# Symbolic Logic

**Instructor:** Dr. Zee R Perry, Visiting Assistant Professor of Practice in Philosophy, NYU Shanghai

**Email Address:** zee.perry@nyu.edu

**Work Phone Number:** +86 16621668372

**Office Location:** * (currently remote)* 1555 Century Avenue, Office 1256 (12th floor)

**Office Hours:** [TBD] **(currently remote)**

**Class Meeting Location:** *(currently remote)*

**Class Meeting Times:** M/W 2:45 – 4:00pm

**Course Description:**

Logic is the formalized study of reasoning and arguments. This course is an introduction to the field, and will cover the core concepts sentential logic, first-order logic, their proof theories, and the basics of their semantics. We will begin by understanding arguments in a simple way, expressing them in coarse-grained formal language. This more precise notation will enable us to evaluate the validity and soundness of various inferences, and to construct inference ourselves, using the Natural Deduction system.

We will then go back through these questions with a finer-toothed comb, and break sentences down into their component parts. First-order logic, or “Predicate logic”, relies on a formalism that breaks sentences down into subjects and predicates, and introduces tools that allow us to represent concepts like “something”, “everything”, and “nothing” and evaluate inferences involving these terms.

During the course, we will learn to construct true tables to break down complex inferences and determine their truth conditions, and we will learn to construct proofs using the tools of first-order logic. Students who complete the course will have gained a greater ability to understand the structure of statements in formal as well as ordinary languages, and to evaluate and construct inferences involving them. These abilities will translate well to more advanced logic courses (whether philosophical or mathematical) as well as advance courses in analytic philosophy, as well as other fields like computer science, mathematics, and linguistics.

# Syllabus:

# Textbook:

# Class Schedule:

*Part 1: Basic Logical Concepts; Translation, Truth Tables, and Arguments*

Aug 30: Admin and syllabus. Introduction: what is logic?

(Class Recording)

Sept 1: Logical notions: validity and consequence. First steps towards symbolization.

*Readings: *Chapter 1-4

(Class Recording) (Slides) (Homework Assigned) (SUBMIT HOMEWORK 1)

Sept 6: The meaning of ‘and’; Logical Connectives and Translations into Truth-Functional Logic.

*Readings: *Chapter 5-7

(Class Recording) (Slides) (Solutions to Homework 1)

Sept 8: More on Logical Connectives and TFL Translations.

*Readings:* Chapters 5-7 (cont'd)

(Class Recording) (Slides) (Homework Assigned) (SUBMIT HOMEWORK 2)

Sept 13: Truth tables and Truth Functionality

*Readings: *Chapters 8-10

(Class Recording) (Slides)

Sept 15: Truth tables and Semantic Concepts (QUIZLET)

Readings: Chapters 11-14

(Class Recording) (Slides) (Homework Assigned) (SUBMIT HOMEWORK 3)

**Sept 20 ^{th} [NO CLASS!] Day before Mid-Autumn Festival**

*Part 2: Natural Deduction in Truth-Functional Logic*

Sept 22: Semantic Concepts and the Foundations of Natural deduction proof systems. (QUIZLET)

*Readings: *Chapter 14-15

(Class Recording) (Slides)

**[Midterm Quiz 1] – ***Covering: *Chapters 1-14 (Midterm Quiz link NOW AVAILABLE at the Brightspace page)

Sept 27: Natural deduction for Truth-Functional Logic, and Basic Proof Theory. (QUIZLET)

*Readings: *Chapter 15-17

(Class Recording) (Slides)

Sept 29: Proof Theory and Proof Strategies. **(NO QUIZLET)**

*Readings:* Chapter 15-17

**(NO QUIZLET TODAY)** (Class Recording) (Slides) (Homework 4 Assigned -- UPDATED) (SUBMIT HOMEWORK 4)

**October 1 ^{st}-7^{th} [NO CLASS!] Fall Break**

Oct 11: More work on Proofs and Proof-theory in TFL (QUIZLET)

*Readings: *Chapters 18 and 19.

(Class Recording) (Slides) (SUBMIT HOMEWORK 4)

Oct 13: More Proofs and Proof-strategies in TFL (QUIZLET)

*Readings: *Chapters 18 and 19.

(Class Recording) (Slides) (Homework 5 Assigned)

*Part 3: First-order Logic (“FOL”)*

Oct 18: Soundness and Completeness of Truth-Functional Logic.

*Readings: *Chapters 20 and 21

(Class Recording) (Slides) (Homework 5 Submission on Brightspace)

Oct 20: Building blocks of FOL: Subjects, Predicates and Quantifiers

*Readings: *Chapter 22 and 23

(Class Recording) (Slides) (No Homework this week!)

Oct 25: Building blocks of FOL: Subjects, Predicates and Quantifiers

*Readings: *Chapter 24 and 25

(Class Recording) (Slides)

Oct 27: More Building blocks of FOL

*Readings: *Chapters 21 and 24

(Class Recording) (Slides) (Homework 6) (Turn in Homework 6)

Nov 1: The full power of First-Order Logic

*Readings: *Chapters 23 and 24

(Class Recording)

Nov 3: Predicates, Interpretations, and the concept of a sentence

*Readings: *Chapters 25, 26, and 28

(Class Recording)

**[Midterm Quiz 2] – ***Covering: *Chapter 14-21

Nov 8: Reasoning about Interpretations

*Readings: *Chapters 32 and 33.

(Class Recording) (Submit Homework 7)

Nov 10: Reasoning about Interpretations

*Readings: *Chapters 32 and 33.

(Class Recording) (Homework 8)

*Part 4: Natural Deduction for FOL*

Nov 15: Basic rules of Natural Deduction in First-Order Logic

*Readings: *Chapter 34

(Class Recording)

(Submit Homework 8 EITHER through BRIGHTSPACE or HERE: https://tinyurl.com/SubmitHW8 )

Nov 17: Using and Manipulating Quantifiers in Proofs

*Readings: *Chapters 35 and 36

(Class Recording) (Slides) (Homework 9)

**[Midterm Exam 3] – ***Covering: *Chapters 22 to 31

Nov 22: More proof theory for FOL, identity and derived rules

*Readings: *Chapters 37 to 39

(Class Recording)

Nov 24: More proofs in FOL, connecting semantic and proof-theoretic notions

*Readings: *Re-read 34-39

(Class Recording) (Submit Homework 9)

**[Midterm Exam 4] – ***Covering: *Chapters 34 to 39

Nov 29: Soundness and Completeness of FoL

*Readings: *Chapter 43 and 44, and [TBD]

Dec 1: Soundness and Completeness of FoL (cont’d)

*Readings: *Chapter 45 and 46, and [TBD] (cont’d)

*Part 5: Non-Classical Logics and Extensions beyond FOL *

Dec 6: Introducing Modal Logic Two Modal Logics: Temporal Logic and the Logic of Possibility.

*Readings: *Chapter 40

Dec 8: Natural Deduction for Modal Logic, and Different Axiomatizations of Modal Logic

*Readings*: Chapters 40-41 and [TBD]