Phil. 160 Symbolic Logic II

PHIL. 160
Deductive Logic II

Spring Semester 2012

Prof. Dowden

Catalog description: Further study of deductive logic. Topics include: principles of inference for quantified predicate logic; connectives; quantifiers; relations; sets; modality; properties of formal logical systems, e.g. consistency and completeness; and interpretations of deductive systems in mathematics, science, and ordinary language. Prerequisite: MATH 031, or PHIL 060, or instructor permission. 3 units.

Textbook: Logic for Philosophy, by Theodore Sider, Oxford University Press, 2010, ISBN 978-0-19-957558-9. In addition to this book, there will be some webpages and class handouts that you should consider to be required reading. The book is available at the CSUS Hornet Bookstore, but here is a website that compares book prices at many online bookstores: http://www.bookase.com. Here is a list of typos in the Sider text.

Grades: Your grade will be determined by four homework assignments (each 14%), a midterm exam (20%), and a comprehensive final exam (24%). Homework questions will be handed out a week in advance of the due date. Class attendance is optional, but you are responsible for material covered in class that isn't in the book.

Due dates:

Homework 1: Feb. 9 (wk 3)

Homework 2: Mar. 1 (wk 6)

Midterm: Mar. 15 (wk 8)

Homework 3: Apr. 12 (wk 11)

Homework 4: May 3 (wk 14)

For homeworks, you are responsible for any announced changes to questions that are made after the homework is handed out but before it is due, even if you didn't attend class the day the change was made.

Late assignments, and make-up assignments: I realize that during your college career you occasionally may be unable to complete an assignment on time. If this happens in our course, contact me as soon as you are able. If you promptly provide me with a good reason for missing a test or homework assignment (illness, accident, ...), then I'll use your grade on the final exam as your missing grade. There will be no make-up tests nor make-up homework. I do accept late homework with a grade penalty of one-third of a letter grade per 24-hour period beginning at the class time the assignment is due. Examples. If you turn in the assignment a few hours after it is due, then your A becomes an A-. Instead, if you turn in the same assignment 30 hours late, then your A becomes a B+. Weekends count. No late work will be accepted after the answer sheet has been handed out (normally this will be at the next class meeting), nor after the answers are discussed in class, even if you weren't in class that day.

Add-Drop: To add the course, try to do so by using the CMS system. If the course is full, then see me about signing up on the waiting list. To drop the course during the first two weeks, use the CMS system. No paperwork is required. After the first two weeks, it is harder to drop, and a departmental form is required, the "Petition to Add/Drop After Deadline." As with any university course, make sure you are dropped officially (by CMS or by the instructor or department secretary); don't simply walk away into the ozone or else you will get a "WU" grade for the course, which is counted as an "F" in computing your GPA (grade point average).

Course Description: Our course presupposes you have had a first course in deductive logic, such as Phil. 60, or have learned this material on your own. The first month will contain a review of Phil. 60, but also will enrich that material. Our goal is to appreciate what can be done with deductive symbolic logic and what can't be done. That is, we will explore the scope and limits of logic rather than its depth in one particular area.

You might think of our symbolic deductive logic as a machine for detecting argument goodness. In our course, we will not only use the machine but also study what it can and cannot do, and whether it can be revised to do other things. For example, can it show that "Obama's father is working in his office" logically implies "Someone's father is working"? Can it represent the claim that most things are massive, and the claim that there exist infinitely many numbers?

Our course will survey the deep results yielded by the developments in symbolic deductive logic. These results concern the surprising extent to which human knowledge can not be freed of contradictions, to what extent our knowledge can be expressed without loss of content inside of a formal language, and what our civilization has learned from the field of symbolic deductive logic about the limits to what people can know and about the limits of what computers can do, the major results here being the Unsolvability of the Halting Problem, the Church-Turing Undecidability Theorem for Predicate Calculus, Tarki's Undefinability Theorem for Truth in Predicate Calculus, and Gödel's Theorems about the Incompleteness of Arithmetic.
We will begin our course with a review of Phil. 60 while providing a rigorous development of both propositional logic (also called statement logic and sentential logic) and predicate logic (also called first-order logic and quantificational logic and predicate calculus). Then we will learn about their applications, extensions, meta-theory, and non-classical variants.
A good analogy for our course is that learning symbolic logic is much like learning a computer language. The big difference is that in symbolic logic the focus is on using the formal language to assess argument correctness rather than on getting a computing machine to follow its intended program. To continue with the analogy, in our course we will not be focusing on doing actual programming so much as learning the capabilities of the computer.

