What is Logic?

The foundation of reasoning, critical thinking, and formal analysis

Premises + Rules → Valid Conclusions
Definition and Core Concepts

Logic is the systematic study of valid reasoning and inference. It provides the foundation for determining what conclusions validly follow from given premises.

Key Characteristics of Logic:

  • Systematic: Uses precise rules and methods
  • Universal: Applies across all domains of knowledge
  • Objective: Independent of personal beliefs or opinions
  • Formal: Uses symbols and structures to represent reasoning
Types of Logic

Propositional Logic

Deals with propositions (statements that are true or false) and how they combine using logical connectives like "and," "or," and "if...then."

P ∧ Q → R

Current Focus: This is the main focus of this course and calculator!

Predicate Logic

Extends propositional logic to include quantifiers ("for all," "there exists") and predicates that describe properties of objects.

∀x (Human(x) → Mortal(x))

🚧 Coming Soon: Predicate logic is not yet included in this course or calculator, but will be added in a future update!

Where Logic is Used

Mathematics

  • • Proofs and theorems
  • • Set theory
  • • Number theory
  • • Abstract algebra

Computer Science

  • • Programming logic
  • • Database queries
  • • Artificial intelligence
  • • Circuit design

Philosophy

  • • Argument analysis
  • • Epistemology
  • • Ethics reasoning
  • • Metaphysics

Daily Life

  • • Decision making
  • • Problem solving
  • • Evaluating news
  • • Planning and organizing
Simple Example

Logical Reasoning in Action:

Premise 1: If it rains, then the ground gets wet.

Premise 2: It is raining.

Conclusion: Therefore, the ground gets wet.

This follows the logical pattern called Modus Ponens: If P implies Q, and P is true, then Q must be true.

Related Concepts

Understanding this concept connects to these important logical concepts: