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Pragmatism, Intuitionism, and Formalism

Published online by Cambridge University Press:  14 March 2022

Henry A. Patin
Henry A. Patin*
Affiliation:
Chicago City Junior College
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Extract

“… there is no distinction of meaning so fine as to consist in anything but a possible difference of practice.”

“… Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.”

One example which Peirce chose to illustrate his pragmatic maxim as thus stated was the familiar theological distinction between transubstantiation and consubstantiation. Now (Peirce says) since these two doctrines agree in all of the effects which they conceive the sacrament to possess and which may have practical bearings, here and hereafter, it is absurd to say that there is any real distinction between the two doctrines. Peirce declares in the same passage that, having used the question as a logical example only, he does not care to pause to anticipate the theologian's reply.

Type
Research Article
Information
Philosophy of Science , Volume 24 , Issue 3 , July 1957 , pp. 243 - 252
Copyright
Copyright © 1957, The Williams & Wilkins Company

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References

Bibliography

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Bell, E. T., The Development of Mathematics, New York: McGraw-Hill Book Company, Inc., 1945.Google Scholar
Born, Max, Atomic Physics, London: Blackie and Son Limited, 1945.Google Scholar
Bridgman, P. W., The Logic of Modern Physics, New York: The Macmillan Company, 1932.Google Scholar
The Nature of Physical Theory, New York: Dover Publications, 1936.Google Scholar
Carnap, Rudolph, The Logical Syntax of Language, London: Kegan, Paul, Trench, Trubner & Co., Ltd., 1937.Google Scholar
“Foundations of Logic and Mathematics”, International Encyclopedia of Unified Science, Vol. I, No. 3, Chicago: The University of Chicago Press, 1939.Google Scholar
Curry, Haskell B., Outlines of a Formalist Philosophy of Mathematics, Amsterdam: North-Holland Publishing Company, 1951.Google Scholar
Dewey, John, Essays in Experimental Logic, Chicago: The University of Chicago Press, 1916.CrossRefGoogle Scholar
Logic: The Theory of Inquiry, New York: Henry Holt and Company, 1938.Google Scholar
Heyting, A., Intuitionism: An Introduction, Amsterdam: North Holland Publishing Company, 1956.Google Scholar
Hilbert, David and Bernays, Paul, Die grundlagen der Mathematik, Leipzig: B. G. Teubner, 1928.CrossRefGoogle Scholar
Lewis, C. I., Mind and the World-Order, New York: Charles Scribner's Sons, 1929.Google Scholar
Peirce, C. S., Collected Papers of Charles Sanders Peirce, edited by Hartshorne, Charles and Weiss, Paul, Cambridge: Harvard University Press, 1931.Google Scholar
Poincaré, Henri, The Foundations of Science, Lancaster, Pa.: The Science Press, 1946.Google Scholar
Russell, Bertrand, “Introduction to the Second Edition” of The Principles of Mathematics, New York: W. W. Norton and Company, Inc., 1943.Google Scholar
Weyl, Hermann, Philosophy of Mathematics and Natural Science, Princeton: Princeton University Press, 1949.Google Scholar
Bourbaki, N. “Foundations of Mathematics for the Working Mathematician,” The Journal of Symbolic Logic, XIV, March, 1949.Google Scholar
Brouwer, L. E. J., “Intuitionism and Formalism,” Bulletin of the American Mathematical Society, XX, November, 1913.Google Scholar
“Zur Begründung der intuitionistichen Mathematik, I.”, Mathematische Annalen, LXXXXIII, 1924.Google Scholar
Dresden, Arnold, “Brouwer's Contributions to the Foundations of Mathematics”, Bulletin of the American Mathematical Society, XXX, 1924.Google Scholar
Hilbert, David, “On the Foundations of Logic and Arithmetic,” The Monist, XV, 1905.Google Scholar
Weïl, Hermann, “Consistency in Mathematics,” The Rice Institute Pamphlet, XVI, May, 1929.Google Scholar
“Mathematics and Logic”, American Mathematical Monthly, LIII, January, 1946.Google Scholar
“A Half-Century of Mathematics”, American Mathematical Monthly, LVIII, October, 1951.Google Scholar