Mathematical Philosophy: A Study of Fate and Freedom; Lectures for Educated Laymen |
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Mathematical Philosophy, a Study of Fate and Freedom; Lectures for Educated ... Cassius Jackson Keyser No preview available - 2022 |
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algebraic analytical geometry angle animal answer called codomain common composed concept congruent constitute continuum corresponding course D₁ defined definition denote difference difference-kind distinction doctrinal function domain dyads elements engineering ensemble equation essential ethics Euclid's Elements Euclidean Euclidean geometry evident example fact false familiar field finite foregoing geometry given Henri Poincaré Hilbert human hyperspace ideal ideas important infinite class infinity integers interpretation invariant k-limit kind lecture limit logical Lucretius magnitude mathe mathematical mathematicians matical matter mean natural neighborhood non-Euclidean non-Euclidean geometry notion ordinary space pair parabolic geometry pathopencil philosophy plane Plato postulate system projective geometry propositional function psychology question range rational numbers real numbers relation represent respect rôle scientific segment sensation sense sequence speak spirit stimulus straight line subject-matter symbols theorems theory things thought time-binding tion transformation true values variable verifiers W. K. Clifford zero
Popular passages
Page 230 - That which hath been is now; and that which is to be hath already been; and God requireth that which is past.
Page 231 - ... predominating, cause universal diffusion — alternate eras of Evolution and Dissolution. And thus there is suggested the conception of a past during which there have been successive Evolutions analogous to that which is now going on ; and a future during which successive other such Evolutions may go on — ever the same in principle but never the same in concrete result.
Page 14 - Through and through the world is infected with quantity. To talk sense, is to talk in quantities. It is no use saying that the nation is large,— How large? It is no use saying that radium is scarce,— How scarce? You cannot evade quantity. You may fly to poetry and to music, and quantity and number will face you in your rhythms and your octaves. Elegant intellects which despise the theory of quantity, are but half developed. They are more to be pitied than blamed.
Page 150 - WE, THE PEOPLE OF THE UNITED STATES, DO ORDAIN AND ESTABLISH THIS CONSTITUTION.
Page 307 - This is not the place to give a detailed account of the Lucretian principles and procedure.
Page 391 - ... it seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men learn the cause; for there is nothing which would surprise a geometer so much as if the diagonal turned out to be commensurable.
Page 231 - Even Epicurus passed away, when his light of life had run its course, he who surpassed in intellect the race of man and quenched the light of all, as the ethereal sun arisen quenches the stars.
Page 333 - Magazine [p. 358, above], have all felt and given evidence of the practical utility of handling space of four dimensions, as if it were conceivable space. Moreover, it should be borne in mind that every perspective representation of figured space of four dimensions is a figure in real space, and that the properties of figures admit of being studied to a great extent, if not completely, in their perspective representations.
Page 318 - Bibliography of non-Euclidean geometry, including the theory of parallels, the foundations of geometry, and space of n dimensions, London, 1911.
Page 315 - We do not assert that there is an absolute limit to the divisibility of matter: what we assert is, that after we have divided a body into a certain finite number of constituent parts called molecules, then any further division of these molecules will deprive them of the properties which give rise to the phenomena observed in the substance.