Module #1 Introduction to Mathematical Philosophy Overview of the discipline, its importance, and relevance to logic
Module #2 What is Logic? Definition, branches, and types of logic; propositional and predicate logic
Module #3 The Foundations of Mathematics A brief history of mathematics, from ancient Greece to modern times
Module #4 The Crisis of Foundations The discovery of paradoxes and inconsistencies in mathematics
Module #5 The Role of Logic in Foundations How logic can help resolve the crisis of foundations
Module #6 Formal Systems Introduction to formal systems, syntax, and semantics
Module #7 Model Theory The study of structures that satisfy a set of sentences
Module #8 Proof Theory The study of proofs as objects, GentzensCut-Elimination Theorem
Module #9 Gödels Incompleteness Theorems The two theorems, their implications, and impact on mathematical philosophy
Module #10 Tarskis Truth Theory The concept of truth, Tarskis definition, and its implications
Module #11 Semantic Consequence The concept of logical consequence, model-theoretic vs. proof-theoretic approaches
Module #12 The Liar Paradox The paradox, its history, and proposed solutions
Module #13 Self-Reference and Truth The importance of self-reference, the liar paradox, and Tarskis truth theory
Module #14 Higher-Order Logics Introduction to higher-order logics, type theory, and their applications
Module #15 Categorical Logic The categorical approach to logic, its relation to type theory and higher-order logics
Module #16 Intuitionistic Logic The intuitionistic approach to logic, its relation to constructivism and proof theory
Module #17 Modal Logic Introduction to modal logic, its application to epistemology and metaphysics
Module #18 Philosophical Applications of Logic The role of logic in philosophical debates, such as free will and determinism
Module #19 The Nature of Truth The concept of truth, its relation to logic, and the nature of reality
Module #20 The Limits of Logic The limitations of logic, the role of intuition, and the importance of philosophical reflection
Module #21 Case Studies in Mathematical Philosophy Applications of logic to specific areas of mathematics, such as set theory and category theory
Module #22 Current Research in Mathematical Philosophy Recent developments, open problems, and future directions in the field
Module #23 Logic and the Philosophy of Mathematics The relationship between logic and the philosophy of mathematics, implications for our understanding of mathematical truth
Module #24 Logic and Epistemology The role of logic in epistemology, the nature of knowledge, and the limits of human understanding
Module #25 Course Wrap-Up & Conclusion Planning next steps in The Role of Logic in Mathematical Philosophy career
