Philosophy 120
Introduction to Logic

Course Introduction

Welcome

In this course, you will learn the basics of logic. By doing so, you will develop the ability to identify, understand, and evaluate arguments relating to any number of issues, ideas, and viewpoints. This is a vitally important set of skills, for they are a crucial part of being able to "think for yourself." You will also learn the rudiments of a simple formal language and learn how such a language can facilitate the evaluation of reasoning.

Overview

The lessons that make up this course are carefully coordinated with the required textbook. Each lesson covers one or two chapters and supplements the textbook by emphasizing key points and providing additional clarification and examples where needed. See below, A Suggested Study Routine, for how best to integrate the text and the lessons.

Prerequisites

This course is intended to be introductory, so no previous familiarity with logic is required or assumed. All you need for this course is an ordinary amount of intelligence and a willingness to work at a steady pace. Since much of the work will be done on a computer, it will help if you are comfortable with computers.

Caveat Emptor: In this course, you will be learning and working in a new, artificial language (called FOL for short). Like earning fluency in any language, time and regular practice will be required to learn FOL. Also, because the course is computer-based, a moderate level of computer literacy is recommended. It is easy to learn how to use the software package and there is very rarely a technical problem. However, a student may find it more difficult to understand the content and what the viable answers are for the assignment if he or she is not fully comfortable working in a computer-based learning system. Please keep these factors in mind as you begin this course.

In addition to the technology requirements and skills noted in the Online Student Handbook, for this course you will need to use word processing software and the software that comes with LPL.

About the Online Environment

Your online course offers several advantages to the traditional classroom, including the comprehensive Online Student Handbook, the ability to communicate electronically with students and with your instructor, and links to a rich array of online resources.

Online Student Handbook

This handbook answers questions about your online learning course, such as how to purchase your text, schedule an exam, obtain a transcript, and get technical help if you need it. The handbook also provides additional resources, such as how to order books or journals from the library and how to study for an online course.

Communication with Your Instructor and Student Peers

• Online Discussion Forums, designed by the University of Washington award winning Catalyst team, allow you to communicate with other currently enrolled students and with your instructor. We encourage you to use the forum to exchange ideas, resources, and comments about your course work with other students in this course. This unstructured forum is monitored by your instructor.
• You can use e-mail to ask me a question or preferably, post your question in the forum so that all students can benefit from the answer. I will reply on the same forum.

Online Resources

As an online student, you have access to a wealth of Web resources compiled to provide fast, easy access to information that supports your online learning experience. Organized by subjects, Online Resources link you to sites with help for writing and research, study skills, language learning, and library reference materials. All links have been assessed for credibility and reliability, and they are regularly monitored to ensure their usability.

Course Objectives

The primary purpose of this course is to introduce you to a field of study known as formal logic or symbolic logic. Logic in this sense is concerned with the question of whether, if all in a given set of reasons are true, they will support the claims that they are alleged to support.

Take an example: Suppose your friend Sonja says, "The deficit will be reduced only if interest rates go up. Interest rates are declining. Therefore, the deficit will not go down."

Formal logic deals with the structure of reasoning such as we find here (and much more besides) and seeks to provide us with tools and techniques to use in understanding whether they are good or bad examples of reasoning. (What "good" and "bad" mean in this context is something we will look at in detail later.) How can we tell, for example, when a given statement "follows from" the reasons given for it? What makes reasoning "logical" or "illogical"?

Our approach to these questions will be the following: First, we will develop a simple artificial language. (You have probably already noticed, if you have thumbed through the required textbook, that some of the text and most of the exercises in the book are written in a language that looks unfamiliar to you. You will also have noticed that this language contains special symbols that are probably also unfamiliar.) Then we will raise our questions (concerning "good" and "bad" reasoning) about the sentences of this language. We'll be able to define in a very precise way what it is for one statement to follow from other statements—what it is for an argument to be valid. We'll also be able to translate English sentences and arguments into our artificial language, and thereby be able to tell when arguments expressed in English are formally valid.

Required Materials

Textbook

The required textbook (with software package included) is:

Barwise, Jon, and John Etchemendy. 2002. Language, Proof, and Logic. Stanford: CSLI Publications. ISBN 157586374X.

Each copy of the Language, Proof, and Logic (LPL) text-and-software package comes with a unique ID number. You will be using this number when you submit solutions for evaluation, and it will be permanently linked to your name and e-mail address. Since this number is nontransferable, you need to be sure that you have purchased an unused copy of LPL. (If your ID number has been used before by someone else, you will be unable to use it.) You can ensure that you get a new copy of LPL by purchasing it from the University Book Store.

I have chosen Language, Proof, and Logic (LPL) for several reasons. First, it is one that is commonly used in the on-campus, face-to-face sections of this course. You will be getting the same training in logic as those who take the course on campus. Second, LPL's unique features make it especially attractive to use in a distance learning format. Finally, LPL is thorough and rigorous without being really difficult to understand on your own. We will cover most of the first 14 chapters.

