Introduction to Symbolic Logic

Table of Contents

1. Unit I

2. Unit II

3. Unit III

4. Unit IV

5. Works Cited

1. Introduction to Course

Homework— N/A

2. Validity

Handout— Validity and Soundness Handout

Homework— The Logic Book (6e), Chapter 1 Glossary

3. Categorical Logic 1.0

Homework— Categorical Logic 1.0 Homework

Advanced Material—

• Book Chapter: Merrie Bergmann, James H. Moor, Jack Nelson, and James Moor, The Logic Book, Chapter 1

4. The Square of Opposition

Homework— Immediate Inferences Homework

5. Categorical Logic 2.0

Homework— Categorical Logic 2.0 Homework

6. Logic and Computing

Unit I STUDY GUIDE

FURTHER READING:

• Link: Robin Smith, Stanford Encyclopedia of Philosophy Entry on Aristotle’s Logic

• Book: John Boole, The Mathematical Analysis of Logic

• Book: John Venn, Symbolic Logic

1. TL (Pt. I)

Homework— Study Summary of Common Connectives

2. TL (Pt. II)

3. Pattern Recognition

Homework— Learn Truth-tables for Connectives

4. Truth-Tables (Pt. I)

Homework—

• Replacement Method Practice

• Arguments

Supplemental Material—

• Reading: Merrie Bergmann, James H. Moor, Jack Nelson, and James Moor, The Logic Book, Chapter 3

  • Note: Here is the student solutions manual for the chapter.

5. Truth-Tables (Pt. II)

Homework— Practice problems on Truth-functional Truth, Truth-functional Falsity, and Truth-functional Indeterminacy, Truth-functional Equivalence, Truth-functional Consistency, and Truth-functional Validity

Unit II STUDY GUIDE

Extra Practice in Translations

FURTHER READING:

• Book: A Companion to Ancient Philosophy

  • Katerina Ierodiakonou, Chapter 26: Stoic Logic

  • Richard Bett, Chapter 27: Stoic Ethics

• Book Chapter: Merrie Bergmann, James H. Moor, Jack Nelson, and James Moor, The Logic Book, Chapter 2

• Reading: Bernard Linsky, Stanford Encyclopedia of Philosophy Entry on Principia Mathematica

• Book: Gottlob Frege, Begriffsschrift

1. Inference Rules (Pt. I)

Homework—

• Memorize: Non-Subderivational Rules

• Reading: The Logic Book (6e), Chapter 5

  • Note: Read from p. 146-152.

2. Inference Rules (Pt. II)

Homework—

• Reading: The Logic Book (6e), Chapter 5

  • Note: Read from p. 155-163 and 167-173.

  • Also do problems in sections 5.1.1E (p. 152-155) and 5.1.2E (p. 163-165).

  • Lastly, memorize all rules of inference, both subderivational and non-subderivational rules.

    • Note: Your success in this class depends on this.

3. Inference Rules (Pt. III)

Homework— The Logic Book (6e), Chapter 5

• Re-do problems in 5.1.2E (p. 166).

• Re-read p. 167-173.

• Do problems in 5.1.3E (p. 173-174).

• Read p. 174-209.

• Do problems in 5.3E #1, a-i (p. 209).

4. Replacement Rules (Pt. I)

Homework— The Logic Book (6e), Chapter 5

• Read p. 214-222.

• Do problems in 5.3E #1 (j-r), #2 (a-j), #3 (a-j), pg. 209-210.

• Study all the new rules of inference and replacement rules of SD+ found on p. 221-222.

5. Replacement Rules (Pt. II)

Homework— Do all problems in 5.4E #1-3, 5 (p. 222-223).

6. Reductio Ad Absurdum

Note: For more knight and knave puzzles, click here.

UNIT III STUDY GUIDE

FURTHER READING:

Chapter: Merrie Bergmann, James H. Moor, Jack Nelson, and James Moor, The Logic Book (6e), Chapter 5

1. Predicate Logic

Homework— The Logic Book (6e), Chapter 7

• Read section 7.1 (p. 262-267) and 7.2 (p.268-274).

• Re-do in class practice problems.

2. Quantifiers

Homework— The Logic Book (6e), Chapter 7

• Read section 7.3 (p. 276-294).

• Do 7.3E #1 (p. 294).

  • Here is the portion of the student solutions manual for the relevant chapter.

• Review FAQ.

3. Translations (Pt. I)

Homework— The Logic Book (6e), Chapter 7

• Do 7.3E #2 (p. 294-5).

  • Here is the portion of the student solutions manual for the relevant chapter.

• Read section 7.4 (p. 296-310), in particular p. 300-310.

4. Translations (Pt. II)

Homework— The Logic Book (6e), Chapter 7

• Review answers for 7.3 #2-4 (p. 294-6)

  • Here is the portion of the student solutions manual for the relevant chapter.

5. Quantifier Rules (Pt. I)

Homework— The Logic Book (6e), Chapter 10

• Read p. 474-490. 

• Do 10.1E #2, p. 491.

  • Note: If you’re brave, try 10.1E #1, p. 490.

  • Here is the portion of the student solutions manual for the relevant chapter.

6. Quantifier Rules (Pt. II)

Homework— The Logic Book (6e), Chapter 10

• Read p. 492-500. 

• Do 10.2E #1, p. 518.

  • Note: If you’re brave, try 10.2E #5, p. 519.

  • Here is the portion of the student solutions manual for the relevant chapter.

7. Conclusions

Supplementary Material—

• Video: Computerphile, Von Neumann Architecture

• Video: Crash Course Computer Science, Boolean Logic & Logic Gates

• Video: Numberphile, Gödel’s Incompleteness Theorem

Advanced Material—

• Reading: Neil Tennant, Logicism and Neologicism

8. Addendum

UNIT IV STUDY GUIDE

FURTHER READING:

• Book: Merrie Bergmann, James H. Moor, Jack Nelson, and James Moor, The Logic Book

• Book: Paul Herrick, Introduction to Logic

• Book: Patrick Hurley, A Concise Introduction to Logic

• Link: James Garson, Stanford Encyclopedia of Philosophy Entry on Modal Logic