Introduction to Logic

Introduction to Logic May 18- June 20, 2015 PHIL 151 http://logic.umwblogs.org Dr. Craig Vasey Trinkle 238 ext 1342 . [email protected]

Department of Classics, Philosophy, and Religion. University of Mary Washington

First off, I have to share with you an honest assessment of the situation: although there is some convenience to the on-line format, it is harder to learn something well in an on-line environment than it is in a face-to-face classroom. There is no one to confront you, encourage you, put you on the spot, repeat things to you, congratulate you, etc. Your own motivation is all you can rely on.

I have set up a website that contains all the information I deliver in classroom lectures as written pages. There are a number of Powerpoint presentations that will also be helpful. I will be available via email and live online chats or skype, to answer questions. These are all resources, but the key is: how will you put them to use? In the on-line classroom, you are on your own to do that. To a greater degree than you may be accustomed to, you must read carefully, repeatedly, and well in order to be successful here. That begins with reading this syllabus carefully, repeatedly, and well. Some of you may be more accustomed to scanning when you read; you need to change that. By the way, your work for this class will require that you read the entire on-line book, section by section in the order in which the chapters are arranged. Repeatedly, and well.

You must make yourself stay focused and make yourself work at Logic every day for a couple of hours. This is crucial; you’ll need to constantly review what you’ve encountered and learned, or else it will fall right off your radar. That is, you won’t learn anything if you don’t review it regularly and if you don’t return to the subject for at least a little while every day. Avoiding it for a few days will be extremely counterproductive. Because of this need to stay focused, there are numerous assignments and quizzes; don’t view them as a nuisance, but as the best help I can offer to get you to keep up with the task of learning Logic. Consider: if this summer class were a face-to-face class, we would meet two hours/ day for four days/ week, and on top of that you would be doing 1- 2 hours of homework every day.

Now to the course content: 1 Introduction to Logic is a course that every student should take during the first year of college. No other course will be as dedicated to the task of understanding and sharpening analytical abilities and skills in general; the benefits of doing this course-work will show up throughout your college career and beyond college as well.

Some thinkers talk about Logic as a field concerned with the analysis of arguments, but that is much too narrow, since argument analysis presupposes appreciation of numerous conceptual distinctions and analytical techniques. We will be covering the basic conceptual foundations of Logic, as well as Informal Fallacies, Categorical Logic, Sentential Logic, and offering an introductory look at Predicate Logic. Although it is a Philosophy course, Logic can be thought of as a “practical skills” course. Success in a practical skills course of study requires practice, regular practice. The ideas or concepts themselves are not difficult to grasp, but the mastery of them only comes through the practice of applying them. Many students are tempted to think that since the concepts seem easy and obvious, little work is needed in the course. They are the ones who get C’s and lower in the course.

For this summer on-line version of the course, weekly papers reviewing the week’s material, a weekly response to another student’s paper and a requirement of bi-weekly discussions of exercises from the on-line book, will ensure that you are monitoring your grasp and appreciation of material; About a third of your grade will come from these papers and responses. Performance on quizzes (frequent short multiple choice quizzes) and exams will account for about two thirds of your grade. A chat session via Canvas will be available every Monday, Tuesday, Wednesday, and Saturday from 5 to6 PM; I’m open to changing this time if I get feedback from you indicating we should (we could vary the hours on different days). You can also contact me by email ([email protected]), and Skype sessions are also an option. You should send me questions by email or join the chat session with questions whenever you are puzzled or bogged down. However, DO NOT email me through or at Canvas; I do not use Canvas for receiving email, although I will post announcements through it. If you use that approach, I will not see your message.

You will be posting your weekly papers and assignments, and responses, to the appropriate Discussion folder in Canvas. Whenever you submit something to me by email or to the Discussion Forum, MAKE SURE YOUR NAME APPEARS IN THE FILENAME.

The course content is delivered at http://logic.umwblogs.org, The chapters at the website (listed along the right hand side) are arranged in the order of the syllabus, and contain Powerpoint reviews of material as well as homework exercises for daily and weekly practice. For exams, I will send you the exam through Canvas, and you will have a determined time period in which to complete it and send it back

Course Goals: Students will learn how to distinguish arguments from non-arguments, and inductive reasoning from deductive reasoning; how to identify fallacies of everyday

2 reasoning; and how to interpret, represent, and determine consequences regarding arguments in three symbolic modes (categorical, propositional, predicate). This course satisfies a General Education requirement in the area of Quantitative Reasoning.

