John Wilder Tukey’s view of science was, as he explained:
“There are diverse views as to what makes a science, but three constituents will be judged essential by most, viz: (1) intellectual content, (2) organization into an understandable form, (3) reliance upon the test of experience as the ultimate standard of validity. By these tests, mathematics is not a science, since its ultimate standard of validity is an agreed-upon sort of logical consistency and provability.” [1]
Thus, Tukey’s definition of science disqualified all mathematics and all of what is known today as ‘logical sciences’.
On the other hand, Cassius Keyser says: “If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.[2] ” Furthermore, Oliver Heaviside said in his piece ‘On Operators in Physical Mathematics:
“Mathematics is an experimental science, and definitions do not come first, but later on.” [3]
So, both Keyser and Heaviside clearly disproved Tukey’s definition, and proved that mathematics and other logical laws can be, rather they are, of the major foundations of scientific knowledge. However, a large part of humanities and social sciences was still neglected by the categories of ‘science’ according to these two definitions.
1. Tukey, J. W. (1962). The Future of Data Analysis. Annals of Mathematical Statistics. 33, No. 1, 5-6.
2. Keyser C. J. Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 65-66.
3. Heaviside, O. (1893, June 15). On Operators in Physical Mathematics, part II. Proceedings of the Royal Society of London, 54-121.