Topics and reading assignments: Click here.

Relevance of logic to other subjects: If you are curious about the relevance of deductive logic to other subjects such as philosophy, mathematics, and computer science, then click on the ticket below:

Student outcome goals: The hope is that by the end of the semester you will have achieved the following goals:

Be able to reason more effectively.

Be able to describe the scope of deductive logic, that is, what it can be used to do; and be able to describe the limits of logic, that is, what it cannot be used to do.

Build on the abilities you learned in Phil. 60 to recognize when an English argument is capable of being analyzed with symbolic deductive techniques, to translate a symbolic deductive argument into English and vice versa, to determine if a symbolic deductive sentence is logically true, to determine if a set of symbolic deductive sentences is consistent, to assess the logical correctness or incorrectness of arguments using the techniques of symbolic deductive logic, to create proofs in both predicate logic and propositional logic, and be capable of creating and analyzing rigorous proofs using the methods of classical symbolic deductive logic.

Know the important extensions of these logics to non-standard logics such as modal logic, deontic logic, free logic, many-valued logic, second-order logic, many-sorted logic, fuzzy logic, and paraconsistent logic.

Understand Hilbert's program and the process of formally axiomatizing a theory.

Be familiar with the most important meta-theoretic results such as Gödel's Theorems, the Church-Turing Undecidability Theorem, Tarski's Undefinability Theorem, and the Löwenheim-Skolem Theorem.

Be able to say how symbolic deductive logic has deepened our knowledge of some important philosophical issues, and how it has led to new issues of its own.

Know the extent to which human knowledge can be freed of contradictions.

Be able to say what our civilization has learned from the field of symbolic deductive logic about the limits to what people can know and about the limits of what computers can do.

Laptops, cell phones: Photographing or recording during class is not allowed without permission of the instructor. During class, turn off your cellphone. Your computers may be used only for note taking, and not for browsing the web, reading emails, or other activities unrelated to the class. If you use a computer during class, then please sit in the back of the room or in a side row so that your monitor's screen won't distract other students.

Testing protocol: For in-class exams (tests), you may use your books and notes but not your computer or cellphone.

Disabilities: If you have a documented disability and require accommodation or assistance with assignments, tests, attendance, note taking, and so forth, then please see me early in the semester so that appropriate arrangements can be made to ensure your full participation in class. Also, you are encouraged to contact the Services for Students with Disabilities (Lassen Hall) for additional information regarding services that might be available to you.

Honesty: See the University's policy on honesty and cheating. A student tutorial on how not to plagiarize is available online from our library.

Food: Except for water, please do not eat or drink during class. You are welcome to leave class anytime if the need arises.

Professor: My office is in Mendocino Hall 3022, and my weekly office hours are TuTh 9:30-10:30 and 12:00-12:30. Feel free to stop by at any of those times, or to call. If those hours are inconvenient for you, then I can arrange an appointment for an alternative time. You may send me e-mail at dowden@csus.edu or call my office at 278-7384 or the Philosophy Department Office at 278-6424. The fastest way to contact me is by email. My personal web page is at http://www.csus.edu/indiv/d/dowdenb/index.htm

Prof. Dowden

Study tips: As you read an assignment, it is helpful first to skim the assignment to get some sense of what’s ahead. Look at how it is organized and what cues, if any, the author provides to signify main ideas (section titles, bold face, italics, full capitals, etc.). Make your own notes as you read. Stop every twenty minutes to look back over what you’ve read and try to summarize the key ideas for yourself. This periodic pausing and reviewing will help you maintain your concentration, process the information more deeply, and retain it longer. Notice connections between one section and another. You’ll be given sample questions now and then to help guide your studying for future assignments, but the homework and test questions in our course will often require you to apply your knowledge to new questions not specifically discussed in class nor in the book. This ability to use your knowledge in new situations requires study activities different from memorizing. You goal is to improve your skills, rather than to memorize information. Think of the textbook more as a math book than a novel, so re-reading is important.

Contact me at dowden@csus.edu if you'd like more information about our course.