Syllabus I am not giving you a precise day-by-day schedule below because this course is asynchronous and I cannot expect you to all be on exactly the same schedule. On the other hand, as I said above, working on this every day is really essential. I’m telling you where you should be in the text by Tuesday and Thursday each week; it’s up to you on Sunday each week to make sure you are aiming for the Tuesday goal. You’ll have a paper due each Saturday reviewing the work of the week, and a response paper each Sunday. Deadlines are days and times by which you must submit materials –you are also welcome to submit them in advance of the deadlines.

Before we begin the course, read through the syllabus carefully twice. Send me an email no later than May 19 telling me that you have read and understand the syllabus. If I do not have this email from you by May 19, I will dock 10 points off your grade at the end of the semester. Make sure you understand the pace and nature of the assignments, and that you are clear on the due dates. Any questions? Email me or come to the chat in Canvas on Monday at5 pm.

At Canvas, take a good look at the Discussion page. Assignments are listed in the order in which they are to be done; there are quite a few of the forums –these are the on-line substitutes for looking you in the eye in the classroom and putting you on the spot.

Week 1 May 18-May 23 Basics: terminology for arguments and non-arguments; deduction and induction; informal fallacies: Read the Introduction and all of Chapters 1-5. (You need not read all of the Jabberwocky selection in Chapter 2.)

By Tuesday you should have finished Chapter 3, and have all the basic terminology from chapters 2 and 3 well in hand: Use/ mention, meaning (sense/ reference); premise and conclusion indicator words. Post discussions of homework exercises from all three chapters, as well as questions in the Forums for me.

By Thursday you should have completed Chapters 4 (the distinction between, and the evaluative language for, induction and deduction) and 5 (validity and counter- examples). You are working on committing quite a vocabulary list to memory this week. Practice memorizing the vocabulary by writing the various lists multiple times daily. You will find that this really works! You can do it!

A review discussion of all of this should be in your 4-5 page Paper & Assignment due Saturday, May 23 by Noon. Advice on how to approach these papers: think of it as though you wanted to impress you parents when they said "What did you learn this week at school?" It would take some explaining, and you'd have to put it in

3 your own words, watching out for the likelihood that from time to time they would say "I don't really quite see what you mean, or why that matters," and you'd need to make it clear. (Do not write the paper as a letter to your parents, however! Write it as a college-level paper! Also, be sure to meet all my expectations about quality-- see below, p. 7.)

Assignment 1:

A. Follow the examples called “The price of gas,” “The case of the ACA,” etc., and make up one good example of each of the 7 non-arguments on a subject of your choice.

B. Also make up 2 examples for each of the deductive and inductive patterns (this will make a total of 22 argument examples).

Week One Paper & Assignment is due in the designated Canvas Discussion forum by Noon Saturday, May 23; your response to another student’s paper is due by Noon Sunday.

QUIZZES: By Saturday you must complete Canvas Quizzes 1, 2 and 3. Each of these has a “retake” option –version “A.” These quizzes will be available beginning on Tuesday May 19 at 5 pm, until midnight Saturday May 30; you can take them anytime during the week but the smart approach will be to space them out, e.g., Quiz 1 on Monday, Quiz 2 on Wednesday, Quiz 3 on Friday. Each time, between taking the first quiz (Canvas Quiz 1) and taking the retake (Canvas Quiz 1A), you should post to the Canvas Quiz forum about what you got wrong: ask a question, say why you thought the answer was what you thought, so you can get some helpful feedback.

Week 2 May 24-May 30 Categorical logic: propositions, operations, syllogisms: Read all of Chapters 6 & 7.

By Tuesday you should have completed Chapter 6 (Informal Fallacies), and Chapter 7 through 7.1 (Venn Diagrams). Post discussion of HW examples.

By Thursday, you should have completed the rest of chapter 7 on Categorical Logic. Post discussion of HW examples you work on.

Assignment 2.

A. Fallacies. Post two examples you find, encounter or make up, of each of the 20 fallacies of reasoning. Memorize these four families of fallacies and the names of their members. Read the examples posted by other students of the fallacies assigned to them, and comment on them, especially if you wonder if they actually fit the pattern. Although this is part of the Assignment due with your paper on Saturday, post these in Canvas in

4 the Fallacy Forum by May 26 so everyone can look at one another’s examples before diving into the next subject of the week.

