Episode 1 - Foundations of Science: Poincarés Method

In this episode we have a conversation talking about Henri Poincaré's The Foundations of Science, focusing specifically on his views on the nature of mathematical reasoning, the role of hypotheses in scientific progress, and the relationship between mathematics, physics and philosophy. Poincaré argues against a purely deductive view of mathematics, emphasizing the importance of intuition and synthetic a priori judgments. He also explores the limitations of positivism in science, highlighting the essential role of creative hypotheses and the inherently hypothetical nature of scientific theories. Furthermore, the text examines the concepts of space, time and causality, questioning conventional understandings and advocating a more nuanced approach to scientific methodology. Finally, Poincaré discusses the value of science, both for its practical applications and for its intrinsic contribution to human understanding and aesthetic appreciation.