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ABSTRACT
George Berkeley is known as “The Good Bishop,” a name celebrating his faith, pastoral ministry and earnest commitment to his philosophical views. To mathematicians, he is known for his agitated performance in his 1734 critique of fluxions, The Analyst. That work and its petulant tone were occasioned by (i) his “philo-mathematical” opponents’ alleged admonitions on religious mysteries’ lack of logical respectability and (ii) what Berkeley saw as a related public appetite for reformist and deist religious movements. This paper questions Berkeley’s saintly reputation by outlining the hostility and flippancy in his handling of Jacob Walton’s contributions to the debate. Berkeley’s interactions with Walton bear many of the hallmarks of contemporary “trolling” culture and this paper emphasises and explains these parallels. Finally, given Berkeley’s theological and political agenda in his mathematical interactions, I argue that we should not read his mathematical rhetoric as straightforwardly representing his philosophical views.
Acknowledgments
I would like to thank two anonymous reviewers for some truly generous and helpful remarks on this article. Additional thanks are due to Kenny Pearce and Peter West for comments on an early version, and to Katherine O'Donnell and Francesca Bratton, for incisive feedback and exuberant enthusiasm about the idea. I am also grateful to Tom Jones for sharing some pivotal sources from his new intellectual biography of Berkeley. Final thanks to Matthew Hornsby and the editors at IHR for helping to get the article to print.
Notes
1 Pope, The Major Works, 402.
2 Hight, Correspondence of George Berkeley, xi.
3 Berman, “Berkeley’s Life and Works,” 28.
4 Ibid., 28.
5 Berkeley and Sampson, Works of George Berkeley, v.
6 Balfour, “Biographical Introduction,” lx–lxi.
7 Breuninger, Recovering Bishop Berkeley, 1.
8 Dugdale, Fueser, and de Castro Alves, Yale, Slavery and Abolition, 5.
9 See Eric Schliesser, “Berkeley’s Racialized Economic Development”, and, for broader context, Claude Rawson,God, Gulliver, and Genocide.
10 When quoting from Berkeley’s works, I refer to the Luce and Jessop editions in the bibliography. Berkeley, The Querist. For suggestions broaching enslavement of the Irish see especially queries 371–86; for racialised diagnosis of the Irish see queries 512–14; for depraved dispositions of the Irish see queries 19, 348, 357 and 359; and, for endorsement of Petty’s political arithmetic, see queries 199 and 530.
11 Rawson, God, Gulliver, and Genocide, 209–10.
12 Brown, The Biter Bitten, 393.
13 Ibid., 394.
14 For example, to read The Analyst in isolation from Alciphron (which is often done by those with a predominant interest in Berkeley’s mathematical thinking) will preclude appreciation of a number of important contradictions between the texts on the issue of pragmatically useful but logically problematic concepts. As the title page of The Analyst makes clear, the text is about comparing mathematical coherence standards to those publicly afforded to religious concepts. Without Alciphron, such comparison is simply unavailable. See Reid, “Faith, Fluxions, Impossible Numbers”; Moriarty, “The ad hominem argument”.
15 Berkeley, The Analyst.
16 Boyer, History of the Calculus; Cajori, “Discussion of Fluxions”; Grabiner, “Newton’s Calculus”; Grattan-Guinness, “Berkeley’s Criticism of Calculus”; Guicciardini, Development of Newtonian Calculus.
17 The most substantial philosophical engagement with The Analyst is in Jesseph, Berkeley’s Philosophy of Mathematics. Numerous papers, recent and remote, have paid it serious attention in elucidations of Berkeley’s philosophy: Cantor, “Berkeley’s The Analyst Revisited”; Levy, “Berkeley Exorcises the Infinite”; Katz and Sherry, “Leibniz’s Infinitesimals”. The Analyst also features in more general texts examining the philosophy of mathematics, including: Mancosu, Philosophy of Mathematics; Hacking, Why Philosophy of Mathematics?; Linnebo, Philosophy of Mathematics.
18 It is worth noting that there are important differences in the theoretical underpinnings of the Newtonian and Leibnizian presentations of calculus. However, in The Analyst, Berkeley claims (controversially) that they both necessitate the invocation of entities with the same kind of metaphysical and logical issues, even if the Leibnizian account invokes them implicitly and the Newtonian account attempts to avoid them. This essay is focused on Berkeley’s rhetorical activity in this debate, so, for brevity’s sake, these equivocations will go largely unchallenged hereafter.
