He wrote several articles on the philosophical interpretation of mathematical logic. Cantor’s set theory was also an object of his criticism. He argued for conventionalism and against both formalism and logicism.
Poincaré was deeply interested in the philosophy of science and the foundations of mathematics. Finally, he clearly understood how radical is quantum theory’s departure from classical physics. His fundamental theorem that every isolated mechanical system returns after a finite time to its initial state is the source of many philosophical and scientific analyses on entropy.
He formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest, and he derived the Lorentz transformation. Poincaré sketched a preliminary version of the special theory of relativity and stated that the velocity of light is a limit velocity and that mass depends on speed. His research on the stability of the solar system opened the door to the study of chaotic deterministic systems and the methods he used gave rise to algebraic topology. Later, Poincaré applied to celestial mechanics the methods he had introduced in his doctoral dissertation. During his studies on differential equations, Poincaré made use of Lobachevsky’s non-Euclidean geometry. He clearly saw that this method was useful in the solution of problems such as the stability of the solar system, in which the question is about the qualitative properties of planetary orbits (for example, are orbits regular or chaotic?) and not about the numerical solution of gravitational equations. He not only faced the question of determining the integral of such equations, but also was the first person to study the general geometric properties of these functions. There he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.Īt the beginning of his scientific career, in his doctoral dissertation of1879, Poincaré devised a new way of studying the properties of functions defined by differential equations. Beginning in 1881, he taught at the University of Paris. Poincaré studied mining engineering, mathematics and physics in Paris.
His sister Aline married the spiritualist philosopher Emile Boutroux. His cousin Raymond was the President and the Prime Minister of France, and his father Leon was a professor of medicine at the University of Nancy. Poincaré was born on April 29,1854 in Nancy and died on Jin Paris. Conventionalism and the Philosophy of Geometry.Thus a scientific theory is not directly falsifiable by the data of experience instead, the falsification process is more indirect. Rather, the scientist declares the law to be some interpolated curve that is more or less smooth and so will miss some of those points. Laws, he said, are not direct generalizations of experience they aren’t mere summaries of the points on the graph. Poincaré had an especially interesting view of scientific induction. So, Poincaré believed that scientific laws are conventions but not arbitrary conventions. For example, it is a matter of convention whether to define gravitation as following Newton’s theory of gravitation, but it is not a matter of convention as to whether gravitation is a force that acts on celestial bodies, or is the only force that does so. Although every scientific theory has its own language or syntax, which is chosen by convention, it is not a matter of convention whether scientific predictions agree with the facts. Although all geometries are about physical space, a choice of one geometry over others is a matter of economy and simplicity, not a matter of finding the true one among the false ones.įor Poincaré, the aim of science is prediction rather than, say, explanation. He maintained that non-Euclidean geometries are just as legitimate as Euclidean geometry, because all geometries are conventions or “disguised” definitions. Mathematicians can use the methods of logic to check a proof, but they must use intuition to create a proof, he believed. He believed that logic was a system of analytic truths, whereas arithmetic was synthetic and a priori, in Kant‘s sense of these terms. Poincaré stressed the essential role of intuition in a proper constructive foundation for mathematics. In the foundations of mathematics he argued for conventionalism, against formalism, against logicism, and against Cantor’s treating his new infinite sets as being independent of human thinking. Poincaré was an influential French philosopher of science and mathematics, as well as a distinguished scientist and mathematician.