“Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena.... but if the employment of mathematical analysis should ever become so preponderant in chemistry (an aberration which is happily almost impossible) it would occasion vast and rapid retrogradation….”

—  Auguste Comte

System of positive polity (1852)

Adopted from Wikiquote. Last update Oct. 3, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irra…" by Auguste Comte?
Auguste Comte photo
Auguste Comte23
French philosopher 1798–1857

Related quotes

Immanuel Kant photo

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. https://books.google.com/books?id=OCJLAAAAMAAJ Ernest Belfort Bax (1883) <br class="br">Metaphysical Foundations of Natural Science (1786)

Hermann Weyl photo

“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”

Hermann Weyl (1885–1955) German mathematician

Symmetry (1952)

“Factor analysis, i. e., isolation by way of mathematical analysis, of factors in multivariable phenomena in psychology and other fields”

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

General System Theory (1968), 4. Advances in General Systems Theory

“As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field… have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems… still remain as challenges.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Marilyn Ferguson photo

“Science has always tried to understand nature by breaking things into their parts. Now it is overwhelmingly clear that wholes cannot he understood by analysis. This is one of those logical boomerangs, like the mathematical proof that no mathematical system can be truly coherent in itself.”

Marilyn Ferguson (1938–2008) American writer

The Aquarian Conspiracy (1980), Chapter Six, Liberating Knowledge: News from the Frontiers of Science

Joseph von Fraunhofer photo

“The number of different optical phenomena has become in our time so great that caution must be taken so as to avoid being deceived, and also to refer the phenomena to the simple laws.”

Joseph von Fraunhofer (1787–1826) German optical physicist

In The Wave Theory, Light and Spectra. Prismatic and Diffraction Spectra. Memoirs by Joseph Von Fraunhofer (1981), p. 14 ISBN 0-405-13867-9

Henri Poincaré photo

“In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general.”

Henri Poincaré book Science and Hypothesis

Source: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Context: This procedure is the demonstration by recurrence. We first establish a theorem for n = 1; then we show that if it is true of n - 1, it is true of n, and thence conclude that it is true for all the whole numbers... Here then we have the mathematical reasoning par excellence, and we must examine it more closely.
... The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.
... to arrive at the smallest theorem [we] can not dispense with the aid of reasoning by recurrence, for this is an instrument which enables us to pass from the finite to the infinite.
This instrument is always useful, for, allowing us to overleap at a bound as many stages as we wish, it spares us verifications, long, irksome and monotonous, which would quickly become impracticable. But it becomes indispensable as soon as we aim at the general theorem...
In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general.<!--pp.10-12

Bertrand Russell photo

“So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Source: 1910s, Introduction to Mathematical Philosophy (1919), Ch. 18: Mathematics and Logic

Max Planck photo

“Experimenters are the shocktroops of science… An experiment is a question which science poses to Nature, and a measurement is the recording of Nature’s answer. But before an experiment can be performed, it must be planned – the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted – Nature’s answer must be understood properly. These two tasks are those of theorists, who find himself always more and more dependent on the tools of abstract mathematics.”

Max Planck (1858–1947) German theoretical physicist

Scientific Autobiography and Other Papers (1949)

John Von Neumann photo

“A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

"The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni, published in John von Neumann : Collected Works (1963) edited by A. H. Taub <!-- Macmillan, New York -->; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz
Context: A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

Related topics