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

The final homework tally is now posted on the schedule page.

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.

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.

(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.

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.

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.

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.

Here is the summary of inference rules for test 2.  It will be available to you tomorrow. Note that there are two pages. Please remember that planning on using these for anything more than a quick reality check is the same as planning on doing poorly.

Solutions to today's homework are here and on the schedule page as Homework 20.

Test 2 is on Thursday.  Here is a sample test.  Here are the solutions. Let me know if you think you spot an error.

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.

For Tuesday's homework turn in problems 2-4 on this sheet.  At the end of class we started problem 2 as follows:

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.)

In case you missed it below, the turn-in homework for today is the last two proofs on the worksheet from Tuesday.

Due to unanticipated circumstances I am not able to keep my afternoon office hours today. Sorry about that.

Complete solutions to the Free Logic homeworks are now posted here and on the schedule page.

On Thursday we'll review some more set-theoretic concepts from the first two readings on set theory (lecture notes 2.1 and 2.2)  We'll finish the worksheet from Thursday and also work on this one. Your turn-in homework from Tuesday's worksheet is below.

The homework tally is updated here and at the link on the top of the schedule page. Tally includes 1 point credit for taking the first test.

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.

I tweaked Thursday's homework sheet slightly by adding one that helps you to figure out another. It doesn't affect the assigned problems.

For Tuesday and Thursday, please read the slides and/or book on Meinongian Free Logic.

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.

Complete solutions to today's homework are posted here and on the schedule page as HW 15. As you saw in class, there are sometimes easier ways to do them than the way I show in the solutions, but they give you more practice with the methods.

Homework for tomorrow is posted below. I should have the full solutions for yesterday's homework up by this afternoon.

This is Thursday's homework. Turn in problems 2 and 5.

I've added ten extra problems to the homework from Thursday here. Please review your answers from last time and turn in answers to the new problems. We'll cover these and go on to derivations in modal logic. Be sure you've read up on that, and we'll review and do some proofs. I'll assign some derivation problems for Thursday sometime this weekend.

Solutions to yesterday's homework are here and on the schedule page as HW12.  Note a couple of important points:

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.

Here is the homework for Thursday. Turn in answers to all of the problems. You'll need to engage the text and/or slides on Leibnizian modal logic in order to do these.

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

Test 1 is graded and grades are posted to SacCT. The grade on SacCT reflects a 2.5 point curve.  Your raw score, which you will see on the front of the test when it is returned, will be 2.5 points less. Check to be sure that your scores reflect this.

Solutions to the first 9 problems from yesterday's homework are posted here and on the schedule page as HW 11.

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.

Here and on the top of the schedule page is a link to the solutions for today's test. Thursday's homework is below.

For Thursday we will do a few of the proofs requiring universal introduction from the last worksheet, and then move on to this one which covers quantifier exchange equivalences and identity. Tun in numbers 1, 4 and 6.

Quantifier exchange and identity are covered here and in the text.

As noted below, the model used in the test is the same as for the practice exam, but I have removed functions, so this is what you will actually see. Click to enlarge.

Our first test on Tuesday will take the entire period and will cover all of the material covered in class through yesterday.  As we did no predicate logic derivations involving the rule of universal introduction, I will not include a proof involving this rule on the test.

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,

Here and on the schedule page are the solutions to all of the problems on today's homework.  Further guidance for Tuesday's midterm will be posted by tomorrow.

Here and on the schedule page are the solutions to all of HW 9.  The homework for Thursday is as stated below.

I'll return the first 8 homeworks in class on Tuesday.  Here and on the top of the schedule page are the accrued credits for each student, indexed to student id number.

In class I was having trouble explaining how to use the semantics of predicate logic to show that a sequent that produces a non-terminating tree is invalid. Here is an explanation. You should definitely take the time to understand it.

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.

For homework Thursday, do numbers 7 and 8 from today's homework sheet on refutation trees in predicate logic. We'll go over these, take questions, then move on to equivalences and derivation in predicate logic.

This is the article that Bradley asked about in class.

Tuesday we'll take any remaining questions on evaluating predicate logic formulas and we'll look at how to extend the tree method to predicate logic. The schedule refers you to the relevant chapter of the text and to Module 10 of Philosophy 60. In Module 10 under "Note" there is a link to these slides, which fully explains trees for predicate logic.  (There is no corresponding video lecture.)

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.

The solutions to today's homework are posted on the schedule page. Each one now contains an abbreviated version of a model-theoretic proof.

I'll post homework for Tuesday by tomorrow.

The complete solution to the predicate logic translation problems are now published on the schedule page.

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

Here is a partial solution to the homework we worked on yesterday.

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.

Thursday's homework is in the post below. It covers materials listed in Weeks 3-4 of the schedule.

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.

Here is the homework for Thursday.

Here is Tuesday's homework. Thursday's homework will be available by Sunday and I will have solutions to all of last week's homework up on the schedule page by Monday.

Here is the homework for Thursday.

See Tuesday homework post below. If you want to subscribe to this blog by e-mail there is a place to do so in the upper-right hand corner.

Here is a homework assignment covering refutation trees due Tuesday.  Follow the instructions at the top of the page. Tuesday we will review the homework and then move on to derivation (propositional calculus.) Homework for natural deduction on Thursday will be posted by Monday.

If you go to our schedule page and look under the Materials column you'll see a link entitled Philosophy 60 Modules 1-4. Today we reviewed Module 1 material. Thursday we will review Module 2 material, which relates to the semantics of propositional logic. You'll want to make sure you are acquainted with the truth tables of the operators and then learn the system of refutation tree rules in Modules 3-4. You can do this by watching the videos and reviewing the slides presented here or you can read Chapters 2 and 3 of 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.

All links on the webpage or now active and up to date.  See you tomorrow.

Hi, this is where you are going to come on a daily basis to find out what's going on in class.

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