“From the standpoint of exact natural science, of the explanation of nature from causes, the assumption of an earth-soul is… an hypothesis for the explanation of Being and of the historical development of the organic world.”

— Bernhard Riemann

Gesammelte Mathematische Werke (1876)

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Bernhard Riemann 43

German mathematician 1826–1866

Steve Stewart-Williams (1971)

Source: Darwin, God and the Meaning of Life: How Evolutionary Theory Undermines Everything You Think You Know (2010), p. 101

“We now apply these laws of mental processes, to which the explanation of our own inner consciousness leads, to explain the order and adaptation observed on the earth, i. e., to explain Being and historical development.”

Bernhard Riemann (1826–1866) German mathematician

Gesammelte Mathematische Werke (1876)

“Now, science cannot completely exclude the possibility of supernatural explanation. It is possible—though very unlikely—that our whole world is controlled by elves. But supernatural explanations like these are simply never needed; we manage to understand the natural world just fine using reason and materialism.”

Jerry Coyne (1949) American biologist

Source: Why Evolution is True (2009), pp. 224-225

“Every explanation is after all an hypothesis.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

Source: 1930s-1951, Philosophical Occasions 1912-1951 (1993), Ch. 7 : Remarks on Frazer's Golden Bough, p. 123

“An immediate consequence of these principles of explanation is that the souls of organic beings, i. e., the compacts of mind-masses, arisen during life, continue to exist after death. (Their isolated persistence is not sufficient). But in order to explain the orderly development of organic nature in which the earlier collected experiences obviously serve as basis for the later creations, it is necessary to assume that these mind-masses enter into a greater compact of mind-masses, the Earth-Soul, and that these serve a higher soul-life according to the same laws as the mind-masses engendered in our nerve-processes observe in their service of our own soul-life.”

Bernhard Riemann (1826–1866) German mathematician

Gesammelte Mathematische Werke (1876)

“Our reliance on naturalism, then, is not an assumption decided in advance, but a result of experience—the experience of men like Darwin and Laplace who found that the only way forward was to posit natural rather than supernatural explanations. Because of this success, and the recurrent failure of supernaturalism to explain anything about the universe, naturalism is now taken for granted as the guiding principle of science.”

Jerry Coyne book Faith vs. Fact: Why Science and Religion are Incompatible

Source: Faith vs. Fact (2015), p. 92

“The elucidation of the theory of centripetal and disturbing forces is necessarily less complete. Still… a general conception of the nature of the action of those forces… sufficient to preserve the student from the gross errors… may be obtained from explanations like those here offered. The methods of ascertaining the weight of the Earth and other bodies are… more difficult of explanation; yet… something may be done even in these.”

George Biddell Airy (1801–1892) English mathematician and astronomer

Introduction
Popular Astronomy: A Series of Lectures Delivered at Ipswich (1868)

“At the same time, as Hayek maintained elsewhere, the facts of the social sciences do not lend themselves to the same degree of prediction, or explanation, as the facts of the natural sciences—it is for this reason that there are degrees of prediction or explanation. Prediction may be expressed numerically, moreover, “not as a unique value or magnitude but as a range,” narrow in the natural sciences and potentially very broad in the social sciences. In the social sciences, Hayek modified the conception of a numerical range to a “range of phenomena to expect.””

Alan O. Ebenstein (1959) American political scientist, educator and author

This was his concept of pattern prediction, or explanation of the principle, broad, general predictions.
Hayek's Journey: The Mind of Friedrich Hayek (2003)

“From the methodological standpoint, however, we see that 'mechanism' and 'vitalism' by no means form the mutually exclusive disjunction they have been supposed to do. If a 'non-mechanist' wishes to deny the assumption of methodological mechanism that biological explanations must also be physico-chemical ones, it is obviously by no means intended that the required explanation must be 'vitalistic', i. e. involving the assumption that in living organisms factors analogous to psychical ones are 'at work'. A 'non-mechanistic' theory which is not all 'vitalistic' thus appears to be logically possible, and if we make a critical study of mechanism and vitalism this possibility will be seen to be of special importance.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Source: 1930s, Modern Theory of Development, 1933, 1962, p. 29

“It is true that M. Fourier had the opinion that the principal end of mathematics was the public utility and the explanation of natural phenomena; but such a philosopher as he is should have known that the unique end of science is the honor of the human mind, and that from this point of view a question of number is as important as a question of the system of the world.”

Carl Gustav Jacob Jacobi (1804–1851) German mathematician

Letter to Legendre (July 2, 1830) in response to Fourier's report to the Paris Academy Science that mathematics should be applied to the natural sciences, as quoted in Science (March 10, 1911) Vol. 33 https://books.google.com/books?id=4LU7AQAAMAAJ&pg=PA359, p.359, with additional citations and dates from H. Pieper, "Carl Gustav Jacob Jacobi," Mathematics in Berlin (2012) p.46

“From the standpoint of exact natural science, of the explanation of nature from causes, the assumption of an earth-soul is… an hypothesis for the explanation of Being and of the historical development of the organic world.”

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