Math 468 Symbolic Logic
Text: Language, Proof and Logic, by Jon Barwise and John Etchemendy, second edition
Instructor: Yuanqian Chen
Office: Marcus White 112
Phone: 832-2858 (office) 676-9511 (home)
e-mail: [email protected]
Office Hour: Mondays, Wednesdays, and Fridays: 3:00-4:30pm;
Mondays and Wednesdays: 6:10-7:10pm;
or by appointment. Please feel free to stop by anytime, an appointment is not necessary
Course Description and Goals:
Introduce some of the most important concepts and tools in logic. We will learn to distinguish a
valid reasoning from an invalid reasoning. We will learn a new language: the language of firstorder logic and will use the language to understand the notion of logical consequence.
Topic Covered:
Part I. Propositional Logic
1 Atomic Sentences
1.1
Individual constants
1.2
Predicate symbols
1.3
Atomic sentences
1.4
General first-order languages
1.5
Function symbols
2 The Logic of Atomic Sentences
2.1
Valid and sound arguments
2.2
Methods of Proof
2.3
Formal proofs
2.4
Constructing Proofs in Fitch
2.5
Demonstrating nonconsequence
3 The Boolean Connectives
3.1
Negation symbol: 
3.2
Conjunction symbol: 
3.3
Disjunction symbol: 
3.4
Remarks about the game
3.5
Ambiguity and parentheses
3.6
Equivalent way of saying things
3.7
Translation
4 The Logic of Boolean Connectives
4.1
Tautologies and logical truth
4.2
Logical and tautological equivalence
4.3
Logical and tautological consequence
4.4
Tautological consequence in Fitch
4.5
Pushing negation around
4.6
Conjunctive and disjunctive normal form
5 Methods of Proof for Boolean Logic
5.1
Valid inference steps
5.2
Proof by cases
5.3
Indirect proof: proof by contradiction
5.4
Arguments with inconsistent premises
6 Formal Proofs and Boolean Logic
6.1
Conjunction rules
6.2
Disjunction rules
6.3
Negation rules
6.4
The proper use of subproofs
6.5
Strategy and tactics
6.6
Proofs without premises
7 Conditionals
7.1
Material conditional symbol:
7.2
Biconditional symbols: 
7.3
Conversational implicature
7.4
Truth-functional completeness
8 The Logic of Conditionals
8.1
Informal methods of proof
8.2
Formal rules of proof for  and 
Part II Quantifiers
9 Introduction to Quantification
9.1
Variables and atomic wiffs
9.2
The quantifier symbols:  and 
9.3
Wiffs and sentences
9.4
Semantics for the quantifiers
9.5
The four Aristotelian forms
9.6
Translating complex noun phrases
9.7
Quantifiers and function symbols
10 The Logic of Quantifiers
10.1 Tautologies and quantification
10.2 First-order validity and consequence
10.3 First-order equivalences and DeMorgan’s laws
11 Multiple Quantifiers
11.1 Multiple uses of a single quantifier
11.2 Mixed quantifiers
11.3 The step-by-step methods of translation
11.4 Paraphrasing English
11.5 Ambiguity and context sensitivity
Grading:
Two Tests (75 minutes, 100 points each)
Final Exam (120 minutes, 150 points)
If your total points are:
315--350, you will get at least A-.
280--314, you will get at least B-.
245--279, you will get at least C-.
210--239, you will get at least D-.
This is exactly how your grade will be calculated:
315-324: A324-350: A
280-289: B
290-299: B
300-314: B+
245-254: C
255-264: C
275-279: C+
210-219: D
220-229: D
230-239: D+
Test Dates:
First test: Wednesday, February 22,
Second test: Wednesday, April 5,
Final exam will be on Monday, May 8, 7:45-9:45pm
Withdrawal Policy:
200
150
------350
Monday, February 6: Last day to drop full semester course without "W"
Monday, April 17: Last day to withdraw from the courses without approval. "W" will be entered;
After April 17, students need permission of instructor and department chairperson to withdraw
from a course.
In the event of a weather emergency with required curtailment or cancellation of classes, listen to
WTIC (1080AM) or call (860) 832-3333 for the ‘general snow message’.
Please contact me privately to discuss your specific needs if you believe you need course
accommodations based on the impact of a disability, medical condition, or if you have
emergency medical information to share. I will need a copy of the accommodation letter from
Student Disability Services in order to arrange your class accommodations.