德勒兹2（三） (6-3)

24. The main aim of Hilbert’s programme, which was fi rst clearly formulated in 1922, was to establish the logical acceptability of the principles and modes of inference of modern mathematics by formalising each mathematical theory into a fi nite, complete set of axioms, and to provide a proof that these axioms were consistent. The point of Hilbert’s approach was to make mathematical theories fully precise, so that it is possible to obtain precise results about properties of the theory. In 1931 Gödel showed that the programme as it stood was not possible. Revised efforts have since emerged as continuations of the programme that concentrate on relative results in relation to specifi c mathematical theories, rather than all mathematics. See José Ferreirós, ‘The Crisis in the Foundations of Mathematics’, inThe Princeton Companion to Mathematics, edited by Timothy Gowers, June Barrow-Green and Imre Leader (Princeton: Princeton University Press, 2008), Ch. 2.6.3.2.

25. Lautman,Essai sur l’unité, p. 282.

26. See Jean Largeault,Logique mathématique. Textes (Paris: Armand Colin, 1972), pp. 215, 264.

27. Lautman,Essai sur l’unité, p. 9.

28. Petitot, ‘La dialectique de la vérité’, p. 98. The term ‘meta-mathematics’ is introduced by Hilbert in ‘Uber das Unendliche’,Mathematische Annalen 95 (1926), pp. 161–90.

29. Lautman,Essai sur l’unité, p. 26.

30. Lautman, Essai sur l’unité, p. 26.

31. Lautman,Essai sur l’unité, p. 26.

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