Technology

LPL comes with a suite of software programs that you will be using to solve problems and to submit your solutions for evaluation. Because the feedback you get electronically after submitting problems is nearly instantaneous, these programs are excellent instructional tools. The book is also filled with exercises designed to help you learn and to enable you to test your own progress. In addition, one of the programs (Tarski's World) enhances your understanding of important logical concepts by allowing you to play an entertaining game against the computer. (Don't worry—even though your computer is supremely logical, it is still possible for you to win the game!)

Installing the Software

Before you start on this course, you will need to install on your computer the software that comes with LPL. For details, look at pages 1–3 of the Software Manual. Here's a quick summary.

You must have an Internet connection. You can use either a PC (Windows NT/98/ME/2000/XP) or a Mac (MacOS 8.5-8.6, MacOS 9.x, MacOS X 10.1-10.3 and Classic environment). The faster the computer the better, since two of the programs (Fitch and Boole) employ Java-emulation and so can be quite slow on a slow machine.

You are advised to load the programs and exercises onto your hard drive, rather than running them from the CD, if at all possible, since this will substantially speed up their operation. When you run the installation program on the CD, it creates a folder labeled "LPL Software," which contains subfolders for each of the programs (and one for "extras"). In doing many of the exercises, you will begin by opening an exercise file from the relevant subfolder, then modify or add to it, and finally save the result. In doing this, it is important to save the modified file to a different folder, both to make it easier to submit the results when necessary and to preserve the original file unaltered in case you make a mistake and need to try again.

When saving, be sure to use the Save As command rather than the Save command, to avoid inadvertently overwriting the original file. It is valuable to spend some time exploring and experimenting with the computer programs. They contain various shortcuts and alternative ways of doing things that you may find helpful. Pay attention especially to the keyboard shortcuts in Tarski's World and Fitch, which for some reason often seem to work faster than the pull-down menu alternatives.

Why Study an Artificial Language?

Artificial languages are invented, and have precise and easily articulated rules. In contrast, "natural" languages—like English or Spanish —have developed over time and have rules that are much more difficult to set out and understand. This makes artificial languages very simple and easy to learn, since their rules are so simple and straightforward. (It will take you only a few minutes to learn the rules for constructing well-formed sentences of the artificial language we will be using; compare that with how long it takes to learn the rules of English grammar!)

For another thing, our language (again, unlike natural languages) is ambiguity-free. That is, each sentence of our language has a precise meaning. This feature has disadvantages, of course, since such sentences cannot have the shades and nuances of meaning that make natural languages so interesting and subtle. But it has one great advantage: it is capable of a kind of precision that cannot be easily achieved in a natural language. This will make our questions more precise and will enable us to understand better the logical relationships we are examining.

Finally, artificial languages are actually quite common. They are widely used in the symbolic sciences (mathematics, linguistics, computer science, philosophy, artificial intelligence, etc.). If you have ever studied a computer programming language (such as Java or C++) you have already been exposed to an artificial language that is very similar to the one we will be studying and using.

The advantages of using an artificial language will become even more apparent in the next section.

Why Study Logic?

In everyday life we naturally rely on our logical "good sense" to tell us if someone is reasoning well or badly. This is easy to do if the reasoning goes like this:

All humans are mortal.
George is a human.
Therefore, George is mortal.

Anyone can see that the "logic" here is correct. It isn't even too hard to evaluate Sonja's reasoning about the deficit. Both of these are "good" logically in the sense that the reasons we are given support the conclusion. (Again, much more about this later). But the task of evaluating reasoning becomes much harder as the reasons and conclusions increase in complexity. When this happens, our native logical abilities often aren't enough. Consider, for instance, these examples of reasoning:

Only superstars like Magic Johnson can be effective spokespersons for the AIDS cause. But some athletes other than basketball players are superstars like Magic. So athletes other than basketball players can also be effective in the fight against AIDS.

Everything that Pete won at the carnival must be junk. I know this because Pete won everything that Bob won, and all the stuff Bob won is junk.

It may not seem so, but these are both examples of "illogical" thinking: the conclusions of these arguments do not follow from the reasons or data given in their support, even though it certainly seems as though they might. (You will learn later the techniques and rules of formal logic that will allow you to see why there is bad reasoning in these cases.) To get around the problem of our limited intuition, logicians have resorted to a different strategy: What would happen if we tried to study the logical structure of reasoning, of good and bad patterns of reasoning, within the context of an artificial language? The answer is that we get much further in the study of logic.

The idea, then, is that we will be taking statements (as in the examples above) and translating them into a rigorous, artificial language. This "language" will enable us to ignore the logically irrelevant features of those statements to reveal their underlying logical structure.

