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Symbolic Logic

Video Summary

YouTube video that gives three answers to the "what is logic?" question by answering (i) how do people commonly understand the term "logic", (ii) what you might learn in a formal (symbolic) logic course, and (iii) what you might learn in an informal logic (critical thinking) course. It doesn't aim to give a more historical account of 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

Slides

Practice Exams

Practice exams (or sample questions) are provided to help students prepare for classroom exams. Practice exams are provided in two formats: a pdf version and an accessible html version. Both versions are packaged in a zip file.

  • Exam 1 Introductory concepts and the language of propositional logic.
  • Exam 2 Propositional logic truth tables and trees.
  • Exam 3 Propositional logic proofs.
  • Exam 4 Propositional logic proofs.
  • Exam 5 The language of quantificational logic.
  • Exam 6. Quantificational logic derivations.

The following .zip file contains older practice exams in pdf format: Older Logic Exams

Videos

The following are videos that correspond to a portion of what is covered in class. The videos are not comprehensive.

PL - Symbols, Syntax, Semantics, Translation

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

PL - Truth Tables

PL - Truth Trees

PL - Derivations / Proofs

QL - Predicate Logic - Symbols, Syntax, Semantics, Translation

QL - Truth Trees

QL - Proofs