PHILOSOPHY DEPARTMENT / PROF. DOWDEN / CSUS
Updated: January 23, 2012


PHIL. 160 Deductive Logic II Spring Semester 2012 Prof. Dowden


	Catalog description: Further study of deductive logic. Topics include: principles of inference for quantified predicate logic; connectives; quantifiers; relations; sets; modality; properties of formal logical systems, e.g. consistency and completeness; and interpretations of deductive systems in mathematics, science, and ordinary language. Prerequisite: MATH 031, or PHIL 060, or instructor permission. 3 units. Textbook: Logic for Philosophy, by Theodore Sider, Oxford University Press, 2010, ISBN 978-0-19-957558-9. In addition to this book, there will be some webpages and class handouts that you should consider to be required reading. The book is available at the CSUS Hornet Bookstore, but here is a website that compares book prices at many online bookstores: http://www.bookase.com. Here is a list of typos in the Sider text. Grades: Your grade will be determined by four homework assignments (each 14%), a midterm exam (20%), and a comprehensive final exam (24%). Homework questions will be handed out a week in advance of the due date. Class attendance is optional, but you are responsible for material covered in class that isn't in the book. Due dates: Homework 1: Feb. 9 (wk 3) Homework 2: Mar. 1 (wk 6) Midterm: Mar. 15 (wk 8) Homework 3: Apr. 12 (wk 11) Homework 4: May 3 (wk 14) For homeworks, you are responsible for any announced changes to questions that are made after the homework is handed out but before it is due, even if you didn't attend class the day the change was made. Late assignments, and make-up assignments: I realize that during your college career you occasionally may be unable to complete an assignment on time. If this happens in our course, contact me as soon as you are able. If you promptly provide me with a good reason for missing a test or homework assignment (illness, accident, ...), then I'll use your grade on the final exam as your missing grade. There will be no make-up tests nor make-up homework. I do accept late homework with a grade penalty of one-third of a letter grade per 24-hour period beginning at the class time the assignment is due. Examples. If you turn in the assignment a few hours after it is due, then your A becomes an A-. Instead, if you turn in the same assignment 30 hours late, then your A becomes a B+. Weekends count. No late work will be accepted after the answer sheet has been handed out (normally this will be at the next class meeting), nor after the answers are discussed in class, even if you weren't in class that day. Add-Drop: To add the course, try to do so by using the CMS system. If the course is full, then see me about signing up on the waiting list. To drop the course during the first two weeks, use the CMS system. No paperwork is required. After the first two weeks, it is harder to drop, and a departmental form is required, the "Petition to Add/Drop After Deadline." As with any university course, make sure you are dropped officially (by CMS or by the instructor or department secretary); don't simply walk away into the ozone or else you will get a "WU" grade for the course, which is counted as an "F" in computing your GPA (grade point average). Course Description: Our course presupposes you have had a first course in deductive logic, such as Phil. 60, or have learned this material on your own. The first month will contain a review of Phil. 60, but also will enrich that material. Our goal is to appreciate what can be done with deductive symbolic logic and what can't be done. That is, we will explore the scope and limits of logic rather than its depth in one particular area. You might think of our symbolic deductive logic as a machine for detecting argument goodness. In our course, we will not only use the machine but also study what it can and cannot do, and whether it can be revised to do other things. For example, can it show that "Obama's father is working in his office" logically implies "Someone's father is working"? Can it represent the claim that most things are massive, and the claim that there exist infinitely many numbers? Our course will survey the deep results yielded by the developments in symbolic deductive logic. These results concern the surprising extent to which human knowledge can not be freed of contradictions, to what extent our knowledge can be expressed without loss of content inside of a formal language, and what our civilization has learned from the field of symbolic deductive logic about the limits to what people can know and about the limits of what computers can do, the major results here being the Unsolvability of the Halting Problem, the Church-Turing Undecidability Theorem for Predicate Calculus, Tarki's Undefinability Theorem for Truth in Predicate Calculus, and Gödel's Theorems about the Incompleteness of Arithmetic. We will begin our course with a review of Phil. 60 while providing a rigorous development of both propositional logic (also called statement logic and sentential logic) and predicate logic (also called first-order logic and quantificational logic and predicate calculus). Then we will learn about their applications, extensions, meta-theory, and non-classical variants. A good analogy for our course is that learning symbolic logic is much like learning a computer language. The big difference is that in symbolic logic the focus is on using