Here's another way of looking at the same point. Each of us, without really thinking about it at all, relies upon certain patterns of reasoning that are valid and "logical" no matter what the specific details. Here's an example:

If USC beat Oregon State, then Arizona will go to the Rose Bowl.
USC did beat Oregon State.
Therefore, Arizona will go to the Rose Bowl.

This is a good argument because the third statement logically follows from the first two statements. That is, there is no way that the first two statements can both be true and the third one false. But there is a deeper point here. The pattern of reasoning that is at stake here goes like this:

If A then B
A
Therefore, B

If you think about it for a moment, you'll see that any argument with this basic pattern or format has got to be good from a logical standpoint—or, as we will say, valid. That is, if the first two statements are true, then the third must also be true. And there are many more patterns of reasoning that are also valid. The artificial language that you will learn as part of your study of logic is designed to help you recognize these valid logical patterns.

Real World Applications

When beginning logic students learn that they will be studying an artificial language, they sometimes leap to the conclusion that what they are studying will have no "real world" applications. This is not true! Consider the following examples:

• You buy the expensive brand of whole grain bread because the wrapper says "No preservatives added." I have spoken to many beginning logic students who say that this means the bread has no preservatives. Not so! A logically experienced person can see the problem here right away: "no preservatives added"—to what? To the preservatives that were already there? How many is that? "No preservatives added"—since when? Since last Tuesday when they finished putting them all in?
• The box of detergent I want to buy says that it is "organic" and adds that "Only organic products are chemical-free." This means that all organic products, like this detergent, are chemical-free, right? Wrong! Logic tells us that it really only means that if a product is chemical-free, then it is organic. But that leaves open the possibility that a product—and this product in particular—may be organic and not chemical-free. Logic comes in handy when shopping! Next time you go to the store, be on guard!
• The following paragraph appears in the editorial section of a weekly business magazine:
  

  No company made it into the Fortune 500 this year unless it had annual sales of more than $700 million. Officials at Stanton Corp. should thus be enraged at the unfairness of those who set the Fortune ratings: for Stanton had sales of over $700 million this year and it is not one of the Fortune 500.

  Should Stanton be upset? No. A logically aware person will see that the first sentence states only one requirement for being in the Fortune 500; it doesn't state that this is the only requirement. (Whatever else is required, Stanton apparently doesn't have it.)
• You want to go to a concert, so you call up the local ticket outlet. You get a recording that says: "All of the tickets will not be sold until Friday." What does that mean? Does it mean that no tickets will be available until Friday? Or does it mean that some tickets are available now, and some will still be available on Friday? Or does it mean that by the time Friday is over, all of the tickets will have been sold? Understanding logical relationships can help you pinpoint when someone else is being vague or unclear.

So much for my pitch for logic. It doesn't have to make you as dull as Mr. Spock from the original Star Trek. (After all, he didn't have to shop in today's supermarkets!)

Organization of the Course

This course is divided into eleven lessons, two of which are exam-preparatory lessons. Each of the remaining nine lessons contains the following:

• assigned readings from the text
• a list of lesson objectives
• a list of key terms from the lesson and readings
• lesson commentary to accompany and enhance your understanding of the assigned readings in the textbook
• a graded assignment consisting of exercises taken from the textbook

This is an asynchronous course, meaning that you start when you are ready after registration. The following table shows the correspondence between the lessons in this course, the assignments and exams, and the chapters of the textbook.

About the Assignments

There are nine assignments (problem sets), one for each lesson other than the exam prep lessons. The exercises have been selected from those in LPL. Most exercises are worth 2 points each; the more difficult ones (marked with a star *) are worth 3 points; the two-star ** problems are worth 4 points. Partial credit will be awarded for solutions that are substantially correct but contain some minor errors. Point totals for individual assignments vary (depending on the number of problems assigned), but the total of all the assignments is 300 points (out of 600 points for the entire course). So half of your grade is determined by how well you do on these assignments.

Examinations

There will be two examinations: a midterm after the first four lessons, and a final at the end of the course. Although the final is not comprehensive (that is, it will cover only material from the second part of the course) it will still presuppose a working knowledge of the material from the first part of the course. The midterm is worth 100 points and final is worth 200. Exam format will be multiple choice—more detail about the exams can be found in Lessons Five and Eleven.

Submitting Assignments

For instructions on how to submit assignments, please see the "About Your Instructor" page on the syllabus.

Evaluation/Grading

There are 600 points possible: 300 for assignments, and 300 for examinations. Grades will be based on the following scale

Additional tenths of a grade-point are based on 7.5 point increments. For example, since a score of 480 is 15 points, or two increments, higher than 465, it is worth an additional .2, for a grade of 3.2.

