The Emergence of Greek Mathematics
A comprehensive guide to the emergence of Greek mathematics, exploring its development, key figures, and impact on Western intellectual traditions.
Philosophy of Mathematics
A Foundational Theorem in Ancient Greek Mathematics
A foundational theorem in Ancient Greek mathematics, exploring its historical context, key terms and concepts, and mechanisms and processes.
The Discovery of Irrational Numbers: A Historical Analysis
A historical analysis of the discovery of irrational numbers, exploring ancient civilizations' contributions to mathematics and the significance of irrational numbers in the natural world.
The Intersection of Mathematics and Greek Philosophy
Exploring how the Greeks' emphasis on mathematics influenced their philosophical thought, and its lasting impact on Western philosophy.
A Formal Account of Numbers
Exploring the idea that numbers are formal entities, deriving significance from form or structure rather than inherent characteristics.
Enumeration and Perception
Exploring the complex relationship between enumeration, perception, and concept formation in human cognition, covering ancient and modern philosophers' views on numerical cognition.
The Geometry of Reality: Platonic Solids and their Philosophical Significance
An exploration of the philosophical significance of Platonic solids, particularly the dodecahedron, and their relationship to the universe in ancient Greek philosophy.
The Timaeus' Theory of Triangles: A Philosophical Analysis
A philosophical analysis of Plato's Timaeus, exploring the theory of triangles as fundamental elements and its significance in understanding reality.
The Limits of A Priori Knowledge
Exploring the relationship between a priori knowledge and empirical knowledge, including Plato's views on mathematical truth.
The Paradox of Geometry in Platonic Theory
Exploring the paradox of geometry in Platonic theory, its implications for reality and knowledge, and how it relates to other areas of philosophy.
The Geometric Influence on Philosophy and Scientific Method
An exploration of how geometric concepts have shaped philosophy and scientific method, from ancient Greece to modern times.
The Independence of Geometry: A Study on the Development of Euclidean Geometry
Exploring the development of Euclidean geometry, its independence from arithmetic, and the impact of incommensurable lengths on the field.
The Pythagorean Conception of Numbers
The Pythagorean school's views on numbers as fundamental building blocks of reality, their relationships, and mathematical expressions had a lasting impact on Western philosophical thought.