then, about the definition of a power set and this allows you to infer from the information provided on line 2. This will also tell you how to perform the "E.
Thursday is test 2, which will cover all of the material we've done since the first test. On the schedule this will be HW's 10-20. The test will have basically the same design as the first test, drawing all proofs from actual homework problems, but providing new models and formulas for interpretation. As before, I will supply any models used the day before the exam. I will provide a set of inference rules updated with the rules for modal logic, free logic, and definitions of set-theoretic relations. (It will not contain the quantifier rules for predicate logic itself.)

## Thursday, November 9, 2017

## Wednesday, November 8, 2017

## Sunday, November 5, 2017

## Friday, November 3, 2017

There was an error in the formulation of problem 11 in free logic derivations, which I assign below due on Tuesday. The page is now corrected. Here is the link. Sorry about that!

Here are the solutions to the free logic proofs we worked in class yesterday.

For homework on Tuesday, please turn in problems 7 and 11 from the same sheet. Also, read the lecture notes entitled Set Theory 2.1 and/or the corresponding reading in BB entitled Set Theory 1.

After reviewing the proofs assigned above, we'll work through as much of this homework as we can. You should attempt all of the evaluation problems (1-17), but you don't need to turn those in.

Thursday the turn-in homework will be the two natural deduction problems at the end of the the above homework.

I'll be updating your homework tally this weekend and returning them on Tuesday.

Please note that I have moved the date of the next test back to 11-16. It will cover the end of predicate logic derivation, modal logic semantics and derivation, free logic semantics and derivation, and as much set theory as we get done by 11-14.

For homework on Tuesday, please turn in problems 7 and 11 from the same sheet. Also, read the lecture notes entitled Set Theory 2.1 and/or the corresponding reading in BB entitled Set Theory 1.

After reviewing the proofs assigned above, we'll work through as much of this homework as we can. You should attempt all of the evaluation problems (1-17), but you don't need to turn those in.

Thursday the turn-in homework will be the two natural deduction problems at the end of the the above homework.

I'll be updating your homework tally this weekend and returning them on Tuesday.

Please note that I have moved the date of the next test back to 11-16. It will cover the end of predicate logic derivation, modal logic semantics and derivation, free logic semantics and derivation, and as much set theory as we get done by 11-14.

## Wednesday, November 1, 2017

## Friday, October 27, 2017

Here is the homework for Tuesday. Please do all of them.

Here is the homework for Thursday. Please turn in numbers 1 and 2. Answer the question asked in the Note after problem 1 as well.

Note that solutions to all proofs for yesterday's homework have been posted on the schedule page. Be sure to work through them all, as they will give you more practice with the N rule which still seems to strike many of you as magical. Free Logic will give you continued practice with this as well.

## Thursday, October 26, 2017

## Wednesday, October 25, 2017

## Monday, October 23, 2017

## Friday, October 20, 2017

## Wednesday, October 18, 2017

1. The last problem we worked in class was problem 13, and I said something that was incorrect about the limitations imposed by the rule for existential elimination. Please study the solution I've given (which is actually the first way we did in class) and the corresponding note, and make sure you understand why it is in fact permissible. (I did not include the ~I proof we did instead. It is fine, but unnecessary.)

2. The solutions, and now the original homework, include a few extra problems. You will not be turning them in, but you should be sure you can do them, as they are fair game for future tests.

Thursday's homework on modal logic is below.

## Tuesday, October 17, 2017

I'll have the solutions to all of the homework problems from today posted by tomorrow morning.

## Saturday, October 14, 2017

## Friday, October 13, 2017

For Tuesday we'll work more on identity and functions. (See my presentation on the latter on the schedule page.)

This is Tuesday's homework. Turn in 2, 4, 6, 8, 13 and 15.

Thursday we will probably move on to Leibnizian modal logic. So you should read my slides in the schedule page and/or the corresponding chapter in the text. I need to wait until Tuesday to make Thursday's turn-in assignment.

