tag:blogger.com,1999:blog-10321981201477148822017-12-10T19:05:14.147-08:00Philosophy 160 Deductive Logic IIG. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.comBlogger49125tag:blogger.com,1999:blog-1032198120147714882.post-44760625085545029202017-12-04T15:22:00.001-08:002017-12-04T15:22:05.259-08:00<a href="https://drive.google.com/file/d/1MloflmZGrpOoe_lHy049Y_fbj2PfXvWo/view?usp=sharing">Here</a> is a sample final and <a href="https://drive.google.com/file/d/1EC4Vxq6hQl82Z4ZYvHzfBhDlTl5yxUfh/view?usp=sharing">here</a> are the solutions. The proof problems are drawn from actual homework problems <u>or</u> 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.<br /><br /><br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-34206017395328038772017-12-01T09:40:00.002-08:002017-12-01T09:40:41.799-08:00For 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 <i>The Infinite</i>, 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.<br /><br />Tuesday turn-in homework is the following question:<br /><blockquote class="tr_bq">State the specific contradictions implied by (a) Russell's Paradox and (b) The Burali-Forti Paradox. In what interesting sense do the <u>proofs </u>of these results resemble each other? <br /><div><br /></div></blockquote><br />Thursday's turn-in homework is the following question:<br /><br /><blockquote class="tr_bq">Clearly identify <u>three</u> significant errors in the following.</blockquote><blockquote class="tr_bq">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.</blockquote><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-70048281200085431172017-11-28T12:24:00.004-08:002017-11-28T12:24:50.930-08:00(I posted this to the wrong class over Thanksgiving, hence everyone who comes to class will get credit for today Tuesday)<br /><br />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 <a href="https://drive.google.com/file/d/1e-QGJrGfruFwuZn318Ag-350i7zYR-As/view?usp=sharing">this sheet</a> as we have time for.<br /><br /><br />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 <a href="https://drive.google.com/file/d/1DvFAiiiYDk9CJ9OAN30UCon_9l0mqAcR/view?usp=sharing">this sheet</a>.<br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-82499490792932668782017-11-19T13:40:00.003-08:002017-11-19T13:40:50.788-08:00Grades 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.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-43055534019747135752017-11-17T15:09:00.001-08:002017-11-17T15:09:09.463-08:00The test solution is posted <a href="https://drive.google.com/file/d/1FSKkQB_9hd9i60E5MhCx-PnW0IF9w6uU/view?usp=sharing">here</a> and at the top of the schedule page.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-80043823795172315132017-11-17T12:42:00.002-08:002017-11-17T12:42:16.559-08:00<a href="https://drive.google.com/file/d/1VKPyPZJbWLpNnBQItoWPhHqh_UzYPliD/view?usp=sharing">Here</a> is the homework for Tuesday. It covers Set Theory 2.3 and the first half of 2.4. Turn in the even numbered problems.<br /><br />I will post the answers to the exam shortly. I expect to have them graded by Tuesday.<br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-23919969272585942422017-11-15T10:21:00.003-08:002017-11-15T10:21:49.379-08:00I 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.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-49433190053993259182017-11-15T09:19:00.003-08:002017-11-15T09:19:32.610-08:00<a href="https://drive.google.com/file/d/1dOc45uTf9ra2zkJM5BKksz_FLhTPxXCn/view?usp=sharing">Here</a> 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.<br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-75270553294074891332017-11-14T15:11:00.001-08:002017-11-14T15:11:07.344-08:00Solutions to today's homework are <a href="https://drive.google.com/file/d/0ByEWimmpVQfWZ1lWbWpiQzJ2ZTQ/view?usp=sharing">here</a> and on the schedule page as Homework 20.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-51823525645918400932017-11-13T16:35:00.000-08:002017-11-13T16:35:05.216-08:00Test 2 is on Thursday. <a href="https://drive.google.com/file/d/1L8Vbib7co-n7SPBzCpDX_mz0gVWCZFwU/view?usp=sharing">Here</a> is a sample test. <a href="https://drive.google.com/file/d/17Ow6aMQw-Xux_lQ5KrBLvY8RyMG-YCJW/view?usp=sharing">Here</a> are the solutions. Let me know if you think you spot an error.<br /><br />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.<br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-71336102488468745112017-11-10T10:15:00.000-08:002017-11-11T20:15:23.333-08:00For Tuesday's homework turn in problems 2-4 on <a href="https://drive.google.com/file/d/0ByEWimmpVQfWOGVXZDhtQWRuZFE/view?usp=sharing">this</a> sheet. At the end of class we started problem 2 as follows:<br /><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-duh9WOAfqnA/WgXlmHmngRI/AAAAAAAAQiA/8EbGyiiDwUEwFyo9uI2dvfucB2Gzdvd8ACLcBGAs/s1600/powersetproblem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="156" data-original-width="435" height="114" src="https://4.bp.blogspot.com/-duh9WOAfqnA/WgXlmHmngRI/AAAAAAAAQiA/8EbGyiiDwUEwFyo9uI2dvfucB2Gzdvd8ACLcBGAs/s320/powersetproblem.jpg" width="320" /></a></div><div><div><br /></div><div>The obvious next move is to do a <span style="font-family: "symbol";">"</span>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 <span style="font-family: "symbol";">"</span>xFx, then I know that <u>every single thing</u> has the property F. So, e.g., since <u>sets</u> are now things for us, I could us <span style="font-family: "symbol";">"E</span> 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 <span style="font-family: "symbol";">"E</span>. </div><div><br /></div><div>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.)