Abstract
Spengler, more than any other student of mathematics as a sociocultural phenomenon, carries us to, if not over, the threshold of a sociology of mathematics that is free of transcendental and idealist assumptions. Bloor notes that the main barrier to a sociology of mathematics is “the idea that mathematics has a life of its own and a meaning of its own”.1 He is sympathetic to Spengler’s viewpoint; but his own version of a naturalistic approach to number contains some contradictions. He believes, on the one hand, in an eternal, material world that is the source of “permanent” truth. On the other hand, he argues that belief in a material world “does not justify the conclusion that there is any final or privileged state of adaptation to it which constitutes absolute knowledge or truth”.2 This statement is at odds with what Bloor has christened “the strong program in the sociology of knowledge”. The strong program is (a) causal (what conditions “bring about belief or states of knowledge”?); (b) “impartial with respect to truth and falsity, rationality, or irrationality, success or failure”, (c) symmetrical: true and false beliefs are explained in terms of the same types of causes, and (d) reflexive: the explanatory patterns in the strong program apply to sociology itself.3 Bloor’s “methodological relativism” is unhinged, however, by the scientistic basis of the strong program: “only proceed as the other sciences proceed”, Bloor asserts, “and all will be well”.4
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
T. S. Kuhn, The Structure of Scientific Revolution, 2nd ed., University of Chicago Press, Chicago, 1970.
D. Hofstadter, Godel, Escher, Bach, Basic Books, New York, 1979, pp. 582–583.
D. Bohm, Fragmentation and Wholeness, Wan Leer Jerusalem Foundation: Jerusalem, 1976, p. 87.
This discussion is based primarily on J. L. Richards, ‘The Art and Science of British Algebra: A Study in the Perception of Mathematical Truth’, Historia Mathematica, Vol. 7, 1980a, pp. 343–365; and ‘Mathematics as a Science’, 1980b, paper presented at the annual meeting of the History of Science Society, Oct. 17,1980, Toronto, Canada.
Richards, 1980a, op. cit. p. 346.
Ibid., p. 360; S. Cannon, Science in Culture: The Early Victorian Period, Dawson Scientific History Publications, New York, 1978.
This discussion is based on R, Collins and S. Restivo, ‘Robber Barons and Politicians in Mathematics’, Canadian Journal of Sociology, 1983, forthcoming; and J. W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite. Harvard University Press, Cambridge, Mass., 1979.
The conjecture that mathematics and religion are intricately intertwined is nowhere more clearly expressed than in Spengler, op. cit., pp. 56, 66, 380, 394.
See, for example, M. Kline, Mathematics: A Cultural Approach, Addison Wesley, Reading, Mass., 1962, pp. 582, 661, 665; cf. D. Gasking, ‘Mathematics and the World’, in Newman, Vol. III, op. cit., p. 1710.
D. Bloor, ‘Polyhedra and the Abominations of Leviticus’, The British Journal for the History of Science, Vol. II, No. 39 1978, pp. 245–272; I. Lakatos, Proofs and Refutations, Cambridge University Press, Cambridge, 1976; M. Douglas, Natural Symbols, Penguin, Harmondsworth, 1973.
Bloor, 1978, op. cit., p. 251.
M. Douglas and A. Wildavsky, Risk and Culture. University of California Press, Berkeley, 1982, p. 138.
D. Bloor, ‘Durkheim and Mauss Revisited: Gassification and the Sociology of Knowledge’, Studies in History and Philosophy of Science, forthcoming (draft ms. 1979 ).
D. MacKenzie, Statistics in Britain, 1865–1930, University of Edinburgh Press, Edinburgh, 1981. This is a slightly edited version of a book review that appeared in the 4S Newsletter Vol. 7, No. 3 (Fall), 1982, pp. 48–51.
Docstocvsky wrote: “… twice-two-makes-four is not life, gentlemen. It is the beginning of death. Twice-two-makes-four is, in my humble opinion, nothing but a piece of impudence… a farcical dressed up fellow who stands across your path with arms akimbo and spits at you. Mind you, I quite agree that twice-two-makes-four is a most excellent thing; but if we are to give everything its due, then twice-two-makes-five is sometimes a most charming little thing, too”. It is not clear that this sort of exercise can be “explained” by referring to it as “merely” an expression of literary priviledge. The ability to imagine “2 + 2 = 5” does not give us “necessary truth” as would be expected if we adhered to the philosopher and mathematician William Whewell’s distinction between necessary and contingent truths, proposed in 1844; F. Doestoevsky, ‘Notes From the Underground’, in The Best Short Stories of Doestoevsky, Modern Library, New York, n.d., p. 139; and see Richards, 1980a, op. dr., p. 362.
“All representations (pictorial, verbal, realistic, abstract) are actively constructed assemblages of conventions or meaningful cultural resources that must be understood and assessed in terms of their role in activities”: B. Barnes, Interests and the Growth of Knowledge, Routledge and Kegan Paul, London, 1977, p. 9.
C. Boyer, A History of Mathematics, John Wiley and Sons, New York, 1968, p. 585; Struik, 1967, op. cit., p. 167.
A. D. Aleksandrov, ‘Non-Euclidean Geometry’, in A. D. Aleksandrov, A. B. Kolmogorov, and M. A. Laurent’ev (eds.), Mathematics: Its Content, Method, and Meaning, MIT Press, Cambridge, Mass., Vol. III, 1969, p. 183.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Restivo, S. (1985). Mathematics and World View. In: The Social Relations of Physics, Mysticism, and Mathematics. A Pallas Paperback, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7058-8_13
Download citation
DOI: https://doi.org/10.1007/978-94-009-7058-8_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-2084-9
Online ISBN: 978-94-009-7058-8
eBook Packages: Springer Book Archive