“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)

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Immanuel Kant200

German philosopher 1724–1804

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“Not only must philosophy be in agreement with our empirical knowledge of Nature, but the origin and formation of the Philosophy of Nature presupposes and is conditioned by empirical physics. However, the course of a science's origin and the preliminaries of its construction are one thing, while the science itself is another. In the latter, the former can no longer appear as the foundation of the science; here, the foundation must be the necessity of the Concept.”

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“Natural science is throughout either a pure or an applied doctrine of motion.”

Immanuel Kant (1724–1804) German philosopher

Preface, Tr. Bax (1883)
(1786)

“[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are… two distinct categories of things of which an account must be given—the ideas or concepts of mathematics, and the propositions of mathematics. …the great majority of writers on the subject have concentrated their attention on the explanation of one or the other… and erroneously supposed that a satisfactory explanation of the other would immediately follow.”

Frank P. Ramsey (1903–1930) British mathematician, philosopher

Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
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“All true metaphysics is taken from the essential nature of the thinking faculty itself, and therefore in nowise invented, since it is not borrowed from experience, but contains the pure operations of thought, that is, conceptions and principles à priori, which the manifold of empirical presentations first of all brings into legitimate connection, by which it can become empirical knowledge, i. e. experience. …mathematical physicists were thus quite unable to dispense with such metaphysical principles…”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 1; Ch. 1. Nature And Design Of This Work, lead paragraph

“Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts.”

Immanuel Kant book Critique of Pure Reason

A 713, B 741
Critique of Pure Reason (1781; 1787)

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

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“All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon.”

John Theophilus Desaguliers (1683–1744) French-born British natural philosopher and clergyman

Source: Course of Experimental Philosophy, 1745, p. v: Preface
Context: All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon. But then we must call in Geometry and Arithmetics, to our Assistance, unless we are willing to content ourselves with natural History and conjectural Philosophy. For, as many causes concur in the production of compound effects, we are liable to mistake the predominant cause, unless we can measure the quantity and the effect produced, compare them with, and distinguish them from, each other, to find out the adequate cause of each single effect, and what must be the result of their joint action.

“In the natural sciences, language (mathematics) is a useful tool: like the microscope or telescope, it enables us to see what is otherwise invisible. In the social sciences, language (literalized metaphor) is an impediment: like a distorting mirror, it prevents us from seeing the obvious.
That is why in the natural sciences, knowledge can be gained only with the mastery of their special languages; whereas in human affairs, knowledge can be gained only by rejecting the pretentious jargons of the social sciences.”

Thomas Szasz (1920–2012) Hungarian psychiatrist

The Untamed Tongue: A Dissenting Dictionary (1990)

“What is knowledge? Ever since class society came into being the world has had only two kinds of knowledge, knowledge of the struggle of production and knowledge of the class struggle. Natural science and social science are the crystallization of these two kinds of knowledge, and philosophy is the generalization and summation of the knowledge of nature.”

Mao Zedong (1893–1976) Chairman of the Central Committee of the Communist Party of China

Original: (zh-CN) 什么是知识？自从有阶级的社会存在以来，世界上的知识只有两门，一门叫做生产斗争知识，一门叫做阶级斗争知识。自然科学、社会科学，就是这两门知识的结晶，哲学则是关于自然知识和社会知识的概括和总结。 note: "整顿党的作风"
Source: "Rectify the Party's Style of Work" (1942)

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