</div><div><br /></div></div>G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-29694344135839697972017-11-09T09:04:00.004-08:002017-11-09T09:09:15.065-08:00In case you missed it below, the turn-in homework for today is the last two proofs on the worksheet from Tuesday.<br /><br />Due to unanticipated circumstances I am not able to keep my afternoon office hours today. Sorry about that.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-31612786205384482032017-11-08T11:34:00.001-08:002017-11-08T11:34:28.276-08:00Complete solutions to the Free Logic homeworks are now posted <a href="https://drive.google.com/file/d/0ByEWimmpVQfWWHlZa2hFZVJzRlk/view?usp=sharing">here</a> and on the schedule page.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-80425050096123725062017-11-08T07:47:00.000-08:002017-11-08T07:47:06.139-08:00On 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 <a href="https://drive.google.com/file/d/0ByEWimmpVQfWOGVXZDhtQWRuZFE/view?usp=sharing">this</a> one. Your turn-in homework from Tuesday's worksheet is below.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-64870794434711280012017-11-05T10:14:00.002-08:002017-11-05T10:14:43.635-08:00The homework tally is updated <a href="https://drive.google.com/file/d/0ByEWimmpVQfWZ1RxMmVpckF3dzg/view">here</a> and at the link on the top of the schedule page. Tally includes 1 point credit for taking the first test.<br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-80250463865550012202017-11-03T22:42:00.000-07:002017-11-03T22:42:28.883-07:00There 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. <a href="https://drive.google.com/file/d/0ByEWimmpVQfWRFdTbm92bWhDdmM/view?usp=sharing">Here</a> is the link. Sorry about that!G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-86051082038548699032017-11-03T11:13:00.001-07:002017-11-03T11:13:40.052-07:00<a href="https://drive.google.com/file/d/0ByEWimmpVQfWaExoM3VwZ3U5NkE/view?usp=sharing">Here</a> are the solutions to the free logic proofs we worked in class yesterday.<br /><br />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.<br /><br />After reviewing the proofs assigned above, we'll work through as much of <a href="https://drive.google.com/file/d/0ByEWimmpVQfWTUVldVo2T2xoU1U/view?usp=sharing">this</a> homework as we can. You should attempt all of the evaluation problems (1-17), but you don't need to turn those in.<br /><br />Thursday the turn-in homework will be the two natural deduction problems at the end of the the above homework.<br /><br />I'll be updating your homework tally this weekend and returning them on Tuesday.<br /><br />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.<br /><br /><br />G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-87451577053647377442017-11-01T14:36:00.003-07:002017-11-01T14:36:48.928-07:00I tweaked Thursday's homework sheet slightly by adding one that helps you to figure out another. It doesn't affect the assigned problems.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-32487822239252636192017-10-27T10:05:00.000-07:002017-11-01T15:41:11.307-07:00For Tuesday and Thursday, please read the slides and/or book on Meinongian Free Logic.<br /><br /><a href="https://drive.google.com/file/d/0ByEWimmpVQfWNlpwZGQzSXpheG8/view?usp=sharing">Here</a> is the homework for Tuesday. Please do all of them.<br /><br /><a href="https://drive.google.com/file/d/0ByEWimmpVQfWRzlBTmFjeXBhV1E/view?usp=sharing">Here</a> is the homework for Thursday. Please turn in numbers 1 and 2. Answer the question asked in the Note after problem 1 as well.<br /><br />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.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-3034881243052287092017-10-26T15:54:00.000-07:002017-10-26T15:54:05.302-07:00Complete solutions to today's homework are posted <a href="https://drive.google.com/file/d/0ByEWimmpVQfWSHZLcjZLQUZuNWs/view?usp=sharing">here </a>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.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-625176642777839552017-10-25T10:15:00.002-07:002017-10-25T10:15:40.847-07:00Homework for tomorrow is posted below. I should have the full solutions for yesterday's homework up by this afternoon.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-76646382560552460142017-10-23T13:33:00.002-07:002017-10-23T19:36:42.999-07:00<a href="https://drive.google.com/file/d/0ByEWimmpVQfWcG9RT2hTN2QxSWc/view?usp=sharing">This</a> is Thursday's homework. Turn in problems 2 and 5.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-16697919181657763932017-10-20T15:11:00.002-07:002017-10-20T15:11:33.975-07:00I've added ten extra problems to the homework from Thursday <a href="https://drive.google.com/file/d/0ByEWimmpVQfWNlE5XzVSLS11cHc/view?usp=sharing">here</a>. 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.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-12893870268095069512017-10-18T11:00:00.001-07:002017-10-18T11:00:24.438-07:00Solutions to yesterday's homework are <a href="https://drive.google.com/file/d/0ByEWimmpVQfWVkRZRlQ4SnZCdHc/view">here</a> and on the schedule page as HW12. Note a couple of important points:<br /><br />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.)<br /><br />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.<br /><br />Thursday's homework on modal logic is below.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0tag:blogger.com,1999:blog-1032198120147714882.post-36663298719914298502017-10-17T15:19:00.000-07:002017-10-17T16:18:54.108-07:00<a href="https://drive.google.com/file/d/0ByEWimmpVQfWNlE5XzVSLS11cHc/view?usp=sharing">Here</a> 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.<br /><br />I'll have the solutions to all of the homework problems from today posted by tomorrow morning.G. Randolph Mayeshttp://www.blogger.com/profile/18285281186698499962noreply@blogger.com0