Phil. 60
Symbolic Logic I Philosophy 60 Spring Semester 2006 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: A Concise Introduction to Logic, by Hurley, special edition with "Professor Bradley Dowden" on the cover.  There will be a few additional articles handed out in class throughout the semester, but the plan is to read this book more or less in order.  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 five homework assignments (each 10%), two tests (each 14%), and a comprehensive final examination (22%). Although the assignments in our course are more like those in a mathematics course than like those in other philosophy courses, the assignments will contain occasional questions whose answers will be evaluated in part for grammar, style, clarity and proper handling of the terms, phrases, and concepts related to the course.  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 Test.  Here is a schedule of when assignments are handed out and when they are due: Jan. 31 Homework 1 handed out Feb. 7   Homework 1 due Feb. 14 Homework 2 handed out Feb. 21 Homework 2 due Mar. 2   Test 1 Mar. 9   Homework 3 handed out Mar. 23 Homework 3 due Mar. 30 Homework 4 handed out Apr. 6    Homework 4 due Apr. 18  Test 2 Apr. 27  Homework 5 handed out May 4    Homework 5 due May 16  Final exam 12:45 p.m.   Professor: My office is in Mendocino Hall, room 3022, and my weekly office hours are TR 10:30-12:00. 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   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 build and use truth tables for assessing the validity or invalidity of arguments in sentence logic. Be able to create proofs in both predicate logic and sentence logic. Be able to reason more effectively. Add-Drop: To add the course, try to do so by using the Casper 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 Casper 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 Casper 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 an assignment (illness, accident, etc.), then I'll use your grade on the final exam as your missing grade. For homework assignments, there is 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. There will be no make-up tests nor make-up homework. 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. 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 algebraic equations. The imprecision is removed during the translation.  So, our course reveals what is at the basis of our civilization's notion of rigorous thinking. 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: propositional logic and predicate logic. Propositional logic is also called sentential logic, statement logic and sentence logic. It is a formalism that is useful for analyzing certain arguments (deductions) that turn especially on the use of the key words "and," "or," "not," and "implies" that we use to connect one sentence to another. 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 1979, 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?  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. Week 1 intro to 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 proofs Week 5 proofs [one-way arguments forms] Week 6 proofs [two-way inference rules] Week 7 conditional proofs indirect proofs Week 8 proving theorems, adding valid forms as new inference rules predicate logic symbolization Week 9 quantifiers expansions of quantifiers Week 10 interpretations (models) proving invalidity Week 11 proofs in predicate logic Week 12 proofs in predicate logic symbolization with relational predicates, overlapping quantifiers Week 13 advanced symbolization Week 14 symbolizing, times, someone, somewhere invalidity & consistency in relational predicate logic Week 15 review for final exam   First week's reading assignment: Read the first four sections of chapter 1.  Here are the important ideas and terminology covered there: argument causal inference claim cogent argument conclusion conditionals deduction indicators inductive inference invalid deductive argument premise proposition sound argument statement strong vs. weak induction syllogism total evidence requirement valid deductive argument   Please contact me 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/s06/syl-s06.htm updated: Apr. 8, 2006