B. Categorical Logic.

i) Fill in and post (at the Square of Opposition forum) HW on square Feb 12 at the end of 7.2.1. Post this by May 28.

ii) After you have practiced putting syllogisms in standard form and analyzing them in 7.3.1.1 (answers to these are provided in the section), go to 7.3.1.2 and choose five to do on your own. Submit these to the weekly homework discussion forum by May 29 with questions they cause you to have. (To be able to discuss the Venn diagrams without scanning them to me (which is an option too), you should do the following: label the left hand circle the Minor term, the right hand circle the Major term, and the bottom circle the Middle term. Number the seven segments beginning at the top left, then you can report which segments are shaded and which have x’s. This is not an optional exercise. If you do not submit five syllogism analyses, you get a zero on this week’s work. Why? Because I know from experience that if you cannot give me five syllogisms, you have not learned anything.

C. Text analysis: MLK’s Letter from a Birmingham Jail. You will find the assignment in the horizontal menu at the top of the website. Detailed instructions are provided there.

Week Two Paper & Assignment is due in the designated Canvas Discussion forum by Noon Saturday, May 30; your response to another student’s paper is due by Noon Sunday.

QUIZZES By midnight Saturday you must complete Canvas Quizzes 4, 5 and 6. Each of these has a “retake” option. The quizzes are available all week until midnight of June 6; don’t wait until Saturday to do them. Quiz 6 and 6A actually contain some material you will not have studied yet, so I will include them in both this week and next week; you can take them each twice, and the higher score will be kept. So take them this week for the Categorical Logic practice, and then retake them next week once you have the basics of Propositional Logic in hand.

Week 3 May 31-June 6. Propositional logic: truth functions, translation, truth tables, rules of inference, proofs: Read all of Chapters 8 & 9

By Wednesday of this week you should have completed Chapter 8 (Symbolic Logic: propositional logic), and know how to build Truth Tables for analyzing statements, sets of statements, and arguments. Post discussion of homework exercises from Chapter 8.

5 By Thursday, you need to know the Rules of Inference in Chapter 9. Until you have them memorized, you will be at a disadvantage, so write them over and over each day, and say them out loud as you do. Post discussion of homework exercises 9.2.1.

Assignment 3:

A) Generate your own example of a tautology and a self-contradiction –in one case needing a 4 line truth table, the other an 8 line table; make a complete truth table for them. (Use the table function in Word).

B) In Homework Discussion Week Three you will find two postings of exercises: one is on recognizing properly written compound statements (WFFs –“well-formed formulas”) and calculating truth values, and one is statement and argument analysis by Truth table. Submit these with your paper. Also submit five truth tables you build for exercises in 8.3.1, clearly saying how they show you what they show. This is not an optional exercise. If you do not submit five truth tables, you get a zero for this week’s work. Why? Because I know from experience that if you can’t draw these tables, you have not learned anything about truth table construction and analysis. Use the “Table” function in Word (in “Insert”: choose 5 lines if you are drawing a 4 line table, 9 if you are doing an 8 line table, 17 if you are doing a 16 line table, so the statements can go along the top line).

C) Find or make up good clear examples of both versions of DeMorgan’s Theorem, and write them out both symbolically and in English.

Week Three Paper & Assignment is due in the designated Canvas Discussion forum by Noon Saturday, June 6; your response to another student’s paper is due by Noon Sunday.

QUIZZES By midnight Saturday you must complete Canvas Quizzes 7, 8, and 9. Each of these (except 9) has a “retake” option. The quizzes are available all week until midnight of June 13; don’t wait until Saturday to do them. Quiz 9 reviews some basic concepts from the first chapters of the course. Some students have reacted to it in the past as a set of “trick questions.” I disagree; the intent is not to trick you, but to make you focus on something you are probably (incorrectly) taking for granted that you understand.

Week 4 June 7-June 13. From Propositional Logic to Predicate Logic. Read all of Chapter 9, and Chapter 10.1.

By Monday, you should be doing exercises in 9.4.2. By Wednesday, you should be doing proofs using Conditional and Indirect Proof (9.5) Make use of the chatroom to get some help, or arrange a skype conversation. Post discussion of homework exercises.

6 By Thursday you should be translating exercises into the notation of Predicate Logic (Chapter 10.1). Post discussion of homework exercises.

