Abstract
If science is dominated by the constant concern to preserve the reality of the substratum of sensation, and if, on the other hand, as we saw in Chapter 1, mathematics has exercised and continues to exercise a considerable and constantly growing influence on the evolution of science, it follows that these two tendencies are capable of being reconciled. And it is easy to see that this is really the case, thanks to the close agreement that exists between our sensation and our reason insofar as it expresses itself through mathematics, an agreement that is without doubt the particular trait most characteristic of both the one and the other. This agreement has often been emphasized by thinkers who have used it — depending on their particular point of view — either to demonstrate the reality of the external world or to establish the dependence of the external world on mental concepts. For example, Sophie Germain, whom, as we know, Auguste Comte considered to be one of his forerunners, wrote:
Can it be doubted that a type of being has an absolute reality when one sees the language of calculation, starting from a single reality it has grasped, give rise to all the realities related to the first by a common nature? If the only thing such relationships had to commend them was the fact that our intellect is able to conceive them, how could it happen that the observation of facts should come, by such a different way, to show a structure outside human thought similar to that whose model man finds within himself?1
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Notes
Sophie Germain, ‘Considérations générales sur l’état des sciences et des lettres aux différentes époques de leur culture,’ OEuvres philosophiques (Paris, 1878 ), p. 157.
Johann Karl Friedrich Rosenkranz, Hegel als deutscher Nationalphilosoph (Leipzig, 1870), p. 329.
Quoted in Federigo Enriques, ‘La critique des principes et son rôle dans le développement des mathématiques,’ Scientia 12 (1912) 178.
Quoted in Adolf Kneser, Mathematik und Natur (Breslau, 1918), pp. 10–12.
Quoted in Gaston Darboux, Eloges académiques et discours (Paris, 1912), p. 142. We should note that this statement, although it is later than K. G. Jacobf s statements, is entirely independent of them, since the latter were not published until after Hermite’s death. Cf. Kneser, p. 12. Analogously, in a letter to Stieltjes Hermite writes: “I am … quite convinced that corresponding to the most abstract speculations of Analysis are realities existing outside ourselves that we shall some day come to know. I even believe that the efforts of geometricians, unbeknownst to them, receive guidance that makes them tend toward such a goal, and the history of science seems to prove that an analytic discovery takes place at the very moment it is needed to make it possible for us to advance in our study of those phenomena of the real world that are accessible to us” (Correspondance d’Hermite et de Stieltjes (ed. B. Baillaud and H. Bourget, Paris, 1905, 1:8). There is no doubt that this agreement in mathematics is what d’Alembert had in mind when he spoke of a “simple and unique piece of knowledge” (cf. § 11 above). It is completely characteristic, on the other hand, that Petzoldt, whose positivistic bias we have noted (Ch. 1, n. 6), loudly protests against this concept of a preestablished harmony between pure mathematics and physics (which had also been affirmed by Minkowski), declaring that “this is an extremely dangerous belief” (SR 123).
Discourse, Pt. 6 [Philosophical Works of Descartes, trans. Elizabeth S. Haldane and G. R. T. Ross (Cambridge, England: Cambridge University Press, 1931; reprint New York: Dover, 1955), 1:121) and ‘Lettre a Mersenne,’ 10 May 1632, OEuvres de Descartes (Paris: Ch. Adam etP. Tannery, 1897–1910), 1:250 [Philosophical Letters of Descartes, trans. Anthony Kenny (Oxford: Clarendon Press, 1970), p. 23]. Cf. Principles, Pt. 4, princ. 199: “And thus by a simple enumeration it may be deduced that there is no phenomenon in nature whose treatment has been omitted in this treatise” [Haldane and Ross, 1:296]. For Hegel, cf. §89 below.
Andrew Seth, Hegelianism and Personality, 2nd ed. (Edinburgh, 1897), p. 132.
Henri Poincaré, Electricité et optique (Paris, 1901), p. 3; Pierre Duhem, L’evolution de la mécanique (Paris, 1902 ), pp. 177–178.
Kant, Metaphysical Foundations of Natural Science, trails. James Ellington (Indianapolis: Bobbs-Merrill, 1970 ), p. 23 [Preussische Akademie ed., 4:484]. Meyerson cites Premiers principes métaphysiques de la science de la nature, trans. Andler and Chavannes (Paris, 1891 ).
‘Allocation de M. H. Poincaré,’ in Gaston Darboux, Eloges académiques et discours (Paris, 1912 ), p. 453.
John Tyndall, Fragments of Science (London, 1871), p. 136.
Sir Oliver Lodge, ‘The Aether of Space,’ Nature 79 (1909) 323.
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© 1985 D. Reidel Publishing Company, Dordrecht, Holland
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Meyerson, É. (1985). The Spatial. In: The Relativistic Deduction. Boston Studies in the Philosophy of Science, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5211-9_4
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