The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

A series of essays examines foundations and methods of mathematics and physics, tracing how hypotheses, conventions, intuition, and logic shape scientific knowledge. Early sections analyze number, magnitude, and the construction of the continuum, and consider non-Euclidean geometries and the status of axioms. Later essays address mechanics, thermodynamics, electrodynamics, probability, optics, and modern physical theories, weighing experiment, mathematical formulation, and explanatory hypotheses. Reflections on mathematical creativity, the role of conventions, the objective value of science, and methodological guidance for future research and education tie the topics together, arguing that scientific principles mediate between experience and theoretical construction.