Phil. 60 Symbolic Logic I

Phil. 60

Symbolic Logic I

Philosophy 60

Fall Semester 2008

Prof. Dowden

Catalog description: Introduction to deductive logic. Topics include: basic concepts of deductive logic; techniques of formal proof in propositional and predicate logic. 3 units.

More description: Logic is the investigation of general principles about what follows from what in reasoning. Our particular course emphasizes the use of symbols, as opposed to English words, in order to represent and evaluate pieces of reasoning. So, a symbolic logic course is much more like a mathematics course than is any other philosophy course. Symbolic logic forces reasoning to be explicit and rigorous in order to get definite answers to questions about whether one statement follows from other statements or whether some statements are inconsistent with each other.

Prerequisites: No other college course needs to be taken before enrolling in Philosophy 60, but you must have passed the ELM (math) exam. Philosophy 60 satisfies your GE requirements for Area B5.

Textbook: Elements of Deductive Inference: An Introduction to Symbolic Logic by Joseph Bessie and Stuart Glennan. There are used books available from other places besides the CSUS bookstore; try online. Here's what the cover looks like.

New books contain a CD with software called "Inference Engine." We won't be using the software, so you can confidently buy a used copy of the book. There will be a few additional short articles handed out in class throughout the semester. The overall plan is to read this book more or less in order up through about section 8.3 while skipping all the material on truth trees. Bring your textbook to class each time. My function is not to "speak" the book to you, but to focus the discussion onto the most significant points, to enrich the material covered in the book, and to clarify it. If the book isn't clear, ask me to explain it. If I'm not clear, ask me to explain in some other way. Don't be shy about asking questions; it's the path to understanding.

Grades: Your grade will be determined by four homework assignments (each 11%), two tests (each 14%), and a comprehensive final examination (28%). Each homework assignment is due at the beginning of class the week after it is handed out. Homework assignments will include some questions from the Law School Admissions Tests. Here is a schedule of when assignments are handed out and when they are due:

Sept. 11 Homework 1 handed out

Sept. 18 Homework 1 due

Sept. 30 Homework 2 handed out

Oct. 7 Homework 2 due

Oct. 16 Test 1

Oct. 23 Homework 3 handed out

Oct. 30 Homework 3 due

Nov. 13 Test 2

Nov. 20 Homework 4 handed out

Dec. 4 Homework 4 due

Dec. 18 Final exam 12:45-2:45

For in-class tests, you may use your books and notes but not your laptop.

Professor: My office is in Mendocino Hall, room 3022, and my weekly office hours will be announced in class on the first day. 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

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

Be able to recognize when an English argument is capable of being analyzed with symbolic techniques.

Be able to translate a symbolic argument into English and vice versa.

Be able to determine if a symbolic sentence is logically true, or logically false, or neither.

Be able to determine if a set of symbolic sentences is consistent or, instead, inconsistent.

Be able to assess the validity or invalidity of arguments using the techniques of symbolic logic.

Be able to create proofs in both predicate logic and statement logic.
Be able to reason more effectively.

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. When there is room, students on the waiting list will be added in this order: seniors graduating this semester, then all others by random selection. 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 "U" grade for the course, which is counted as an "F" in computing your GPA (grade point average).

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 provide me with a good reason for missing a test or homework assignment (illness, accident, etc.), 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 (often 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.

Laptops and cell phones: No photographing, recording or text messaging during class is allowed without permission of the instructor.

Disabilities: If you have a documented disability and require accommodation or assistance with assignments, tests, attendance, note taking, etc., 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.

Plagiarism: A student tutorial on how not to plagiarize is available online from our library at http://library.csus.edu/content2.asp?pageID=357

Food: Except for water, please don't eat and drink during class. You're welcome to leave class anytime temporarily if the need arises.

Course Description: The techniques of symbolic logic provide the paradigm method of precisely displaying knowledge (about anything) and of precisely drawing only legitimate inferences from that knowledge. The field gets its name because, unlike informal logic, symbolic logic uses symbols in place of English words. When the logician translates English sentences and arguments into logical symbols, this makes everything very explicit and precise. The process is somewhat like a computer programmer translating informal commands into code for a computer program, or a mathematician translating a word problem into a set of algebra equations. The imprecision is removed during the translation. So, our course reveals what is at the basis of our civilization's notion of rigorous reasoning.