Study Suggestions

Logic can be fun and exciting. The software you'll be using in this course makes it even more fun for most students. For myself, I find that I feel great when I can finally solve a problem I have been grappling with for half an hour! If you want to study and learn logic in a way that is rewarding, here are some handy guidelines for you to follow.

Take Your Time

This is really important. You will have a lot of material to absorb in the coming weeks and months, and you need to let it sink in. When we begin working on proofs, for example, you will be manipulating formulas using a number of logical rules. This requires that you learn the rules thoroughly and become comfortable working with them—and this takes time.

Don't Get Overly Frustrated

You are almost certain (unless you are an undiscovered logical genius) to encounter frustrations from time to time: problems you can't see how to solve, rules you don't understand, and so on. This is natural; it happens to nearly every logic student. So recognize this and allow yourself to be frustrated. But don't let the frustrations take over. If you have reread a section of the text twice and just don't get it, set the book aside and pick it up again tomorrow; chances are things will make more sense after a break. This piece of advice relates closely to the next two.

Reread Each Textbook Assignment

Again, unless you are a natural whiz at logic, not everything is going to sink in the first time you read a chapter of your textbook. I strongly urge you to make it a habit to read each assigned part at least twice; three times won't hurt. As you will see, the reading assignments are not that long, certainly not by comparison with what you might be reading for other courses. They are, however, compact (after all, they were written by a couple of logicians!). So rereading is almost always beneficial.

Don't Procrastinate

Experience has shown me that those students who consistently do best are those who don't wait until the last minute and then try to cram two or three chapters' worth of material into one study session. If you try to cram in too much at one time, there's a good chance that none of it will stick. Use the calendar included on the syllabus to plan your time.

Set Up a Study Routine

The content of this course is cumulative: each chapter you read and each assignment you do will build on your knowledge of the ideas covered in the previous lessons. Therefore, it is vital to establish good study habits soon. Students who complete this course in a single (ten-week) quarter usually spend about 15 hours a week on the course. If you cannot spend that much time weekly, you will probably need more than ten weeks to complete the course. In any case, I recommend that you set aside at least four two-hour time blocks per week for reading the assigned portions of the text and online lesson commentary and working on your exercises and assignments. I know this may sound like a lot when you are working too, but there is a critical mass of time that you simply must devote to the course if you want to do well.

Practice, Practice, Practice!

The best way to learn logic (and to assure yourself that you are learning it) is to work on problems, solve them, and have your solutions checked for accuracy. LPL is loaded with many more exercises than I have assigned; do as many of them as you can until you are satisfied that you've learned the corresponding material. (Remember, the Grade Grinder is there 24/7 to check your work!) There are also supplementary problems on the course Web site for you to try your hand at. When I mention one of them in the lesson commentary, it's a good idea to work along with me as I take you through the solution. Or, try working ahead to see how your solution compares to mine.

When All Else Fails . . .

If—after dutifully following all of my guidelines—you still feel yourself at a loss, please e-mail your instructor and say what you need help with. Very often a simple hint is all that it takes to get things back on track.

A Suggested Study Routine

To get the maximum benefit from the course, I recommend that you make the following procedure part of your study routine for each lesson:

• Read the lesson's learning objectives first. This will give you a quick run-down on what you will be learning.
• Read the assigned material in LPL.
• Whenever you reach a group of exercises in LPL, do at least one or two to confirm that you understand the material. These may include some assigned problems, so in this way you can complete some of the assignment by the time you get to the end of the lesson.
• Read the rest of the online lesson commentary for the lesson you are working on. This will emphasize the most important concepts in the assigned reading from the textbook, and will provide extra practice on any difficult material.
• Do the You try it exercises in LPL—all of them!—and any other problems that I suggest in the online lesson commentary. Always do the best you can to solve the problems before you look up the answers on the course Web site.
• Do the assigned exercises and (for electronically graded ones) submit them to the Grade Grinder. Choose the Just Me option. Read the Grade Grinder's response and, if necessary, fix any mistakes you've made and resubmit.
• When you are satisfied with your assignment, submit it again to the Grade Grinder, this time choosing the Instructor Too option.

Academic Integrity

Students enrolled in this course are required to follow the University of Washington guidelines for academic honesty. Please review the "Academic Honesty Policy" section of the Online Learning Student Handbook.

About the Course Developer

S. Marc Cohen
Professor of Philosophy

I joined the faculty of the Department of Philosophy at the University of Washington as an Associate Professor in 1973, and became a Professor in 1979. I served as Chair of the department from 1981–86. My major research interest is in ancient Greek philosophy, an area in which I offer several courses at both undergraduate and graduate levels. I also teach courses in logic and philosophy of language. I have taught previously at Indiana University, Rutgers University, the University of California at Berkeley, and the University of Minnesota.

Student Information Sheet

Your instructor would like to know about you. Please fill out the Student Information Sheet—the link can be found on the course syllabus.

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