„The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics "knows nothing of causation" could only be taken to express the whole truth, if by the term "causation" is understood "efficient causation." The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.“

Fuente: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 290 ; Cited in: Moritz (1914, 29): The Nature of Mathematics.

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E. W. Hobson Foto
E. W. Hobson
matemático británico 1856 - 1933

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—  George Holmes Howison American philosopher 1834 - 1916

Fuente: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Harmony of Determinism and Freedom, p.332

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„Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena.“

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

From Lettre à Maurice Solvine, by A. Einstein (Gauthier-Villars: Paris 1956)
Attributed in posthumous publications, Albert Einstein: A guide for the perplexed (1979)

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„Throughout Nature, as distinguished from idealising mind, there reigns, in fine, no causation but transmission.“

—  George Holmes Howison American philosopher 1834 - 1916

Fuente: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Limits of Evolution, p.39

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„Lucretius and his tradition taught Shelley that freedom came from understanding causation.“

—  Harold Bloom American literary critic and scholar 1930 - 2019

The Anatomy of Influence (2011), p. 142.

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„Fifty years ago Kurt Gödel… proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics.“

—  Freeman Dyson, libro Infinite in All Directions

Fuente: Infinite in All Directions (1988), Ch. 3 : Manchester and Athens
Contexto: Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.

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„To plead the organic causation of a religious state of mind, then, in refutation of its claim to possess superior spiritual value, is quite illogical and arbitrary, unless one have already worked out in advance some psycho-physical theory connecting spiritual values in general with determinate sorts of physiological change.“

—  William James American philosopher, psychologist, and pragmatist 1842 - 1910

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Contexto: To plead the organic causation of a religious state of mind, then, in refutation of its claim to possess superior spiritual value, is quite illogical and arbitrary, unless one have already worked out in advance some psycho-physical theory connecting spiritual values in general with determinate sorts of physiological change. Otherwise none of our thoughts and feelings, not even our scientific doctrines, not even our dis-beliefs, could retain any value as revelations of the truth, for every one of them without exception flows from the state of their possessor's body at the time.

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„It is known that the mathematics prescribed for the high school [Gymnasien] is essentially Euclidean, while it is modern mathematics, the theory of functions and the infinitesimal calculus, which has secured for us an insight into the mechanism and laws of nature. Euclidean mathematics is indeed, a prerequisite for the theory of functions, but just as one, though he has learned the inflections of Latin nouns and verbs, will not thereby be enabled to read a Latin author much less to appreciate the beauties of a Horace, so Euclidean mathematics, that is the mathematics of the high school, is unable to unlock nature and her laws. Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members.
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Fuente: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 37.

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—  Robert Spitzer (priest) American Jesuit priest, scholar and educator 1952

Can scientific methods prove the existence of God? https://www.americamagazine.org/content/all-things/god-and-science-qa-robert-spitzer-sj (December 29, 2015)

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