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The Functions of Definition in Science

Published online by Cambridge University Press:  14 March 2022

Peter Caws
Peter Caws*
Affiliation:
University of Kansas
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Abstract

Definition is viewed in this paper as a cohesive element of theory, providing links between scientific constructs. The problem is approached first in terms of three orders—the historical, the logical, and the heuristic—in which the structure of science may be put together; a study of these is necessary if difficulties about priority of definition are to be resolved. The main part of the paper is devoted to an exercise in theory-construction which illustrates the five principal functions of definition—the grounding of constructs in observation, their descriptive interrelation, the development of logico-mathematical calculi, the interpretation of these calculi, and the provision of precise, quasi-mathematical relations between the constructs themselves. Reference is made throughout to the many names for the defining process found in earlier works, and problems of contextual definition, reduction, stipulative and lexical definition, etc., are dealt with briefly. The theory thus constructed is represented diagrammatically. It is shown that the analysis may be simplified, in general terms, by the use of two new categories, “internal” and “external” definition; and that this innovation may prove helpful in clarifying some traditional obscurities, and in preserving a necessary balance between a purely logical and a purely empirical approach to the philosophy of science.

Type
Research Article
Information
Philosophy of Science , Volume 26 , Issue 3 , July 1959 , pp. 201 - 239
Copyright
Copyright © 1959 by Philosophy of Science Association

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Footnotes

1

This paper is based, in part, on an unpublished dissertation, “The Functions of Definition in Modern Physical Science,” presented to the faculty of the Graduate School of Yale University in candidacy for the Ph. D. degree in Philosophy, 1956. The project was supported by a grant from the National Science Foundation.

References

2 Richard Robinson, Definition, Oxford, 1950, p. 7.

3 Henry Leonard, Principles of Right Reason, New York, Henry Holt, 1957, p. 311.

4 Peter Caws, “A Reappraisal of the Conceptual Scheme of Science,” Philosophy of Science, 24, 3, 1957, p. 223.

5 Essay Concerning Human Understanding, III, iii, 10.

6 Critique of Pure Reason, tr. Norman Kemp Smith, London, Macmillan, 1956, p. 586 (A 727).

7 Ibid., p. 587 (A 729).

8 Ibid., p. 587 (A 730).

9 James Bryant Conant, ed., The Overthrow of the Phlogiston Theory, Harvard, 1950, p. 20.

10 Victor Lenzen, The Nature of Physical Theory, New York, John Wiley, 1931, p. 273.

11 Rudolf Carnap, “The Interpretation of Physics”, in Herbert Feigl and May Brodbeck, Readings in the Philosophy of Science, New York, Appelton-Century-Crofts, 1953, p. 313.

12 Walter Dubislav, Die Definition, Leipzig, Felix Meiner, 1931.

13 Robinson, op. cit.

14 Henry Margenau, The Nature of Physical Reality, New York, McGraw-Hill, 1950, p. 232.

15 Carl G. Hempel, Fundamentals of Concept Formation in Empirical Science, University of Chicago Press, 1952, I.

16 Irving M. Copi, Introduction to Logic, New York, Macmillan, 1953, p. 108.

17 Homer H. Dubs, “Definition and its Problems”, Philosophical Review, LII, 6, 1943, p. 573.

18 See e.g. Filmer S. C. Northrop, The Meeting of East and West, New York, Macmillan, 1946, p. 316.

19 Benjamin Lee Whorf, “Language, Mind and Reality”, in Language, Thought, and Reality, The Technology Press of the Massachusetts Institute of Technology, and John Wiley, New York, 1956, p. 246.

20 Alonzo Church, “Definition”, in The Dictionary of Philosophy, New York, Philosophical Library.

21 Cf. Alfred North Whitehead and Bertrand Russell, Principia Mathematica, Cambridge, 1910, vol. I, p. 12.

22 Percy W. Bridgman, The Logic of Modern Physics, New York, Macmillan, 1928, p. 5.

23 Alfred Jules Ayer, Language, Truth and Logic, New York, Dover Publications, p. 60.

24 Gottlob Frege, “On Concept and Object”, in Peter Geach and Max Black, Translations from the Philosophical Writings of Gottlob Frege, New York, Philosophical Library, 1952, p. 42.

25 Whitehead and Russell, op. cit., Vol. I, ch. III.

26 Whitehead and Russell, op. cit., vol. I, p. 11.

27 Russell, Introduction to Mathematical Philosophy, London, Allen and Unwin, 1919, p. 169.

28 Ibid., p. 169.

29 Michael Scriven, “Definitions, Explanations, and Theories”, in vol. II, Minnesota Studies in the Philosophy of Science, University of Minnesota Press, 1958, pp. 99-195.

30 Ibid., p. 112.

31 Ibid., p. 122.

32 Ernst Mach, tr. McCormack, The Science of Mechanics, Chicago, Open Court, 1902, p. 221.

33 Henri Poincaré, tr. W. J. G., Science and Hypothesis, New York, Dover, p. 103.

34 Bridgman, op. cit., p. 103.

35 Caws, “Definition and Measurement in Physics”, in Churchman and Ratoosh, eds., Measurement: Definitions and Theories, New York, John Wiley, in press.

36 Margenau, op. cit., p. 232.

37 Hans Reichenbach, The Rise of Scientific Philosophy, University of California Press, 1957, p. 132.

38 Carroll C. Pratt, The Logic of Modern Psychology, New York, Macmillan, 1939, p. 74.

39 Norman Campbell, Physics, The Elements, Cambridge, 1920, p. 122.

40 Filmer S. C. Northrop, op. cit., p. 443.

41 William Kneale, Probability and Induction, Oxford, The Clarendon Press, 1949, pp. 93 ff.

42 Margenau, op. cit., p. 335.

43 On this point see Hempel, “The Theoretician's Dilemma”, in vol. II, Minnesota Studies in the Philosophy of Science, University of Minnesota Press, 1958, pp. 37-98.

44 For a good treatment of this see Lewis White Beck, “Constructions and Inferred Entities”, Philosophy of Science, 17, 1, 1950.

45 Karl Menger, “On Variables in Mathematics and Natural Science”, British Journal for the Philosophy of Science, V, 18, 1954, p. 135.

46 Copi, “Further Remarks on Definition and Analysis”, Philosophical Studies, VII, 1-2, 1956, p. 19.

47 Cf. H. W. B. Joseph, Lectures on the Philosophy of Leibniz, Oxford, 1949, pp. 34, 54.

48 Carnap, “Testability and Meaning”, Philosophy of Science, 3, 4, 1936 and 4, 1, 1937.

49 Scriven, op. cit., p. 101.

50 Margenau, op. cit., p. 236.

16a If we forget about the ether, then the behavior of light in this experiment is no different from that of sound in a quiet room. No transformations are necessary.

17a Henry Margenau and Richard A Mould, Philosophy of Science 24, 306 (Oct. 1957).