So it is that, just as nature abhors a vacuum, philosophy abhors an answer, for once the truth is truly attained, the game is truly up.
Dan Garfat-PrattTags: truth philosophy philosophers games vacuums
I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
Max BornTags: science causality progress thinking knowledge philosophy time understanding ideas philosophers space physics atoms matter quantum-theory illuminating theoretical-physics revolution-relativity
It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.
Bernhard RiemannTags: science relationships darkness definitions philosophers space mathematics geometry euclid axioms scientist mathematician adrian-marie-legendre legendre renown
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
Nicholas Murray ButlerTags: science reason philosophy philosophers scientists isaac-newton newton leibniz mathematics geometry descartes calculus sylvester supremacy gauss carl-friedrich-gauss gottfried-leibniz gottfried-wilhelm-leibniz analytical-geometry lobachevsky rene-descartes riemann
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