Assignment 4:

A) In 9.4.3 (Yet More Proof Exercises) do the fill-in-the-blank sheet and submit discussion of your answers to the homework discussion forum. Then go to the Natural Deduction Exercises links farther down the page. Read the example proofs in II, then do any four of the eight in section III. In the link Natural Deduction Exercises2, write and submit two proofs (to the homework discussion forum) from section V and two from section VI (your choice). This is not optional. Not submitting your efforts (and your questions) at proofs will get you a zero for this week’s work. Why? Because learning how to do proofs is a matter of practice and working through being puzzled and frustrated; it is not enough to follow it on the board or in a powerpoint. Important: Do not work unproductively on this material: it can be quite challenging. When you have trouble knowing what to do, don’t hesitate to send me an email or post a comment about it in the Discussion forum. Don’t drive yourself crazy or bang your head against the proverbial wall –it is normal to ask for some help in order to tune in to this.

In Homework Discussion Week Four, you will find an exercise on determining Assumptions for Conditional and Indirect Proofs. Submit this with your paper.

B) Find or construct your own examples of three arguments that can be represented in Predicate Logic (you can even use examples you find in Chapter 7 or Chapter 8 exercise sets).

Week Four Paper & Assignment is due in the designated Canvas Discussion forum by Noon Saturday, June 13; your response to another student’s paper is due by Noon Sunday.

QUIZZES By Saturday, you must complete Canvas Quizzes 10 and 11. Each of these has a “retake” option. The quizzes are available all week until midnight of June 20; don’t wait until Saturday to do them.

Week 5 June 14-June 20. Predicate Logic. Finish reading Chapter 10.

Monday you should be doing simple proofs using UI, EI, UG, and EG (10.2) Post Discussion of exercises. Submit your effort to write a proof for the following:

7 1. (x) (Tx >Vx) / (x) ((Tx . Gx) > Vx)

Tuesday, you should be working with CQ (10.3). Post discussion of exercises.

QUIZZES By midnight Wednesday, July 22, you must complete Canvas Quizzes 12 and 13. Each of these has a “retake” option. The quizzes are available as of Sunday; don’t wait until Wednesday to do them.

Saturday 25. Final exam. Arrange a pick-up time with me, and return the exam within 2 ½ hours.

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WORK FOR THE COURSE:

I. Four 3-4 page papers, posted to Canvas. Posted with the pledge that the paper was written prior to reading any papers posted by others. Post these papers as Word Documents. Due Date: Saturday Noon.

Paper must discuss: a) a review of the material since the last paper: what we’ve studied: presented in your words –no cutting, pasting, or quoting from any text; b) what significance it has; why it is worthwhile knowing; again, in your words; c) what you found the most difficult aspect of learning or mastering it; d) what steps you took to learn/ master the material (which/ how many exercises you did, what problems you encountered); e) what questions you want to hear discussion of; f) In addition to the paper reviewing the material, you must submit the Assignment for the week. This part is worth 8 of the 25 points, unless otherwise noted. In weeks 2, 3 and 4, you get no credit for the paper if you do not turn in the Assignment.

These papers are 25 points each, 40% of your overall grade. Grades on the papers will reflect: being on time (if any problem with Canvas, make sure to submit by email to prof), flawlessly written (no misspellings, no grammatical mistakes, etc.), and minimal 4 full pages in length (double-spaced, TimesNewRoman 12 pt; absolute maximum length: 5 pages), addressing all six areas, a-f above; being in your own words, clear, insightful, exhibiting good understanding. Lacking any of these, it is unlikely to be better than a 17 (a C). 8 II. Four 2-page responses to the papers of others. You must respond specifically to points made in the paper of another student, posted to Canvas by noon Sunday (i.e., within 24 hours of the due date of your own paper). You might offer what you think is a correction of something she said, you might try to answer a question he raises, you might suggest a clarification of a point, you might disagree about something; you cannot just say something empty like “good job,” or “well done,” however.

These are 10 points each. These responses have to be constructive and genuine (as well as technically flawless). If they are merely perfunctory and on time (or not technically flawless), you get a 5.

III. 27 on-line quizzes. These function somewhat the way homework would, in that they force you to keep moving and keep up with the material. Each quiz has an “A” version, a re-take. They are 5 points each, and provide an extra-points option if you take them all, which can only help your final grade. Unfortunately, these are multiple-choice style quizzes (inevitably), so they test you in a passive mode rather than an active mode.

