Overview of Philosophical Logic

Definition: 'Logic' (Gr. - logike) is the systematic investigation of arguments (or, the process of rational thinking).

  1. The Three Basic Questions of Logic:

    1. What is an argument?

    2. What makes an argument work?

    3. What makes an argument fail?

  2. The Primary Types of Logical Systems:

    1. Syllogistic Logic - relations of categorical propositions

    2. Propositional (or Sentential) Logic - relations of propositions

    3. Predicate (First-Order) Logic - relations of quantifiers (i.e., particulars and universals)

    4. Modal Logic - relations of modalities ('possible', 'necessary', etc.)

  3. A Brief History of Logic:

    1. Pre-Aristotelian Logic: Logos vs. Muthos - the birth of Philosophy

      1. Pythagorianism/Euclid (c. 300 BCE) - linear deduction

      2. Zeno of Elea (c. 450BCE) - reductio ad absurdum

      3. Socrates/Plato (428-347 BCE) - truth and definition

    2. Aristotle (384-322 BCE) - first systematic Logic

    3. Stoicism - Chrysippus (280-206 BCE)

      1. Modalities (potential/actual)

      2. Conditionalities (hypothetical)

    4. Medieval Logic:

      1. Western (Scholasticism)

      2. Islamic

    5. Modern Logic:

      1. Enlightenement -

        1. Francis Bacon
        2. Rene Descartes
        3. Gottfried Leibniz

      2. Nineteenth Century-

        1. Algebraic Logic
        2. Logiscism

    6. Twentieth Century -

      1. Mathematical Logic

      2. Set Theory

      3. Computability


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