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In April 1826, Comte began teaching a Course of Positive Philosophy, he experienced a period of poor health, and he resumed teaching in 1829.
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Over the course of thirteen years, he wrote six volumes. The Course of Positive Philosophy dissected the epistemological perspective of positive philosophy.
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In 1838 Comte describes a science of studying society and names it sociology. Along with it, he describes the law of three stages theological, metaphysical, and positive.
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Mach's critique of absolute space inspired Einstien to develop relativity. He was anti-metaphysical, and a monist meaning he believed we all share one perceptive reality.
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Poincaré is best known for his critique of logicism and for his geometric conventionalism.
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Between 1873 and 1893 Mach developed both methods of measurement of sound waves and propagation.
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After receiving his degree, Poincaré began teaching as a junior lecturer in mathematics at the University of Caen in Normandy.
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In 1881, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He demonstrated that for certain families of equations it is possible to find important information about the solutions without having to solve the equations.
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In 1887 he established the principles of supersonics, and the mach number, speed relative to the speed of sound.
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In 1889 Poincaré won a prize from the King of Sweden for a question posed by Weierstrass on the stability of the solar system, that is, the three-body problem in classical mechanics. Becoming the first person to discover a chaotic deterministic system. Proving that the problem of determinism and predictability are distinct.
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Described as the greatest empiricist of the 20th century. Reichbach in response to the clash of neo-Kantian priorism and Einstein's relativity developed a scientifically inspired philosophy and a steadfast empiricist epistemology.
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“Here I wish simply to consider the growth of natural knowledge in the light of the theory of evolution. For knowledge, too, is a product of organic nature. And although ideas, as such, do not comport themselves in all respects like independent organic individuals, and although violent comparisons should be avoided, still if Darwin reasoned rightly, the general imprint of evolution and transformation must be noticeable in ideas also.” Ernst Mach
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The book is divided into two parts, one on special relativity and the other on general relativity. This book is his most original work, but it is flawed and suffers from his lack of familiarity with the work done by his English-speaking contemporaries.
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In 1928 he published Philosophy of Space and Time. In this book he further developed a philosophical framework based on Relativity from Axiomatization of the Theory of Relativity.
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Though it was published posthumously, it is one of his most well-received and influential books. It discusses why we perceive time as linearly progressing even though almost all of the physics works both forwards and backwards in time.