![Sample our Humanities journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5939/TOC-Subject-Sample-2021-Humanities.jpg"})
ABSTRACT
This article reconstructs Henri Bergson’s argument at the beginning of the second chapter of his Essai sur les données immédiates de la conscience for his view that every idea of number involves space. It begins by criticizing previous interpretations of this view. Most controversially, it argues that Bergson’s view specifically relates to our ideas of what Bertrand Russell calls ‘pluralities’, i.e. particular trios, quadruples, etc., and not to our ideas of ‘abstract numbers’ such as 3 and 4. The article goes on to elucidate the premises of Bergson’s argument. It concludes that the first step in the argument is either invalid, or it turns on a premise that is plainly false, depending on how a particular scope ambiguity is resolved. It suggests that the second step in Bergson’s argument turns on the assumption that space and time differ in the following respect: while it is impossible for the same thing to be wholly present at different spatial locations, it is perfectly possible for the same thing to be wholly present at different temporal locations.
KEYWORDS:
Acknowledgements
I am grateful to two anonymous reviewers for the British Journal for the History of Philosophy for their extremely helpful comments. I would also like to thank Matt Dougherty, Anil Gomes, James Studd and Cécile Varry. Special thanks go to my colleague Steve Fisher, whose insightful postprandial questions about Russell and Bergson prompted me to write this paper in the first place.
Notes
1 This article was based on a paper that Russell had given at a Cambridge undergraduate discussion group called ‘The Heretics’ on the 11 March 1912, and was reprinted in the United States later that year. The Cambridge Review carried a response to Russell’s article by Herbert Wildon Carr on the 12 April 1913, as well as a further salvo by Russell himself on the 26 April. The three pieces in the Cambridge Bergson controversy were published together as a longer pamphlet in 1914, and a truncated version of Russell’s paper would appear three decades and two world wars later as a chapter of his History of Western Philosophy. For more extensive discussion of Russell’s engagement with Bergson, including their face-to-face meeting in the autumn of 1911, see e.g. Monk (Spirit of Solitude, 232–8), Soulez and Worms (Bergson: Biographie, 119ff.), Vrahimis (“Russell’s Critique of Bergson”). For specific discussion of the broader significance of this engagement for the divide between ‘analytic’ and ‘continental’ traditions in philosophy, see Chase and Reynolds (Analytic versus Continental, 23ff), and especially Vrahimis (“Russell’s critique of Bergson”).
2 In his article in The Monist, Russell lumps Bergson together with Hegel as someone who has “preferred traditional errors in interpretation to the more modern views which have prevailed among mathematicians in the last half century” (“Bergson”, 337–8). This is not to say that Russell regards Bergson as a part of the Hegelian tradition. As Vrahimis has pointed out, Russell explicitly contrasts Hegelians and Bergsonians in his article, but he also criticizes the latter for continuing to accept the Hegelian account of mathematics (see Vrahimis, “Russell’s critique of Bergson”, 131, and “Russell Reads Bergson”).
3 E.g. Guerlac, Thinking in Time, 61, Ansell-Pearson, Thinking Beyond, 59–60, Milič Čapek, Bergson and Modern Physics, 176.
4 The most popular point of comparison is Kant. See e.g. Sinclair, Bergson, 42–4, Worms, Deux Sens, 42–4, Capek, Bergson and Modern Physics, 177, Goldschmidt, “Le vide pythagoricien”.
5 E.g. Sinclair, Bergson, 42–3, Sinclair “Habit and Time”, 134, Lovejoy, “Some Antecedents”.
6 There is a similarity between Costelloe’s claim and one made by Gilles Deleuze, viz. that when Bergson argues that the idea of number is the idea of a particular sort of ‘multiplicity’, he is using this word not as “an imprecise noun corresponding to the well-known philosophical notion of the multiple in general” (Le Bergsonisme, 31), but rather in a more specific sense derived from Bernhard Riemann’s comments on the mathematical distinction between discrete and continuous multiplicities. For a recent sceptical discussion of Deleuze’s claim, see Nathan Widder’s “The Mathematics of Continuous Multiplicities: The Role of Riemann in Deleuze’s Reading of Bergson”.