IV. Homework. Actually doing homework (not just taking the quizzes) is necessary for an active grasp, a genuine understanding. Twice each week (totaling 9 times; just once in the final week) you are expected to post discussion of your work on Exercises offered in the relevant sections of the relevant chapters; you might also post discussion of a quiz question. This will not be graded per se, but it will be expected and checked. If you do not do it, there will be a penalty: minus 1 point each time (2 pts per week or 9 pts total by the end of the course). This can be brief –it is not meant to be busy work, but to make you show that you are doing homework. Like other work, it must be on time and proofread to receive credit.

IV. Monday quizzes. Each Monday you go to the Monday Quizzes folder in Canvas to pick up the week’s “active” quiz. From the time you open it, you have a maximum of 30 minutes to submit it back to me via email (make sure your name is in the filename when you attach it). These are 15 points each.

V. Exams. In the third week, and on the final exam day, you will have access to an exam that must be returned within 2 ½ hours. It will consist of exercises using all the techniques learned, and essay questions about terminology and principles. The Honor Pledge will be required, and the slightest indication of a breach of it will bring a charge. 50 pts each. (On the final exam, exercises requiring CQ (Change of Quantifier) will count as Extra Credit.)

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Course Work and Grades:

9 100 points: Four 4-5 page papers with weekly assignments

40 points: Four 2-page responses to another’s papers

60 points: Four 20 minute Monday quizzes

100 points: Two 50-point exams

100 pts: Twenty-seven on-line quizzes (ten questions each). There are two versions of each, so take one, learn from your mistakes (ask questions!), then take the other. (These are 5 points each, so you could earn as many as 135 points if you take them all and ace them all.)

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400 points possible

Course grades will be assigned in terms of total points earned by the end of the course:

Course grades: A 360-400 B 320-359 C 280-319 D 240-279

Extra credit: You may turn in up to 3 Argument Analyses in weeks 2-5 for extra credit (worth 3 points each). These must meet the following criteria: a) Each must be from a newspaper no more than three days old when you turn it in. (It can be from the internet if it is from an internet edition of a newspaper, in which case, provide the url.) b) On the Argument Analysis form, you must follow all instructions completely. Copy the worksheet below and paste it into a Word document.

------Argument Analysis Worksheet AA # ______Date: ___

Before beginning this exercise, make sure that the passage you have identified is really an argument, and not something else! This optional assignment gives you extra points if you analyze an argument well (for up to 3 points each time, for up to three times total); but if you submit a non-argument, thinking that it is an argument, it will cost you 2 points! (Why? Because in that case you have not properly mastered the assignment, and so shouldn’t be doing it, and you will have wasted my time!)

10 To submit this, fill out this worksheet and submit it by email to [email protected]. No more than one will be accepted per week. Note: You may not use the same examples on this exercise as you use on the end-of-the-week Assignment.

A. Copy the argument in exactly the wording in which you found it:

Example: (delete this and fill in your own)

As evidence of Bush’s left agenda, Viguerie cites Bush’s signing of the No Child Left Behind bill, his wildly expensive prescription-drug-benefits bill, soaring farm subsidies, steel tariffs, higher federal deficits, plus “nation-building on a scale never attempted before.”

State the Source and Date: Free Lance Star Aug 25, 2007. p. A8. Alexander Cockburn, “Rove: Doesn’t Rhyme with ‘Love’ on Left or Right.” If it's on line, provide the url.

B. Analysis. Rewrite the argument as a series of discrete, numbered propositions that best capture the sense of the original. You do not need to repeat the exact wording of the original –very often it is best to “step back” from it and recast it in new words to make it as clear as possible. There is no set number of premises you have to generate.

Premise 1: Bush signed the No Child Left Behind act and prescription-drug-benefit bills.

Premise 2: Bush endorsed soaring farm subsidies, steel tariffs, etc

Premise 3: Anyone who endorses these sorts of things is a leftist.

Conclusion 4 : Therefore Bush is a leftist

C. Is it an Inductive or a Deductive argument? Why do you say so? What pattern does it fit? Is it strong or weak? Why? Is it valid or invalid? Why? Is it a fallacy we’ve studied? If so, explicate how it commits the fallacy.

Deductive. It can be seen as an Argument from definition, because this arguer is claiming that you can’t promote these sorts of programs without being a leftist –he’s equating support for them with being leftist, as though this were a matter of definition.

But since it’s not at all clear that that is what “being a leftist” means or entails, this deductive argument is not valid. Since it’s not valid, it’s also not sound (since validity is one of two conditions that must be met for soundness).