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PHIL/MATH 330: Symbolic Logic

"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic." --Lewis Carroll

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Fall Semester, 2012

Dr. Scott Kimbrough

Office Hours: M/W 1:00-2:00, T/R 1:15-2:15, or by appointment

Office: Council 121

Phone: 256-7118

Direct questions and comments to my e-mail.

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Last updated 11/9/12

Resources and Announcements

• Reading assignments
• Grades are posted on Blackboard
• Final exam time: Friday, December 14th from 8:00-11:00am

Course Description

Logic, according to Gottlob Frege, the founder of modern symbolic logic, is the science of thought. By this, he did not mean that logic studies how we actually do think -- psychology does that. Rather, he meant logic is the most general science, the study of rules of correct thinking that govern every discipline. No matter what you're thinking about, you have to obey the laws of logic if you want to avoid error. Following Frege, this course studies rules of formal deductive reasoning. We will study validity and invalidity of argument forms, consistency, and translation between the formal system and ordinary language. We will study truth-functional logic (the logic of sentences related by 'and', 'or', 'not', 'if...then', and 'if and only if') and predicate logic (the logic of sentences containing terms such as 'all', 'every', and 'some').

Required Book

Hausman, Kahane & Tidman. Logic and Philosophy: A Modern Introduction, 12th Edition. Thomson Wadsworth Publishing. 2012.

Course Requirements

• Attendance: Since logic is a cumulative affair, it is critical to keep up: once behind, few students manage to recover. As such, attendance at lectures is strongly encouraged.
• Homework: Ungraded homework will be assigned. Because practice is the only way to gain familiarity with the logical systems we will be studying -- and the only way to learn strategies for approaching various types of logic problems -- doing the homework is essential to getting a good grade even though it does not figure formally into your average.
• Quizzes (15%): Brief quizzes will be given most Wednesdays. The purpose of these quizzes is to insure that you are keeping up with the material. The quizzes cover terminology and problems similar to those in previously assigned homework. Your high and low quiz grades will not be counted towards your average.
• Exams (3 exams, each worth 20%): An exam will be given on (approximately) the following dates: 9/21, 10/15, and 11/12. These dates are subject to change depending on class progress. The exams will be open book and open notes, but long enough that relying heavily on these materials will be counterproductive.
• Final Exam (25%): The final exam is comprehensive. As with the previous exams, books and notes are allowed.

Reading assignments

• 8/31 Arguments (1-16)
• 9/5 Truth-functions (19-30)
• 9/7 Disjunctions (31-34)
• 9/10 Material conditionals (35-42)
• 9/12 Translation practice (43-52)
• 9/15 Truth tables (55-70)
• 9/17-9/19 Truth table test for equivalence and validity (71-88)
• 9/21 First test
• 9/24-9/26 Implicational rules (90-106)
• 9/28 Equivalence rules (107-114)
• 10/1-10/5 Proofs with equivalence rules (115-126)
• 10/8 Conditional proofs (127-135)
• 10/10 Indirect proof (136-142)
• 10/12 Zero premise deductions (143-146)
• 10/15 Proof practice
• 10/17 Second test
• 10/19 Predicates and quantifiers (169-180)
• 10/22 Translation (180-185)
• 10/24 Expansions (185-194)
• 10/26-10/31 Interpretations (chapter 8: 195-203)
• 11/2 Class canceled
• 11/5 Predicate logic proofs (204-212)
• 11/7 Restrictions on UG and EI (213-224)
• 11/9 Quantifier Negation (224-229)
• 11/14 Third exam
• 11/16 Relational predicate logic translation (230-234)
• 11/20 Expansions and more translation (234-244)
• 11/26 Relational interpretations (244-246)
• 11/28 Relational proofs (246-255)
• 11/30 Identity (291-298)
• 12/3 Philosophical problems (309-316)

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