the formal language to assess argument correctness rather than on getting a computing machine to follow its intended program. To continue with the analogy, in our course we will not be focusing on doing actual programming so much as learning the capabilities of the computer. Topics and reading assignments: Click here. Relevance of logic to other subjects: If you are curious about the relevance of deductive logic to other subjects such as philosophy, mathematics, and computer science, then click on the ticket below: Student outcome goals: The hope is that by the end of the semester you will have achieved the following goals: Be able to reason more effectively. Be able to describe the scope of deductive logic, that is, what it can be used to do; and be able to describe the limits of logic, that is, what it cannot be used to do. Build on the abilities you learned in Phil. 60 to recognize when an English argument is capable of being analyzed with symbolic deductive techniques, to translate a symbolic deductive argument into English and vice versa, to determine if a symbolic deductive sentence is logically true, to determine if a set of symbolic deductive sentences is consistent, to assess the logical correctness or incorrectness of arguments using the techniques of symbolic deductive logic, to create proofs in both predicate logic and propositional logic, and be capable of creating and analyzing rigorous proofs using the methods of classical symbolic deductive logic. Know the important extensions of these logics to non-standard logics such as modal logic, deontic logic, free logic, many-valued logic, second-order logic, many-sorted logic, fuzzy logic, and paraconsistent logic. Understand Hilbert's program and the process of formally axiomatizing a theory. Be familiar with the most important meta-theoretic results such as Gödel's Theorems, the Church-Turing Undecidability Theorem, Tarski's Undefinability Theorem, and the Löwenheim-Skolem Theorem. Be able to say how symbolic deductive logic has deepened our knowledge of some important philosophical issues, and how it has led to new issues of its own. Know the extent to which human knowledge can be freed of contradictions. Be able to say what our civilization has learned from the field of symbolic deductive logic about the limits to what people can know and about the limits of what computers can do. Laptops, cell phones: Photographing or recording during class is not allowed without permission of the instructor. During class, turn off your cellphone. Your computers may be used only for note taking, and not for browsing the web, reading emails, or other activities unrelated to the class. If you use a computer during class, then please sit in the back of the room or in a side row so that your monitor's screen won't distract other students. Testing protocol: For in-class exams (tests), you may use your books and notes but not your computer or cellphone. Disabilities: If you have a documented disability and require accommodation or assistance with assignments, tests, attendance, note taking, and so forth, then please see me early in the semester so that appropriate arrangements can be made to ensure your full participation in class. Also, you are encouraged to contact the Services for Students with Disabilities (Lassen Hall) for additional information regarding services that might be available to you. Honesty: See the University's policy on honesty and cheating. A student tutorial on how not to plagiarize is available online from our library. Food: Except for water, please do not eat or drink during class. You are welcome to leave class anytime if the need arises. Professor: My office is in Mendocino Hall 3022, and my weekly office hours are TuTh 9:30-10:30 and 12:00-12:30. Feel free to stop by at any of those times, or to call. If those hours are inconvenient for you, then I can arrange an appointment for an alternative time. You may send me e-mail at dowden@csus.edu or call my office at 278-7384 or the Philosophy Department Office at 278-6424. The fastest way to contact me is by email. My personal web page is at http://www.csus.edu/indiv/d/dowdenb/index.htm Prof. Dowden Study tips: As you read an assignment, it is helpful first to skim the assignment to get some sense of what’s ahead. Look at how it is organized and what cues, if any, the author provides to signify main ideas (section titles, bold face, italics, full capitals, etc.). Make your own notes as you read. Stop every twenty minutes to look back over what you’ve read and try to summarize the key ideas for yourself. This periodic pausing and reviewing will help you maintain your concentration, process the information more deeply, and retain it longer. Notice connections between one section and another. You’ll be given sample questions now and then to help guide your studying for future assignments, but the homework and test questions in our course will often require you to apply your knowledge to new questions not specifically discussed in class nor in the book. This ability to use your knowledge in new situations requires study activities different from memorizing. You goal is to improve your skills, rather than to memorize information. Think of the textbook more as a math book than a novel, so re-reading is important. Contact me at dowden@csus.edu if you'd like more information about our course. PHILOSOPHY DEPARTMENT / PROF. DOWDEN / CSUS Updated: January 23, 2012