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  1. Henri Poincaré, in full Jules Henri Poincaré, (born April 29, 1854, Nancy, France—died July 17, 1912, Paris), French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics. Poincaré grew ...

    • Philosophy
    • Early life and family
    • Education
    • Research
    • Work
    • Criticism
    • Overview
    • Classification
    • Definition
    • Introduction
    • Quotes
    • Analysis
    • Purpose
    • Significance

    Poincaré was an influential French philosopher of science and mathematics, as well as a distinguished scientist and mathematician. 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 stressed the ess...

    Poincaré was born on April 29,1854 in Nancy and died on July 17, 1912 in Paris. Poincaré's family was influential. 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. His sister Aline married the spiritualist philosopher Emile Boutroux.

    Poincaré studied mining engineering, mathematics and physics in Paris. Beginning in 1881, he taught at the University of Paris. There he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.

    At 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. 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...

    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. 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...

    Logicists such as Bertrand Russell and Gottlob Frege believed that mathematics is basically a branch of symbolic logic, because they supposed that mathematical terminology can be defined using only the terminology of logic and because, after this translation of terms, any mathematical theorem can be shown to be a restatement of a theorem of logic. ...

    Poincaré made this point in his investigation of Peano's axiomatization of arithmetic. Italian mathematician Giuseppe Peano (1858-1932) axiomatized the mathematical theory of natural numbers. This is the arithmetic of the nonnegative integers. Apart from some purely logical principles, Peano employed five mathematical axioms. Informally, these axio...

    Logic is -- according to Poincaré -- the study of properties which are common to all classifications. There are two different kinds of classifications: predicative classifications, which are not modified by the introduction of new elements; and impredicative classifications, which are modified by new elements. Definitions as well as classifications...

    For Poincaré, impredicative definitions are the source of antinomies in set theory, and the prohibition of impredicative definitions will remove such antinomies. To this end, Poincaré enunciates the vicious circle principle: a thing cannot be defined with respect to a collection that presupposes the thing itself. In other words, in a definition of ...

    According to Poincaré, all geometric systems deal with the same properties of space, although each of them employs its own language, whose syntax is defined by the set of axioms. In other words, geometries differ in their language, but they are concerned with the same reality, for a geometry can be translated into another geometry. There is only on...

    We can regard the first statement as a principle, as a convention; thus it becomes the definition of gravitation. But then the second statement is an empirical law.

    Poincaré's attitude towards conventionalism is illustrated by the following statement, which concluded his analysis on classical mechanics in Science and Hypothesis:

    For Poincaré, the aim of the science is to prediction. To accomplish this task, science makes use of generalizations that go beyond the experience. In fact, scientific theories are hypotheses. But every hypothesis has to be continually tested. And when it fails in an empirical test, it must be given up. According to Poincaré, a scientific hypothesi...

    Regarding Poincaré's point of view about scientific theories, the following have the most lasting value:

  2. Jules Henri Poincaré ( UK: / ˈpwæ̃kɑːreɪ / [4] [US: stress final syllable], French: [ɑ̃ʁi pwɛ̃kaʁe] ( listen); [5] [6] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", [7] since he excelled in all fields of the discipline as it existed during his lifetime.

    • 17 July 1912 (aged 58), Paris, France
    • Jules Henri Poincaré
    • Biography
    • The Structure of Science
    • Philosophy of Mathematics
    • Philosophy of Physics
    • The Influence of Poincaré

    Jules Henri Poincaré was born on April 29, 1854 in Nancy in theLorraine region of France. His father was professor of Hygiene in theSchool of Medicine at the University of Nancy. His cousin Raymond wasto become the President of the Republic of France during the period1913–1920 and his younger sister Aline married the philosopherEmile Boutroux. Henr...

    Poincaré sets out a hierarchical view of the sciences inScience and Hypothesis(1902), although he does notexplicitly use this terminology. In his view the special sciencespresuppose physics, which presupposes geometry, which in turnpresupposes arithmetic. Poincaré treats topics in a serialorder—first arithmetic, then geometry, then physics, etc. In...

    3.1 Logic and foundations: intuition and predicativity

    Concerning logic and foundations of mathematics,Poincaré’s position is governed by two theses: 1. Logical inferences alone are epistemically inadequate to expressthe essential structure of a genuine mathematical reasoning in view ofits understandability (see Poincaré 1908: 159; 1913b:452). 2. As a consequence of the logical antinomies, one should avoid anyimpredicative concept formation. Historically, both theses are directed broadly against the founders ofmodern logic and set theory such as...

    3.2 Geometry: conventions, intuition and aesthetics

    Poincaré was strongly influenced by and attuned to the Frenchphilosophical scene, which refers to the Kantian tradition to show thelimits of methodological positivism. Members of the so-calledCritique de la sciencemovement (Benrubi 1928), whichincludes members of the “Boutroux Circle” (Nye 1979)advocate a mixture of positivism and Neo-Kantianism. They criticizeboth Comte’s determinism and Kant’s static view of themind’s structure. According to Poincaré, mathematicsrequires intuition not only...

    Concerning the epistemological status of mechanics, Poincarépositions himself, as in his discussion of geometry, as holding aposition between empiricism and a priorism (Poincaré 1902: 111;2017: 71). The principles of mechanics certainly have, according toPoincaré, an empirical origin, but they nonetheless surpass thebounds of strict empiricism sinc...

    There is no doubt that Poincaré’s work has been veryinfluential both in the sciences and in philosophy. It was alreadywidely discussed at the time it was first presented — not onlyin France but also in Germany (e.g. Ferdinand von Lindemann (1904) andEmil Meunier (1919))— and his geometric conventionalism alsogreatly influenced the logical empiricis...

  3. Raymond Poincaré, (born August 20, 1860, Bar-le-Duc, France—died October 15, 1934, Paris), French statesman who as prime minister in 1912 largely determined the policy that led to France’s involvement in World War I, during which he served as president of the Third Republic. The son of an engineer, he was educated at the École Polytechnique. After studying law at the University of Paris ...

    • The Editors of Encyclopaedia Britannica
  4. Signature. Raymond Nicolas Landry Poincaré ( UK: / ˈpwæ̃kɑːreɪ /, [1] French: [ʁɛmɔ̃ pwɛ̃kaʁe]; 20 August 1860 – 15 October 1934) was a French statesman who served as President of France from 1913 to 1920, and three times as Prime Minister of France . Trained in law, Poincaré was elected deputy in 1887 and served in the cabinets of Dupuy and Ribot.

  5. How to use Poincaré in a sentence. Different representations of the Poincaré group are particles with different numbers of spin labels, or degrees of freedom that are affected by rotations. Professor Milhaud also appears to be one; and the great Poincare misses it by only the breadth of a hair.

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