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The Validity of Unique Mathematical Models in Science

Published online by Cambridge University Press:  14 March 2022

Eugen Altschul  and
Erwin Biser
Eugen Altschul
Affiliation:
University of Kansas City, Kansas, Mo. and Rutgers University, New Brunswick, N. J.
Erwin Biser
Affiliation:
University of Kansas City, Kansas, Mo. and Rutgers University, New Brunswick, N. J.
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Extract

Prior to statistical mechanics and especially before the advent of the new quantum mechanics, it was traditionally held, following in the main the Kantian philosophy, that the task of science is to attain a unique quantitative representation of reality. It was thought—and with justifiable zeal—that a scientific discipline is exact to the extent to which a mathematical pattern yielding quantitative relations can be applied to its subject matter. This view was based on the implicit assumptions that functional relatedness conducive to quantitative evaluation is bound to reveal the most generic, and hence, the most essential traits of events.

Type
Research Article
Information
Philosophy of Science , Volume 15 , Issue 1 , January 1948 , pp. 11 - 24
Copyright
Copyright © Philosophy of Science Association 1948

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References

1 Die Grenzen der naturwissenschaftlichen Begriffsbildung. Eine logische Einleitung in die historische Wissenschaften. Tuebingen 1898–1901.

2 See E. Altschul's review of second edition of Rickert's “Grenzen”. Archiv fuer Sozialwissenschaft,“ vol. 37, 1913.

3 Before the development of topology as a mathematical discipline in its own right, mathematics as applied to science connoted the possibility of quantification. This restricted view of mathematics was generally accepted at the turn of the century.

4 As for the notion of “vectorial reference” see “Entity and Aspects” by E. Biser in “Philosophy of Science”, vol. 14, No. 2, April 1947.

5 Kennard, Phys. Zeitsch., Vol. 30, pp. 495–7.

6 Heisenberg, loc. cit., pp. 177–181.

7 See the paper: “Methodology of Research and Progress in Science” by E. Biser and E. E. Witmer, “Philosophy of Science”, vol. 14, No. 4, October, 1947.

8 A Tehuprov. Grundbegriffe und Grundprobleme der Korrelationtheorie, p. 20 Berlin, 1925.

9 The uncertainty relations—hence non-uniqueness in microscopic phenomena—can not be attributed solely to a statistical interpretation. The uncertainty relation between energy and time (Δt·ΔE ≧ h) can be derived from Bohr's frequency condition which is assumed to deal with individual processes.

10 Heisenberg, loc. cit. pp. 61–62.

11 See Yule, G. U., An Introduction to the Theory of Statistics, Tenth Edition, also the Eleventh Edition, published in collaboration with H. G. Kendall London 1937, p. 368–369.