World 4 now has more members than when I first posted the model.

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!

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.

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.

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. 

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 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?  

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. 

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.

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.

Here is the homework for Monday. Turn in the first two, but try to work through them all. These are simple problems that give you good practice with the form. Be sure to review the slides and/or text on mathematical induction.

Answers to today's homework are posted. Please be sure to study them and come Monday with any questions. We'll go over a couple more on Monday and then move on to mathematical induction. I'll post homework for Monday by tomorrow.

Tomorrow's homework is posted below. It covers the last part of Set Theory 2.4. We will also get started on mathematical induction.

Here is Wednesday's homework. Please turn in the even numbered problems.

Here is Monday's homework, which covers Set theory 2.3 and about half of 2.4.  Please turn in the even numbered problems.

Solutions to all of today's homework problems are posted on the schedule page.  See below for previous post regarding test results.

Scores for test 2 have been posted to Blackboard and tests will be returned in class today. The score on BB reflects a 2 point curve. Check to be sure that it is two points higher than the score written on your test.

In case you are also trying the even numbered problems for tomorrow's, homework, there was a typo in problem 4 that I have just corrected. I'm sorry about that.

The solution to test 2 has been posted to the top of the schedule page. Let me know if you detect any errors.

Here is the homework for Wednesday. Turn in odd numbered problems.

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

This is the summary of rules with which you will be provided on Monday. Be sure that you understand the condensed statement of the free logic rules as I will not clarify them for you during the test. Note that, as before, you must know the quantifier rules for classical predicate logic. Note, also, that on this test you must know the valuation rules for multi-valued logics. For the 2 pt. extra credit problem you must also know the 3rd definition of validity in infinite valued logic.

Also, I neglected to mention that there will be 1 extra credit problem worth 2pts. This will involve evaluating the validity of an argument according to the third definition of validity as you did on HW 14.

Note: For Monday's test, calculators may not be used on the problem that involves computing truth values in infinite valued logic. See previous posts for other information about the test.

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:

1. The semantics of modal logic, in which you evaluate formulas with respect to a model.
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.)

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.

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.

Solutions to today's homework are on the schedule page. I will give some studying advice for the test on Monday by tomorrow.  There is no homework due on Monday, but I will post homework for Wednesday by Sunday.

Here is the homework for tomorrow. Turn in odd numbered problems.  Please review posts below.

Unfortunately I won't be able to hold all of my usual office hours on Wednesday. I can will be there from 8:45-9:45 and from 1 to 1:30.

Solutions to today's homework are posted on the schedule page.  Please read the first reading on set theory in BB which corresponds to 2.1 lecture slides on the schedule page. I will have homework problems available by tomorrow morning.

Here is the homework for Monday. Turn in the odd numbered problems.

Chaz was right that there was a typo in the statement of the valuation rule for the conditional. I inadvertently substituted a + for a - .  Thanks to Chaz for pointing this out!  I will try to post homework for Monday by tomorrow but Friday at the latest. We fill be talking about inference in multi-valued logic and perhaps a little bit of set theory.

Wednesday's homework is below. Since many philosophy majors wish to attend the Nammour Symposium during our class period, I will accept the homework if turned in to me in my office before class on Wednesday.

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 ponens is 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 for modus ponens for 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 of modus ponens as defined above? 

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

 

Solutions to derivation problems in free logic are posted to the schedule page as HW11.  On Monday we will move on to multi-valued logic.  Slides are posted to the schedule page. I will post homework by tomorrow.

Wednesday we will work on derivation in free logic. Your turn-in homework assignment is to do #1 on this page.  At 9AM this morning there is only one problem, but I will add several more by noon and you should try as many as you can. Be sure that you are using the quantifier rules for free logic as described in the text and the lecture slides.

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.

Here is the homework for Monday 3/27.  Your turn-in assignment is to do all of them. Be sure you have acquainted yourself with the text/slides on the semantics of Meinongian free logic.

