Graduate Certificate in Philosophy of Mathematical Objects
-- ViewingNowThe Graduate Certificate in Philosophy of Mathematical Objects is a compact, specialized course that bridges the gap between mathematical theory and philosophical inquiry. This program delves into the abstract nature of mathematical objects, their metaphysical status, and the methods used to study them.
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⢠Foundations of Mathematics: Analyzing the fundamental principles that underpin mathematics, including set theory, logic, and axiomatic systems.
⢠Philosophy of Mathematical Objects: Examining the nature and existence of mathematical entities, such as numbers, shapes, and sets.
⢠Mathematical Platonism vs. Formalism: Delving into the debate between Platonic realism and formalism, which propose contrasting views on the nature of mathematical objects.
⢠Philosophical Analysis of Mathematical Proofs: Dissecting the structure, validity, and implications of mathematical proofs.
⢠Infinity and Infinitesimals: Investigating the concept of infinity in mathematics and its implications for mathematical reasoning.
⢠The Continuum Hypothesis: Exploring the question of whether there exists a set whose cardinality is strictly between that of the integers and the real numbers.
⢠Category Theory: Understanding the philosophical implications of category theory and its role in unifying different branches of mathematics.
⢠Mathematical Constructivism: Examining the constructivist perspective, which asserts that mathematical objects are mental constructs based on intuition and experience.
⢠The Interplay of Philosophy and Mathematics: Discussing the historical and ongoing interaction between philosophical and mathematical ideas.
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