# Symbolic Logic

Logic is the science of determining whether an argument is good or bad. Achieving this goal requires a great many things. First, it requires specifying what an argument is and what we *mean* when we say an argument is "good" or "bad". Second, we not only want to know what it means for an argument to be "good", but also how to *identify* good and bad arguments. Third, we want to know how to *construct* good arguments.

This is a first course in symbolic (formal) logic. The course is divided into three parts.

**Part 1**informally introduces the key concepts of logic. Students learn about the goals of logic, what an argument is, three objective criteria for evaluating arguments, and two informal methods for identifying "good" and "bad" arguments. This part concludes with a discussion of our natural (informal) methods for identifying arguments.**Part 2**covers the basics of propositional logic. Students learn the symbols, syntax, and semantics of the language, along with various ways to translate English sentences into propositional logic. Students also learn truth tables and truth trees as methods for identifying "good" arguments and proofs as a way to construct "good" arguments.**Part 3**concludes the course with a discussion of predicate logic. Students again learn the language of predicate logic, along with trees and proofs.

In addition to learning about logic, students will also be exposed to the multitude of ways that logic applies and intersects with other subject matters and daily life. The course includes countless extra-credit opportunities involving the use of spreadsheets, cryptography, logic puzzles, search engines, typesetting mathematics, and human cognition.

## Handouts

- Spring 2018 Syllabus
- H0: Getting to Know You
- H1: Elements of Logic
- H2: PL: Symbols, Syntax, Semantics, Translation
- H3: PL: Truth Tables
- H4: PL: Truth Trees
- H5: PL: Derivations
- H6: RL: Symbols, Syntax, Semantics, Translation
- H7: RL: Truth Trees
- H8: RL: Derivations
- H4s: Six Tips For Truth Trees
- H4e: Four Theories of Truth
- H8s: Further Explanation on the use of Existential Elimination (EE)
- H9: RL: Variable Assignments, Identity, Functions, Definite Descriptions
- LX: LaTeX Commands for Logic
- LSAT: Logic Games
- Quantificational Ambiguities

## Slides

## Practice Exams

Starred exams are the practice examples we will use to review during the review sessions.

- Exam 1D
- Exam 1E
- Exam 1F
- Exam 1G (answers)
- Exam 1I* (answers)
- Exam 1J
- Exam 2D
- Exam 2F
- Exam 2G (answers)
- Exam 2H* (answers)
- Exam 3B
- Exam 3C
- Exam 3D
- Exam 3F (answers)
- Exam 3J*, answers
- Exam 4E*
- Exam 4I
- Exam 4J
- Exam 4 - combined A (answers)
- Exam 4 - Ch.6 and Ch.7 (answers)
- Exam 5B*
- Exam 5C
- Exam 5G

## Videos

### PL - Symbols, Syntax, Semantics, Translation

For a comprehensive video, see An Introduction to Symbolic Logic - 2022.

- PL: Symbols
- PL: Syntax, Part 1 (well-formed formulas)
- PL: Syntax, Part 2 (subformulas and scope)
- PL: Syntax, Part 3 (five wffs, literal negation, conventions)
- PL: Semantics, Part 1 (Interpretations and valuations)
- PL: Semantics, Part 2 (valuations rules)
- PL: Translation, Part 1 (atomic and negated wffs)
- PL: Translation, Part 2 (conjunctions)
- PL: Translation, Part 3 (disjunctions)
- PL: Translation, Part 4 (conditionals)
- PL: Translation, Part 5 (biconditionals)
- PL: Translation, Part 6 (complex translations)

### PL - Truth Tables

- PL: Truth Tables: Introduction
- PL: Truth Tables: Practice, Part 1
- PL: Truth Tables: Relations between Semantic Properties

### PL - Truth Trees

- PL: Truth Trees, Part 1 (Introduction and Setup)
- PL: Truth Trees, Part 2 (Decomposition Rules)
- PL: Truth Trees, Part 3 (Tree Terminology)
- PL: Truth Trees, Part 4 (Recovering an Interpretation)
- PL: Truth Trees, Part 6 (Contradiction, Tautology, Contingency)
- PL: Truth Trees, Part 7 (Equivalence)
- PL: Truth Trees, Part 8 (Validity)
- PL: Tips for Trees

### PL - Derivations / Proofs

- PL, Derivations: Syntactic entailment and proof
- PL, Derivations: How to set up a proof
- PL, Derivations: Conjunction introduction
- PL, Derivations: Conjunction elimination
- PL, Derivations: Conditional elimination
- PL, Derivations: Conditional introduction
- PL, Derivations: Disjunction introduction
- PL, Derivations: Negation introduction and negation elimination
- PL, Hypothetical Syllogism
- PL, Derivations: Disjunctive Syllogism
- PL, Modus Tollens
- PL, De Morgan's Laws
- PL, Implication
- PL, 5 Tips for Proofs

### Predicate Logic (RL) - Symbols, Syntax, Semantics, Translation

- RL: Symbols
- RL: Basic Syntax
- RL: Semantics (Models)
- RL: Valuation of Unquantified Formulas
- RL: Valuations, Part 2 (Quantified Wffs)
- RL: Basic Translation
- RL: Semantics with Variable Assignments (Part 1)
- RL: Semantics with Variable Assignments (Part 2)

### RL - Truth Trees

- RL Trees: Introduction
- RL Trees: Negated decomposition
- RL Trees: Completed open branch
- RL Trees: Recovering a model from a completed open branch

### RL - Proofs

- RL, Proofs: Introduction
- RL, Proofs: Universal Elimination
- RL, Proofs: Existential Introduction
- RL, Proofs: Universal Introduction
- RL, Proofs: Existential Elimination
- RL, Proofs (Practice), Part 1
- RL, Proofs (Practice), Part 2

## Textbook

In the Spring of 2009, I began writing *Symbolic Logic: Syntax, Semantics, and Proof*. The first edition took the form of lecture notes and handouts that I distributed in the summer of 2009, a course packet in the fall of 2009, and finally I used it as a textbook in the Summer 2010, Fall 2010, and Spring 2011 semesters.

The development of the textbook benefited greatly from the feedback I received from instructors and students at Penn State: Deniz Durmus (Spring 2011); Mark Fisher (Spring 2011); Cameron O'Mara (Summer 2011); Ryan Pollock (Fall 2011), Christopher Allaman, Ashley Brooks, Aurora Cooper, Maureen Dunn, Elliannies Duran, Ariel Endresen, Nayib Felix, Joy Garcia, Alex Kirk, Edward Lackner, Brooke Santkiewicz, Ariel Valdez, Isaac Bishop, Kristin Nuss, Karintha Parker, Sarah Mack, Amanda Wise, Meghan Barnett, Alexander McCormack, and Kevin Bogle.

The textbook is in its 2nd printing. The erratum (list of corrections from the first printing) can be found here: Errata for Symbolic Logic (SP2013). I am currently working on a second edition!