We will translate sentences from our natural language (English) into a formal language, a language of symbols. Because arguments are composed of sentences, we can translate whole arguments into the formal language. Then we can use special symbolic techniques to test the quality of those arguments.

Using these techniques will make you better able to distinguish a sound argument from a near miss. You will become more logical not only in analyzing arguments and claims but also in generating them. In addition, you will discover what it means to prove something with complete rigor in which nothing is left hidden in the background. That is, you will see what a real proof is.

The course will focus on learning two different symbolic logics: statement logic and predicate logic. Statement logic is also called sentential logic, propositional logic and sentence logic. It is a formalism that is useful for analyzing certain arguments (deductions) that crucially use the words "and," "or," "not," and "implies." The words connect statements together; so that's why the logic is called "statement logic." Predicate logic is more complicated and more powerful. It can break sentences down into their subjects and predicates. This logic is used to represent relationships among objects and to represent the quantity of those objects. We will be learning techniques for symbolizing the subjects and predicates of sentences and for assessing the quality of arguments using those sentences.

Logic is concerned primarily with arguments forms, and only secondarily with arguments, so these assessment mechanisms will be applied to the form rather than the content of the argument.

Symbolic logic had its beginning in ideas promoted by ancient Greek philosophers, especially Aristotle and the Stoics. But most of their reasoning with and about logic was carried out without using a formalism, that is, without a symbol system. In 1879, symbolic logic as we will be studying it was developed in Germany by Gottlob Frege. He constructed the first propositional logic and the first predicate logic. A few years later, but independently, the Italian mathematician Giuseppe Peano also invented predicate logic.

Our course also will pay some attention to the relevance of symbolic logic to three fields: philosophy, computer science, and mathematics. Click here to learn more about this.

What is logic? Philosophers disagree on the answer to this question. Is it about the human mind, or about the world itself, or about how languages work? Aristotle, the father of logic, was never clear about this. The German philosopher Kant (1724-1804) said logic is descriptive of mental processes; it describes how we do think and perhaps how we must think, when we make inferences. But the American philosopher Peirce (1839-1914) disagreed and said logic is prescriptive of mental processes; it prescribes how we ought to think. The German philosopher Frege (1848-1925) disagreed with both Kant and Peirce.

Topics and Outline of the Course: The plan is to work through the book in order and cover the following topics. The date when a certain topic will be covered isn't definite, but the order is. The dates of homework assignments and tests are definite.

Week 1
consistency and contradiction
argument detection and evaluation
Week 2
translating in and out of the formalism
Week 3
truth tables and validity
Week 4
truth tables and validity
elementary proofs
Week 5
proofs using one-way arguments forms
Week 6
proofs using two-way inference rules
Week 7
conditional proofs
indirect proofs
Week 8
proving theorems, adding valid forms as new inference rules
Applications to electricity: series-parallel switching circuits (switching algebra)
Week 9
Applications to electronics: combinational and sequential circuits using logic gates
predicate logic symbolization
quantifiers
Week 10
interpretations (models)
expansions of quantifiers
demonstrating invalidity
Week 11
proofs in predicate logic
Week 12
proofs in predicate logic
symbolization with relational predicates, overlapping quantifiers
Week 13
invalidity & consistency in relational predicate logic
Week 14
advanced symbolization, the identity symbol
Week 15
review for final exam

First week's reading assignment: Read this discussion of implicit assumptions, then chapter 1 in your textbook.

We will be reading the first eight chapters of the textbook, except that we will skip sections 3.10, 3.11, 5.9, and chapter 6. Also, we will read chapter 5 in this order: 5.1, 5.2, 5.3, 5.6, 5.7, 5.4, 5.5, 5.8.

Please contact me at dowden@csus.edu if you would like more information about the course.