## Tuesday, October 10, 2017

## Friday, October 6, 2017

As already noted, the problem on the test will be drawn from the solved homework problems posted on the schedule page. The only exception is a problem in which you will evaluate the truth and falsity of predicate logic formulas in a model. We will use the same model that is on the sample exam posted below, but the formulas to be evaluated will be different. The only difference is that there will be no function symbols, since we have not yet introduced those.

Here is a copy of the solutions to the sample exam.

I will also provide this summary of rules and equivalence. It does not include derivation rules for predicate logic.

__Please__resist the temptation to be comforted by this. You will not do well on this test if you lack a thorough working knowledge of these rules. I am providing them only so that you can check that you are using them properly.
Thursday we will do more on derivation in predicate logic, including identity and functions. I will post a homework this weekend. You will get homework credit on Tuesday for showing up and taking the test,

## Thursday, October 5, 2017

## Tuesday, October 3, 2017

## Monday, October 2, 2017

## Friday, September 29, 2017

The complete solutions for yesterday's homework on predicate logic trees are posted here and on the schedule page.

For Tuesday please do what was originally due yesterday, i.e., the problems from this worksheet, turning in problems 3 and 9. You should definitely try to do them all. Refer to the previous posts for a summary of the propositional logic equivalences. We'll work several of these problems and then review the inference rules for derivations in predicate logic, which are also posted below.

For Thursday we will move on to derivations in predicate logic. See previous post for summary of inference rules for the quantifiers. Here is the homework. Turn in problems 4 and 5.

The following Tuesday, October 10th, is our first midterm. It will cover all previous material. I'll provide more details next week, but it will resemble this test. Most problems will be drawn directly from previous homeworks.

## Tuesday, September 26, 2017

This is the article that Bradley asked about in class.

## Friday, September 22, 2017

Here is the homework for Tuesday. Turn in numbers 3 and 5.

Thursday we'll move on to derivation using equivalences in propositional logic and introduce the rules for derivation in predicate logic. A summary of propositional equivalence rules may be found here and at the bottom of the Philosophy 60 schedule page. The rules for derivation in predicate logic are addressed in the text as well as modules 11 and 12 of Philosophy 60. The rules are summarized here and at the bottom of the Philosophy 60 schedule page.

Here is the homework for Thursday. Turn in problems 3 and 9.

I have decided to move our first exam back one class meeting to Tuesday October 10th.

## Thursday, September 21, 2017

I'll post homework for Tuesday by tomorrow.

## Wednesday, September 20, 2017

See below for Thursday's homework. Do them all and we will review them in class.

## Friday, September 15, 2017

Homework for Tuesday is to do the remaining problems. On Tuesday we will clarify the formation rules of predicate logic and, given time, move on to evaluating formulas in a model. All of this material is covered by me here. You should engage the material in all three rows labeled "Watch". The "Lecture" and "YouTube" links are the same videos stored in different places. The "Slides" are the slides I use in the videos, which may be sufficient for some of you.

This will be the homework for Thursday.

## Wednesday, September 13, 2017

I have posted a video review of the last 4 problems of homework 3 on the schedule page and here. Those of you struggling with proofs in propositional logic should spends some quality time with it. While making it I noticed a few errors in the posted solutions to that homework and those have been corrected.

## Friday, September 8, 2017

## Tuesday, September 5, 2017

## Saturday, September 2, 2017

## Friday, September 1, 2017

## Tuesday, August 29, 2017

*Logics*, which you will find in the reading folder in Blackboard. We'll review these on Thursday.

There is no homework to be turned in on Thursday.

## Sunday, August 27, 2017

I'm sorry for the slight delay in posting the syllabus and schedule. It's undergoing some minor revisions. It will be up by Monday noon or so.

You will not be required to purchase any books or other materials for this class.

Check back before class, read the syllabus and come with questions.

Randy Mayes

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