Overview

Logic is the anatomy of thought. It is the study of correct reasoning. It provides the rules for moving from premises to valid conclusions.

Core Idea

The core idea is validity. An argument is valid if the conclusion must follow from the premises. Logic doesn’t care if the premises are true (that’s science); it cares if the structure is correct.

Formal Definition

The study of the principles of correct inference.

  • Deductive Logic: Certainty (If A then B. A. Therefore B).
  • Inductive Logic: Probability (The sun rose yesterday, so it will rise today).

Intuition

Logic is the grammar of reason. Just as grammar rules tell you how to build a sentence, logic rules tell you how to build an argument.

Examples

  • Syllogism:
    1. All men are mortal.
    2. Socrates is a man.
    3. Therefore, Socrates is mortal.
  • Modus Tollens:
    1. If it is raining, the ground is wet.
    2. The ground is not wet.
    3. Therefore, it is not raining.

Common Misconceptions

  • Misconception: “Logical” means “unemotional” (like Spock).
    • Correction: Logic is a system of rules, not a personality trait. You can logically analyze emotions.
  • Misconception: Logic proves truth.
    • Correction: Logic only preserves truth. Garbage in, garbage out. (Valid argument + False premises = False conclusion).
  • Fallacy: A flaw in reasoning.
  • Mathematics: Math is essentially logic applied to numbers and structures (Russell/Whitehead).
  • Computer Science: Computers are logic machines (0s and 1s).

Applications

  • Programming: Boolean logic (AND, OR, NOT) is the basis of all code.
  • Law: Constructing sound legal arguments.
  • Philosophy: The primary tool for analyzing concepts.

Criticism and Limitations

  • Paradoxes: Logic can lead to contradictions (This sentence is false) that are hard to resolve.
  • Incompleteness: Gödel showed that logic cannot prove everything about math.

Further Reading

  • Logic: A Very Short Introduction by Graham Priest
  • Introduction to Logic by Harry Gensler