Mathematical Logic

1. Historical Context
   1. Development of Logic
      1. Ancient Logic
         1. Origins in Ancient Greece
            1. Contributions of Pre-Socratic Philosophers
            2. Role of Socratic Method
         2. Aristotle’s Syllogistic
            1. Structure of Syllogisms
            2. Influence on Later Philosophical and Logical Thought
      2. Medieval Logic
         1. Boethius and the Transition to Medieval Logic
         2. Scholastic Logic
            1. Development During Middle Ages
            2. Merging Aristotelian Logic with Religious Doctrine
      3. Early Modern Logic
         1. Renaissance Humanism’s Impact
         2. Advancements by Descartes and Leibniz
         3. Symbolic Logic Introduction
      4. 19th Century Logic Revolution
         1. Algebraic Logic by De Morgan and Boole
            1. Boolean Algebra Formation
            2. Influence on Computing and Digital Logic
         2. Frege’s Begriffsschrift
            1. Foundations of Predicate Logic
            2. Logic’s Shift Towards Mathematics
      5. 20th and 21st Century Logic
         1. Formalization and Formal Systems
         2. Rise of Mathematical Logic
            1. Developments in Set Theory and Model Theory
         3. Integration with Computer Science
            1. Impact on Artificial Intelligence and Computational Logic
   2. Influential Logicians
      1. Aristotle
         1. His Work on Syllogistic Logic
         2. Influence on Philosophy and Education
      2. George Boole
         1. Development of Boolean Algebra
         2. Impact on Information Theory and Digital Computing
      3. Bertrand Russell
         1. Contributions to Analytic Philosophy
         2. Principia Mathematica and Foundations of Modern Logic
      4. Kurt Gödel
         1. Incompleteness Theorems
            1. Implications for Mathematics and Logic
         2. Contributions to Model Theory and Proof Theory
      5. Alfred Tarski
         1. Work on Semantics and Model Theory
            1. Tarski’s Definition of Truth
         2. Influence on Conceptual Developments in Linguistics and Philosophy