PROF. DOWDEN / PHILOSOPHY DEPT.
COLLEGE OF ARTS AND LETTERS / CSUS

The web address of this file is
http://www.csus.edu/indiv/d/dowdenb/60/f08/syl-f08.htm
updated: Jan. 16, 2009

Phil. 60
Symbolic Logic I Philosophy 60 Fall Semester 2008 Prof. Dowden


	Catalog description: Introduction to deductive logic. Topics include: basic concepts of deductive logic; techniques of formal proof in propositional and predicate logic. 3 units. More description: Logic is the investigation of general principles about what follows from what in reasoning. Our particular course emphasizes the use of symbols, as opposed to English words, in order to represent and evaluate pieces of reasoning. So, a symbolic logic course is much more like a mathematics course than is any other philosophy course. Symbolic logic forces reasoning to be explicit and rigorous in order to get definite answers to questions about whether one statement follows from other statements or whether some statements are inconsistent with each other. Prerequisites: No other college course needs to be taken before enrolling in Philosophy 60, but you must have passed the ELM (math) exam. Philosophy 60 satisfies your GE requirements for Area B5. Textbook: Elements of Deductive Inference: An Introduction to Symbolic Logic by Joseph Bessie and Stuart Glennan. There are used books available from other places besides the CSUS bookstore; try online. Here's what the cover looks like. New books contain a CD with software called "Inference Engine." We won't be using the software, so you can confidently buy a used copy of the book. There will be a few additional short articles handed out in class throughout the semester. The overall plan is to read this book more or less in order up through about section 8.3 while skipping all the material on truth trees. Bring your textbook to class each time. My function is not to "speak" the book to you, but to focus the discussion onto the most significant points, to enrich the material covered in the book, and to clarify it. If the book isn't clear, ask me to explain it. If I'm not clear, ask me to explain in some other way. Don't be shy about asking questions; it's the path to understanding. Grades: Your grade will be determined by four homework assignments (each 11%), two tests (each 14%), and a comprehensive final examination (28%). Each homework assignment is due at the beginning of class the week after it is handed out. Homework assignments will include some questions from the Law School Admissions Tests. Here is a schedule of when assignments are handed out and when they are due: Sept. 11 Homework 1 handed out Sept. 18 Homework 1 due Sept. 30 Homework 2 handed out Oct. 7 Homework 2 due Oct. 16 Test 1 Oct. 23 Homework 3 handed out Oct. 30 Homework 3 due Nov. 13 Test 2 Nov. 20 Homework 4 handed out Dec. 4 Homework 4 due Dec. 18 Final exam 12:45-2:45 For in-class tests, you may use your books and notes but not your laptop. Professor: My office is in Mendocino Hall, room 3022, and my weekly office hours will be announced in class on the first day. 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 Student outcome goals: The hope is that by the end of the semester you will have achieved the following goals: Be able to recognize when an English argument is capable of being analyzed with symbolic techniques. Be able to translate a symbolic argument into English and vice versa. Be able to determine if a symbolic sentence is logically true, or logically false, or neither. Be able to determine if a set of symbolic sentences is consistent or, instead, inconsistent. Be able to assess the validity or invalidity of arguments using the techniques of symbolic logic. Be able to create proofs in both predicate logic and statement logic. Be able to reason more effectively. 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. When there is room, students on the waiting list will be added in this order: seniors graduating this semester, then all others by random selection. 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 "U" grade for the course, which is counted as an "F" in computing your GPA (grade point average). 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 provide me with a good reason for missing a test or homework assignment (illness, accident, etc.), 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 (often 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. Laptops and cell phones: No photographing, recording or text messaging during class is allowed without permission of the instructor. Disabilities: If you have a documented disability and require accommodation or assistance with assignments, tests, attendance, note taking, etc., 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. Plagiarism: A student tutorial on how not to plagiarize is available online from our library at http://library.csus.edu/content2.asp?pageID=357 Food: Except for water, please don't eat and drink during class. You're welcome to leave class anytime temporarily if the need arises. Course Description: The techniques of symbolic logic provide the paradigm method of precisely displaying knowledge (about anything) and of precisely drawing only legitimate inferences from that knowledge. The field gets its name because, unlike informal logic, symbolic logic