“Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development…. Philosophy of mathematics… has its paradoxes and antimonies, and also diverse schools of thought…”

— George Frederick James Temple

100 Years of Mathematics: a Personal Viewpoint (1981)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as '…" by George Frederick James Temple?

George Frederick James Temple photo

George Frederick James Temple21

British mathematician 1901–1992

Related quotes

“Speculative Philosophy is the endeavour to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted. By this notion of 'interpretation' I mean that everything of which we are conscious, as enjoyed, perceived, willed, or thought, shall have the character of a particular instance of the general scheme.”

Charles Hartshorne (1897–2000) Philosopher

The Logic of Perfection and Other Essays in Neoclassical Metaphysics (1962) p. viii.

“Classical mechanics is mathematical not only in the sense that it makes use of mathematical terms and methods for abbreviating arguments which might, if necessary, also be expressed in the language of everyday speech; it is so also in the much more stringent sense that its basic concepts are mathematical concepts, that mechanics itself is a mathematics.”

Eduard Jan Dijksterhuis (1892–1965) Dutch historian

Source: The mechanization of the world picture, 1961, p. 499

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

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

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

“The above interpretation has been introduced, not on account of its immediate value in the present system, but as an illustration of a significant fact in the philosophy of the intellectual powers, viz., that what has commonly been regarded as the fundamental axiom of metaphysics is but the consequence of a law of thought, mathematical in its form.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 50

“We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.”

James Clerk Maxwell book A Treatise on Electricity and Magnetism

A Treatise on Electricity and Magnetism (1873), §36.

“Only if mathematical rigor is adhered to, can systems problems be dealt with effectively, and so it is that the systems engineer must, at least, develop an appreciation for mathematical rigor if not also considerable mathematical competence.”

A. Wayne Wymore (1927–2011) American mathematician

Source: A Mathematical Theory of Systems Engineering (1967), p. 3.

“If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. 2

“For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?”

Richard Courant (1888–1972) German American mathematician (1888-1972)

Richard Courant, What is Mathematics?, (1941) p. xix

“The life of the law has not been logic; it has been experience… The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.”

Oliver Wendell Holmes Jr. book The Common Law

The Common Law (1881), p. 1.
1880s

“The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him understand the usage of the general term.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

Source: 1930s-1951, The Blue Book (c. 1931–1935; published 1965), p. 19

Related topics