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Some Observations on the Role of Singularity in the Exact, Mathematical, and Social Sciences

Published online by Cambridge University Press:  28 February 2024

Jacques Hamel
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Extract

At first glance singularity would seem to be necessarily opposed to the physical sciences, indeed to any kind of science. As the hallowed saying goes: “Science deals only in universals.” According to this view, the aim of any true scientific endeavor must be the discovery of universals or, in other words, the value of such an endeavor is based on its ability to explain phenomena in terms of universals. The status of singularity in science is a direct result of this approach. Singularity is associated with the presence, either in a person or an object, of an unusual or exceptional quality, or of an individual trait. Singularity so conceived must therefore be seen as inherently compromising the aims of any scientific endeavor, since the purpose of that endeavor is universality as defined above. In this sense, the basis of scientific explication is the ability to determine a feature common to a collection of objects, thus allowing them to be explained by deductive reasoning. This common feature can therefore not be individual, if individual is understood as unusual or exceptional.

Type
Research Article
Information
Diogenes , Volume 41 , Issue 161 , March 1993 , pp. 43 - 65
Copyright
Copyright © 1993 Fédération Internationale des Sociétés de Philosophie / International Federation of Philosophical Societies (FISP)

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Footnotes

1.

This article is a result of my research in the field of qualitative methodology. The research was underwritten by a grant from le Conseil de recherches en sciences humaines du Canada and la Fondation F.C.A.R. I also wish to thank my two young colleagues, Stéphane Dufour and Dominic Fortin, for their timely and penetrating comments and criticisms. The same thanks go to Dominique Boucher of the philoso phy department at the University of Montreal.

References

Notes

2. Javeau, Claude, “Singularité et sociologie,” Société, 6, Autumn 1989, p. 229.

3. On this point, see Charlotte Heinritz and Angela Rammstedt, “L'approche biographique en France,” Cahiers internationaux de sociologie, vol. XCI, 1991, p. 1 and pp. 331-370; Jacques Hamel (ed.), The Case Study Method in Sociology, Current Sociology, vol. 40,1, Spring 1992.

4. Bourdieu, Pierre and Wacquant, Loïc, Réponses, Paris, Seuil, 1992, p. 57.

5. Canguilhem, Georges, “Du singulier à la singularité en épistémologie biologique,” Etudes d'histoire et de philosophie des sciences, Paris, Vrin, 1968, p. 213.

6. Ibid., p. 214.

7. Ibid.

8. Ibid.

9. Ibid., p. 218.

10. Thom, René, Modèles mathématiques de la morphogenèse, Paris, Bourgois, 1980, p. 116.

11. Ibid., p. 87.

12. The translator has decided, in this case and in several others farther on in the text, to indicate the presence of the French word global. It is the opposite of the word local. However, unlike in English, the distinction in French between “local” and “global” also carries an abstract meaning. Thus local/global can sometimes refer to the distinction between particularity and universality, or between the micro and macro levels of phenomena. I have kept “global” here both to highlight the distinc tion with the use of the word “local” above it and to enrich the meaning of the term “universal” with which I translate it in this case. This distinction runs throughout the essay. (translator's note)

13. Ibid., p. 216.

14. Thom, René, Paraboles et catastrophes, Paris, Flammarion, 1983, p. 91.

15. Petitot, Jean, “Entretien avec René Thom,” Mathématiques et sciences humaines, 59, 1977, p. 4.

16. Petitot, Jean, “Catastrophes (théories des),” Encyclopaedia Universalis, Universalia 1978, Paris, Encyclopaedia Universalis France 1978, p. 198. On this point, see Jean Petitot (ed.), Logos et théorie des catastrophes, Geneva, Patiño, 1988. This con cept raises the question of determinism; on this point, see Krzystof Pomian (ed.), La querelle du déterminisme, Paris, Gallimard, 1990.

17. The development of “catastrophe models” in the social sciences is in large measure a result of the work of E.C. Zeeman and his followers at Warwick University. His ideas are adroitly presented in Catastrophe Theory, Reading (Mass.), Addison-Wesley, 1978. The development of this model provoked a controversy that René Thom discusses in chapter seven (“La Controverse”) of his book, Modèles math ématiques da la morphogenèse.

18. Thom, René, Modèles mathématiques de la morphogenèse, op. cit., p. 109.

19. Ibid., p. 123.

20. On the question of the experimental method see René Thom's article “La méthode expérimentale: un mythe des épistémilogues (et des savants?),” in Jean Hamburger (ed.), La Philosophie des sciences aujourd'hui, Paris, Gauthier-Villars 1986, pp. 7-20.

21. Thom, René, Modèles mathématiques de la morphogenèse, op. cit., p. 115.

22. Thom, René, Paraboles et catastrophes, op. cit., p. 135.

23. On this subject, see René Thom, Paraboles et catastrophes, op. cit., pp. 59-60; and Modèles mathématiques de la morphogenèse, op. cit., p. 109.