Solutions to Homework 9 covering derivations in modal logic have been posted to the schedule page.

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.

The homework tally has been updated.  See the small table on the top of the schedule page. Be sure that my tally agrees with yours and see me with all of your returned assignments if it does not. Recall that you were awarded 1 homework credit for taking the first test.

I forgot to mention in class today that if you are submitting to the Nammour student essay contests and wish to earn credit in this class for your work, please cc me on your submission.

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.

I modified and corrected the Monday homework a little bit. The problems assigned below are now number 3 & 4, rather than 2 & 3. (The turn-in problems have not been changed, only the numbering.)

Here is the homework for Monday.  Turn in problems 2 and 3.

The solution to HW 8 is posted on the schedule page. Be sure you can follow and produce the proofs I provided in the left hand column and come to class with any questions.  We'll start with derivations in modal logic on Monday and I'll provide some as homework for you by tomorrow.

Here is the Wednesday homework.  Turn-in all of them. We'll begin by discussing it in class.

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.

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.

I've posted the solution to the test to the top of the schedule page.

Next week we move on to Leibnizian modal logic. Lecture slides based on the text are posted on the schedule page.  I will post your homework by tomorrow.

Also, Javeeria just pointed out that I wrote the wrong answer down for the sample question on the model. It's fixed now. Thanks Javeeria.

I made an important clarification to the model that will be used for problem 5 on the test, specifically regarding the meaning of the successor function and the relation 'subsequent to."

Here is the model we will be using for the fifth problem on Wednesday.  The solutions to HW 7 are on the schedule page.

See previous posts for anything you may have missed.

There will be no homework due on Wednesday.  You will get 1 homework credit for showing up for the test and spelling your name correctly on the top of the paper.

Complete solutions to Homework 6 are now posted on the schedule page.

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.

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.

See previous two posts for other important stuff.

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.

See previous post for Wednesday's homework.

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.)

This is Wednesday's homework.  Turn in #4, 8 and 14.

I have posted full solutions to our most recent homework as HW5 on the schedule page. For Monday we move on to what we were previously scheduled to do today, derivations in predicate logic. This is it. Turn in problem 4 and 8.

Here is the announcement for the Nammour Symposium Student Essay Contest.  Please refer to the syllabus to see the incentive provided for participating in it. Note that the submission deadline is March 14th.

Correction to previous post. We will spend one more day doing natural deduction in propositional logic. Be sure to take this time to consolidate your memory of the inference rules and equivalences. For Wednesday homework turn in numbers 7 and 8.

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

Please see below for Monday's homework.

This is Wednesday's homework. Turn in problem 4 and 8.

Please see yesterday's post.

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.

The full solution to today's homework is available as HW4 on the schedule page.

Full solution to today's homework on evaluating predicate logic formulas in a model are on the schedule page and here. Let me know if you detect any mistakes.

Wednesday's assignment is in the previous post.

Monday's assignment is below. On Wednesday we will plan to do trees in predicate logic. I do not have an audio lecture for predicate logic trees, but there is a set of slides provided in Module 10 of the philosophy 60 schedule.

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

I have posted the solutions to the last homework as HW 2 in the schedule page. I have commented extensively on some of the ones that we didn't get to and I suggest reviewing it. I will add Monday's homework to this post sometime today.

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.

This is homework we'll review on Wednesday. You will not turn it in, but bring your work to class as I'll call on people to provide their answers.

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.

I just uploaded a bookmarked copy of our primary text 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.

This is the homework due Monday at the beginning of class.  On Monday we will review some of these, and then move on to predicate logic as scheduled.

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.

In case I wasn't clear about this enough in class, please note that when you are reviewing materials from my Philosophy 60 course, you are not required to do any specific exercises or homework that I do not specifically assign. It is there strictly so that you can brush up on your propositional and predicate logic knowledge.

Hi and welcome back to spring semester.

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!