Introduction to Logic

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Class Time and Location
Monday & Wednesday, 5:30-6:45pm – FN 2.202
Office Location and Hours:
JO 4.120, MW 4-5pm
Contact Policy
I will be available to speak to you for several minutes before and after class each week. I will be fully engaged during class, with plenty of time for questions and discussion. I will be prompt to office hours each week, and will announce any cancellations well in advance. I will answer my phone during office hours unless I am with another student. I will happily make appointments before of after class, or by the website. Generally, I will not respond to emails or phone messages. The only reason to email me would be: (1) to inform me of a genuine emergency situation before or during an exam that will prevent you from being at the exam, or (2) to remind me to do something I promised to do, such as post bonus readings.

Formal logic is the formal study of reasoning, inference, and proof. This course will focus on deductive logic, including formal analysis of statements and arguments, sentential and quantified logics, formal semantics and models, and logical proofs. At the end of the course, we will also briefly examine the logic of statistical inference and the logic of scientific reasoning.

General Core Area 020 Mathematics

Courses in this category focus on quantitative literacy in logic, patterns, and relationships. Courses involve the understanding of key mathematical concepts and the application of appropriate quantitative tools to everyday experience.

Core Curriculum Objectives:

Critical Thinking (CT)
to include creative thinking, innovation, inquiry, and analysis, evaluation, and synthesis of information
Communication (COM)
to include effective development, interpretation, and expression of ideas through written, oral, and visual communication
Empirical and Quantitative Skills (EQS)
to include the manipulation and analysis of numerical data or observable facts resulting in informed conclusions

Learning Outcomes

Upon successful completion of this course, students will:

  1. Determine the logical structure of English arguments by identifying premises and conclusions. (COM, CT)
  2. Understand basic concepts in logic, such as truth functionality, validity, soundness, counter-examples, tautology, self-contradiction, logical equivalence, logical contradictoriness, and logical consistency. (CT, EQS)
  3. Translate English statements into Sentential Logic (propositional notation). (COM, CT)
  4. Translate English statements into Quantified Logic (predicate notation) (COM, CT)
  5. Determine the validity of symbolic logical arguments using (a) truth tables, (b) models, and (c) natural deduction. (COM, CT, EQS)

Textbook

P.D. Magnus, forall x: An Introduction to Formal Logic (Order) (Download)

Schedule of Readings and Assignments

Changes may be made and will be announced in class and reflected on the course website.

Date Topic (Readings) Practice Exercises / Notes
M 8/21 Welcome & Introduction
W 8/23 No Class Office Hours Cancelled
M 8/28 Basic Concepts in Logic (Ch 1) 1.A-D
W 8/30 Sentential Logic (Ch 2.1-2.2)  2.A-C
M 9/4  Labor Day Holiday, No Class  Office Hours Cancelled
W 9/6  Sentential Logic (2.3-2.4)  2.D-F
M 9/11  Sentential Logic Continued  2.G-H
W 9/13  Truth Tables (Ch 3)  3.A-F
M 9/18  Review
W 9/20  FIRST EXAM
M 9/25  Quantified Logic (4.1-4.4)  4.A-B
W 9/27  Quantified Logic Continued  4.C-D
M 10/2  Quantified Logic Continued  4.E-G
W 10/4  Quantified Logic (4.5)  4.H-I
M 10/9  Quantified Logic (4.6)  4.J-L
W 10/11  Review
M 10/16  SECOND EXAM
W 10/18  Formal Semantics (5.1-5.2)  5.A-C
M 10/23  Models (5.3-5.4) 5.D-G
W 10/25  Models (5.5)  5.H-J
M 10/30  Review
W 11/1  THIRD EXAM
M 11/6  Proofs (6.1)  6.A
W 11/8  Derived Rules, Replacement (6.2-6.3)  6.B-C
M 11/13  Proof strategy (6.6–6.7)  6.D-E
W 11/15  Continued  6.F-G
M 11/20 – Fall Break, No Class – W 11/22
M 11/27  Proofs in Quantified Logic (6.4)  6.H-J
W 11/29  Continued  6.K-M
M 12/4  Proofs & Semantics (6.8-6.9)  6.N-R
W 12/6  Final Review  6.S-U
W 12/13 FINAL EXAM 5-7:45PM

Grades and Assignments

Assignment Types

  1. Practice Exercises (61 Parts)
  2. Midterm Exams
  3. Final Exam
  4. Engagement Points
    a. Participation (1-3 points)
    b. Logic Puzzles (2 points)
    c. Textbook Corrections (1 point)
    d. Complete 6 extra Practice Exercise Parts (1 point)

Grading Policy

Grades will be determined as follows:

  • A:
    • Satisfactory Grade on all 3 Midterm Exams
    • Satisfactory Grade on all parts of Final Exam
    • Completion of 50 Practice Exercise Parts
    • Assures satisfactory completion of all Learning Outcomes
  • B:
    • Satisfactory Grade on First and Second Midterm Exam
    • Satisfactory Grade on Parts 1-2 of Final Exam
    • Completion of 40 Practice Exercise Parts
    • Assures satisfactory completion of Outcomes 1, 2, 3, 4, 5a, 5b
  • C:
    • Satisfactory Grade on First Midterm Exam
    • Satisfactory Grade on Part 1 of Final Exam
    • Completion of 30 Practice Exercise Parts
    • Assures satisfactory completion of Outcomes 1, 2, 3, 5a
  • D:
    • 50% or Better on all 3 Midterm Exams
    • 50% or Better on all parts of Final Exam
    • Completion of 20 Practice Exercise Parts
    • Poor performance on all Learning Outcomes
  • F:
    • Failure to satisfy the criteria for grades A-D.

Clarifications:

  • “Satisfactory” is 85% (or B-level) correctness.
  • “Completion” of Practice Exercises means reasonable effort
  • Add plus (+) to your base grade if you earn at least 6 engagement points.
  • Add a minus (-) to your base grade if x > 3, where x = A + (T + M)/2
  • A: Absences
  • T: Tardies (more than 5 minutes late)
  • M: Missed Practice Exercise Parts for your grade level.
  • If you have a (+) and a (-) they cancel out. If a (-) cancels your (+), you can still gain another (+), and vice versa.
  • During each midterm exam period, you will have the opportunity to take the midterm or retake the previous midterm exam(s). During the final exam period, you will have the opportunity to take the final or retake any of the midterms.

More Resources

Use the following resources as study aids and sources for additional practice problems. Keep in mind that not all textbooks will use the exact same conventions or notations we do, so you’ll have to do a little translating.

Course Policies