24. Ibid., p. 108.

25. Granger, Gilles-Gaston, Pour la connaissance philosophique, Paris, Odile Jacob, 1988, pp. 116-117.

26. Granger's position on the philosophical debate concerning continuity and dis continuity - that is, on whether the former is anterior to the latter, or vice versa - is that no rupture exists at all between the continuous and discontinuous: there is unity.

27. Ibid., p. 109.

28. Granger, Gilles-Gaston, Pour la connaissance philosophique, op. cit. p. 112.

29. Granger, Gilles-Gaston, “Modèles qualitatifs, modèles quantitatifs dans la con naissance scientifique,” Sociologie et sociétés, vol. XIV, 1, April 1982, p. 10.

30. Ibid., pp. 10-11.

31. De Bruyne, Paul, et al., Dynamique de la recherche en sciences sociales, Paris, P.U.F., 1974, p. 212.

32. Bromberger, Christian, “Monographie,” in Pierre Bonte and Michel Izard (eds.), Dictionaire de l'ethnologie et de l'anthropologie, Paris, P.U.F., 1991, p. 484.

33. Maget, Marcel, Guide d'étude directe des comportements culturels, Paris, C.N.R.S., 1953, p. 57.

34. Champagne, Patrick, “Statistique, monographie et groupes sociaux,” Études dédiées à Madeleine Grawitz, Genève, Dalloz, 1982, p. 8.

35. Leach, Edmund, Les Systèmes politiques des hautes terres de Birmanie, Paris, Maspero, 1972, p. 87.

36. See Samir Amin on this subject, Le Développement inégal, Paris, Editions de Minuit, 1973.

37. See Georges Charbonnier, Entretiens avec Claude Lévi-Strauss, Paris, Plon-Julliard, 1961.

38. Dumont, Fernand, L'Anthropologie en l'absence de l'homme, Paris, P.U.F., 1981, p. 69.

39. Grafmeyer, Yves, and Joseph, Isaac, L'École de Chicago, Paris, Aubier 1984, pp. 6-52.

40. Zonabend, Françoise, “Du texte au prétexte. La monographie dans le domaine européen,” Études rurales, 97-98, 1985, p. 37.

41. See Gilles-Gaston Granger, Langages et épistémologie, Paris, Klincksieck, 1979.

42. Petitot, Jean, “Catastrophes (théories des),” in Encyclopaedia Universalis, op. cit., p.198.

43. This methodological analysis by Godelier figures most prominently in the fol lowing articles: “D'un mode de production à l'autre: théorie de la transition,” Recherches sociologiques, vol. XII, 2, 1981, pp. 161-193; “La théorie de la transition chez Marx,” Sociologie et sociétés, vol. XXII, 1, April 1990 pp. 53-81; “L'objet et les enjeux,” in M. Godelier (ed.), Transitions et subordinations au capitalisme, Paris, Editions de la Maison des sciences de l'Homme, 1991, pp. 7-56. These texts are based on his epistemological study of Marx that began with Rationalité et irrationalité en économie, Paris, François Maspero, 1974, two volumes.

44. Godelier, Maurice, “D'un mode de production à l'autre: théorie de la transi tion,” Recherches sociologiques, op. cit., pp. 173-174.

45. On the geneology of the idea of work and the tradition passed on to Marx by the classical economists, see Maurice Godelier, “L'anthropologie économoique,” in L'anthropoligie en France, situation actuelle et avenir, Paris, Éditions du C.N.R.S., 1979, pp. 47-62.

46. On the subject of just how these empirical data influenced Marx's elaboration of his theory, see the absolutely fascinating biography of Marx's two daughters, written by Yvonne Kapp, Eleanor Marx. Chronique Familale des Marx, Paris, Éditions sociales, 1980. It is in large measure thanks to their labors that the documentary authenticity and accuracy on the manufacturing process, as well as on the lives and working conditions of workers, and on other subjects, is achieved, although Marx himself gave them little credit for their contribution to his work.

47. That is, the process understood as a medium of production and exchange. “In order to grasp the specific nature of a social mode of production, attention must be paid exclusively to its forms of production and of exchange” (Karl Marx, Théories sur la plus-value, Paris, Éditions sociales, 1974, p. 338).

48. Godelier, Maurice,“D'un mode de production à l'autre,” Recherches soci ologiques, op. cit., p. 174.

49. Godelier, Maurice,“La théorie de la transition chez Marx,” Sociologie et sociétés, op. cit., p. 58.

50. Marx, Karl, Fondements de l'économie politique, Paris, Anthropos, 1973, p. 424. Quoted by Maurice Godelier in “La théorie de la transition chez Marx,” in Sociologie et sociétés, op. cit., pp. 58-59.

51. Ibid., p. 59.