Philosophy of Sciences and Mathematics up to the 19th century 1000-00FN1-OG

1) Basic notions of philosophy. Ontology, epistemology, the philosophy of nature. Greek roots of philosophy and science. Arche, logos. Philosophy stemming from wonder and philosophy stemming from distrust. Selected characters and problems in the history of philosophy. Thales, Ionic philosophers of nature, Pythagoreans, Heraclitus, Parmenides and Zeno of Elea, Eubulides and aporiae, Democritus, the sophists, Socrates, Plato, Aristotle, the skeptics. The Middle-Age: the role of convents and universities. The universals debate, Robert Bacon, Ockham; Francis Bacon, Descartes, Pascal, Leibniz; Locke, Berkeley, Hume, d'Alembert. Determinism, the principle of causality, Laplace, Kant and the Critique of Pure Reason; Bolzano, Comte and positivism, J. St. Mill, dialectic materialism.

2) Problems of the philosophy of mathematics. Various formulations of the principle of parallelism (relations between ontogenesis and philogenesis). Mathematics and music. Difficulties with basic mathematical notions - historical examples. Potential and actual infinity. Platonic approach to geometry. Euclid, his work and influence. Difficulties related to the analysis of the infinitely small and the notion of function. Philosophical problems of probability theory. The change in the approach to algebra, geometry and analysis in the 19th century; non-euclidean geometries. The notion of a model and its evolution. Klein's Erlanger Program.

3) Selected philosophical problems of astronomy and physics. Ancient conception of the world and mechanics; Eudoxos, Aristotle, Ptolemy, Archimedes. Copernicus, his predecessors and followers, Tycho Brahe, Kepler. The work of Galileo and Newton; their influence on the comprehension of the world. Computational transformations from Kepler's laws to Newton's gravitation law. The problem of an inertial system. Inertial mass and gravitational mass. Incomprehensible effectiveness of mathematics in the scientific description of the world. The philosophical meaning of variational theorems. Problems related to the second principle of thermodynamics (entropy, thermal death) and statistical mechanics.