7 The reference is to Bergson, L’évolution créatrice, 204.
8 Andreas Vrahimis has recently provided the first detailed and rigorous treatment of Costelloe’s debate with Russell regarding Bergson’s philosophy (“Sense data and logical relations”), focusing primarily on her response to Russell’s criticisms of Bergson’s theory of duration. One of the claims that Vrahimis defends in this article is that “though she presents her work in the guise of a defence of Bergson, Costelloe-Stephen in fact develops various original views inspired by Bergson’s work” (“Sense data and logical relations”, 3). Following Vrahimis, it may be suggested that Costelloe’s aim in her discussion of Bergson’s view about space and number is really to develop a position of her own, inspired by Bergson’s writings, that is defensible against Russell’s objections. So understood, her restatement of Bergson’s view is not open to the objections I have raised. However, the question that I am addressing specifically concerns Bergson’s own view about number, as opposed to a more defensible modification of that view.
9 Compare Gilbert Harman’s discussion in “The Intrinsic Quality of Experience” (35).
10 In his History of Western Philosophy, Russell characterizes particular numbers such as 3 as “pluralities of pluralities” (858). On this view, the relevant distinction is really between those pluralities that are pluralities of pluralities and those that are not – call them first-order pluralities. This is helpful in considering an obvious counterexample to Bergson’s claim. The idea of the natural numbers is the idea of a plurality, but it surely does not involve space. Bergson could respond that this is not a counterexample to his claim because the latter is only about first-order pluralities, not pluralities of pluralities.
11 Frédéric Worms writes that “this spatial moment of the representation of distinct units holds even for ‘abstract numbers’” (Deux Sens, 41). Mark Sinclair writes: “The same applies … even in the case of abstract number” (Bergson, 41). Sinclair goes on to mention that “[of] course we can and usually do manipulate numbers without the vision of unities in an ideal space” (Bergson, 41), but he suggests that Bergson doesn’t think that this involves any idea of number.
12 This interpretation also indicates how Bergson would respond to the debate between Russell and Carr over the question whether we can form the idea of an abstract number such as 3 if we’ve never come across any particular trio (Carr takes Russell to be committed to a negative answer, which he denies, noting that he can form the idea of 34,361 even though he has never come across a corresponding plurality). Bergson would deny that we can form an abstract idea of 3 at all.
13 Similarly, if I asked: ‘are there are churches in all towns, even those with fewer than one hundred residents?’ you might reasonably conclude that I thought that there were in fact towns with fewer than one hundred residents.
14 Another advantage of this interpretation is that it allows us to argue that Bergson is not open to some of the objections pressed by Frege in Grundlagen, e.g. if Bergson thinks that the idea of 5 is the idea of five qualitatively identical but spatially distinguished units, he is open to the objection that there must be as many ideas of 5 as there are different spatial arrangements of five qualitatively identical units (Frege, Grundlagen der Arithmetik, 53). It is also not clear how Bergson’s view, if applied to abstract numbers, would work in the case of numbers such as 0 and 1.
15 The stronger interpretation would make sense if Bergson were discussing abstract number, since then he would need the idea at which we arrived in counting the sheep to be exactly the same as the idea at which we would have arrived if we were counting soldiers (see Dummett, Frege: Philosophy of Mathematics, 86). But even philosophers who accept the standard view discussed in Section I would accept that Bergson is not talking about abstract number in his discussion of the flock of sheep.
16 Qualitative differences were typically contrasted with quantitative differences in late nineteenth-century French interpretations of Leibniz’s Principle of the Identity of Indiscernibles. Louis Couturat specifically contrasted quality, which he defined as “that which is known in a thing considered separately”, with “magnitude (grandeur)” (Logique de Leibniz, 311). See also Boutroux (Leibnitz: La Monadologie, 145).
17 This would confirm one of Russell’s other complaints against Bergson, which is that he is guilty of confusing “the act of knowing and that which is known” (“Bergson”, 343).
18 I here use the standard A/B reference system for the first Critique and the translation by Guyer and Wood.
19 The starting point of Ted Sider’s introduction to the doctrine of temporal parts is the general thought that “time is like space” (“Temporal Parts”, 241). The contrast could scarcely be greater between this and Bergson’s famous remark: “le temps n’est pas de l’espace” (Worms, “Lire Bergson”, 5).