Logic II

Exercise your rationality and learn the mathematical dialects of logic!

Continue your adventures in logic with puzzles involving Venn diagrams and syllogisms, propositional logic, and first-order logic.

By the end of this course you'll have explored the deep foundations of truth as well as applied logic to AI expert systems and linguistic analysis.

Interactive
quizzes

21

Concepts and
exercises

190+
  1. 1

    Introduction

    Survey the logical languages in the course, and solve some interesting puzzles on the way.

    1. Fallacies

      Deduce which arguments are valid or invalid.

    2. Knights, Knaves, and Logic

      Practice some classic knights and knaves puzzles.

    3. Knights and Formal Logic

      Use a knight and knaves puzzle to learn the beginnings of advanced logic.

  2. 2

    Syllogisms and Sets

    Visual tools for laying out logical thinking and avoiding fallacies.

    1. Included with
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      Euler and Venn Diagram Basics

      Using diagrams to relate categories is an essential tool for approaching syllogisms.

    2. Included with
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      All, Some, and None

      What do the statements "all", "some", and "none" look like visualized with Venn diagrams?

    3. Included with
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      Spot the Fallacies!

      Try to tell logic from illogic.

    4. Included with
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      The Square of Opposition

      See how different syllogism statements are related to each other.

  3. 3

    Propositional Logic

    Turn logic puzzles into logic symbols.

    1. Included with
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      Introduction to Formal Logic

      Learn the basic terminology of formal logic.

    2. Included with
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      Formal De Morgan

      Prove De Morgan's Laws with formal logic tools.

    3. Included with
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      Using Implication

      Apply implication to break open new laws of thought!

    4. Included with
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      Rules of Substitution

      Which rules of substitution are logically valid?

  4. 4

    First-Order Logic

    With a little extra logical power, describe the universe.

    1. Included with
      Brilliant Premium

      For All and There Exists

      Practice using "all" and "some" formally and logically.

    2. Included with
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      Formal Symbolization

      Learn how to represent statements in first-order logic with formal notation.

    3. Included with
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      Multiple Generality

      Modify multiple logical variables rather than just one.

    4. Included with
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      Duals and Prenex

      Transform first-order logic statements using duals and learn about prenex form.

  5. 5

    Paradox and the Limits of AI

    Use logic to control and befuddle AIs

    Coming Soon