uses symbols in place of English words. When the logician translates English sentences and arguments into logical symbols, this makes everything very explicit and precise. The process is somewhat like a computer programmer translating informal commands into code for a computer program, or a mathematician translating a word problem into a set of algebra equations. The imprecision is removed during the translation. So, our course reveals what is at the basis of our civilization's notion of rigorous reasoning. We will translate sentences from our natural language (English) into a formal language, a language of symbols. Because arguments are composed of sentences, we can translate whole arguments into the formal language. Then we can use special symbolic techniques to test the quality of those arguments. Using these techniques will make you better able to distinguish a sound argument from a near miss. You will become more logical not only in analyzing arguments and claims but also in generating them. In addition, you will discover what it means to prove something with complete rigor in which nothing is left hidden in the background. That is, you will see what a real proof is. The course will focus on learning two different symbolic logics: statement logic and predicate logic. Statement logic is also called sentential logic, propositional logic and sentence logic. It is a formalism that is useful for analyzing certain arguments (deductions) that crucially use the words "and," "or," "not," and "implies." The words connect statements together; so that's why the logic is called "statement logic." Predicate logic is more complicated and more powerful. It can break sentences down into their subjects and predicates. This logic is used to represent relationships among objects and to represent the quantity of those objects. We will be learning techniques for symbolizing the subjects and predicates of sentences and for assessing the quality of arguments using those sentences. Logic is concerned primarily with arguments forms, and only secondarily with arguments, so these assessment mechanisms will be applied to the form rather than the content of the argument. Symbolic logic had its beginning in ideas promoted by ancient Greek philosophers, especially Aristotle and the Stoics. But most of their reasoning with and about logic was carried out without using a formalism, that is, without a symbol system. In 1879, symbolic logic as we will be studying it was developed in Germany by Gottlob Frege. He constructed the first propositional logic and the first predicate logic. A few years later, but independently, the Italian mathematician Giuseppe Peano also invented predicate logic. Our course also will pay some attention to the relevance of symbolic logic to three fields: philosophy, computer science, and mathematics. Click here to learn more about this. What is logic? Philosophers disagree on the answer to this question. Is it about the human mind, or about the world itself, or about how languages work? Aristotle, the father of logic, was never clear about this. The German philosopher Kant (1724-1804) said logic is descriptive of mental processes; it describes how we do think and perhaps how we must think, when we make inferences. But the American philosopher Peirce (1839-1914) disagreed and said logic is prescriptive of mental processes; it prescribes how we ought to think. The German philosopher Frege (1848-1925) disagreed with both Kant and Peirce. Topics and Outline of the Course: The plan is to work through the book in order and cover the following topics. The date when a certain topic will be covered isn't definite, but the order is. The dates of homework assignments and tests are definite. Week 1 consistency and contradiction argument detection and evaluation Week 2 translating in and out of the formalism Week 3 truth tables and validity Week 4 truth tables and validity elementary proofs Week 5 proofs using one-way arguments forms Week 6 proofs using two-way inference rules Week 7 conditional proofs indirect proofs Week 8 proving theorems, adding valid forms as new inference rules Applications to electricity: series-parallel switching circuits (switching algebra) Week 9 Applications to electronics: combinational and sequential circuits using logic gates predicate logic symbolization quantifiers Week 10 interpretations (models) expansions of quantifiers demonstrating invalidity Week 11 proofs in predicate logic Week 12 proofs in predicate logic symbolization with relational predicates, overlapping quantifiers Week 13 invalidity & consistency in relational predicate logic Week 14 advanced symbolization, the identity symbol Week 15 review for final exam First week's reading assignment: Read this discussion of implicit assumptions, then chapter 1 in your textbook. We will be reading the first eight chapters of the textbook, except that we will skip sections 3.10, 3.11, 5.9, and chapter 6. Also, we will read chapter 5 in this order: 5.1, 5.2, 5.3, 5.6, 5.7, 5.4, 5.5, 5.8. Please contact me at dowden@csus.edu if you would like more information about the course. PROF. DOWDEN / PHILOSOPHY DEPT. COLLEGE OF ARTS AND LETTERS / CSUS The web address of this file is http://www.csus.edu/indiv/d/dowdenb/60/f08/syl-f08.htm updated: Jan. 16, 2009