19 Berkeley, The Analyst, §2.
20 Berkeley, The Analyst, §8.
21 Stock, “Life of George Berkeley,”30.
22 For discussion of Berkeley’s use of this kind of argumentative strategy, see Prince, Philosophical Dialogue, ch. 3-4; Walmsley, Rhetoric of Berkeley’s Philosophy.
23 When citing the central texts of “The Analyst Controversy,” I use the versions compiled by David Wilkins at www.maths.tcd.ie: Wilkins, “The ‘Analyst’ Controversy: Index.”
24 Maclaurin, A Treatise on Fluxions, vii.
25 Maclaurin and Mills, Letters of Colin MacLaurin, 60, 250, 254, 274, 410.
26 Robinson, “Metaphysics of the Calculus,” 28–40.
27 Wallis, “Who was J. Walton?,” 539–40.
28 For a survey of Berkeley’s broader missionary intentions for Siris, see Benjamin, Politics of Berkeley’s Tar-Water.
29 Jurin, A Letter, 24.
30 Siris in the Shades, 17–18.
31 Berman, Idealism and the Man, 189.
32 Berkeley, Principles of Human Knowledge, Preface.
33 Hereafter “Vindication.”
34 Hereafter “Catechism.”
35 Hereafter “Appendix.”
36 Hereafter “Defence.”
37 Hereafter “Reasons.”
38 Wallis, “Who was J. Walton?,” 539.
39 Ibid., 540.
40 My thanks are due to Sue Hemmens for this library discovery.
41 Walton, Vindication, 4.
42 See Berkeley’s claim in The Analyst that, “however useful it may be, [calculus] must be considered only as a Presumption, as a Knack, an Art, rather an Artifice, but not a scientific Demonstration.” Berkeley, The Analyst, §25.
43 Walton, Vindication, 10.
44 Ibid.
45 Berkeley, Defence, 1.
46 Ibid., 21.
47 Ibid., 21–2.
48 Ibid., 22.
49 Ibid.
50 Ibid., 23.
51 Walton, Catechism, 1, 9.
52 Ibid., 8.
53 For discussion of the dynamics of ad hominem arguments, see Walton, Ad Hominem Arguments.
54 Berkeley, Reasons, 1.
55 Ibid.
56 Ibid.
57 Ibid.
58 Swift, “Mr. Collins’s Discourse,” 163–92.
59 Ibid, 169.
60 Swift, “Against Abolishing Christianity,” 1–20.
61 Jurin, A Letter, 2.
62 Berkeley, Reasons, 1.
63 Ibid., 6.
64 Ibid., 7.
65 Halasz, The Marketplace of Print, 14–46.
66 Ibid., 1.
67 Ibid., 14–15.
68 For a discussion of this climate and its relation to the publication of illustrations, seeGatrell, City of Laughter.
69 Pope, The Major Works, 34.
70 Paku, “Anonymity in the Eighteenth Century,”1.
71 Hight, Correspondences, 470.
72 Greene, The Trouble with Ownership, 271.
73 Brown, The Biter Bitten, 400–1.
74 Maclaurin and Mills, Correspondences, 411.
75 Goodwin, “Cuming, Sir Alexander.”
76 UKHL 2019.
77 Hanna, Some Remarks, 1.
78 For scholarship on the priority debate and its aftermath, seeHall, Philosophers at War; Guicciardini, Development of Newtonian Calculus.
79 The developmental consequences for European mathematics are laid out in Koppelman, “The Calculus of Operations,”; Cajori, Discussion of Fluxions, and refined in Grabiner, Was Newton’s Calculus a Dead End?
80 See Hardaker, “Trolling in Asynchronous Comuter-Mediated Communication”; Phillips, Why We Can’t Have Nice Things; Shin, “Morality and Internet Behavior”; Nogami and Takai, “Effects of Anonymity.” Barney, “[Aristotle], on Trolling,” also provides a helpful analysis, albeit via a satirical peripatetic account.
81 Cheng et al., “Anyone Can Become a Troll.”
82 Nogami and Takai, “Effects of Anonymity.”
83 Hardaker, “Trolling in Asynchronous Comuter-Mediated Communication,”237.
84 Roache, “What’s wrong with trolling,”4.
85 Phillips, Why We Can’t Have Nice Things, 42.
86 Berkeley, The Analyst, §1.
87 Jurin, Geometry No Friend, 2.
88 Berkeley, Siris, §271: fn 1.
89 The Manuscript referenced is BL Add MS 39312, f.227r-v. Quoted inJones, George Berkeley: Philosophical Life, 440.
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Clare Marie Moriarty
Clare Moriarty is an Irish Research Council Postdoctoral Fellow working at the Long Room Hub in Trinity College Dublin. She is also a Fellow for Public Philosophy at The Forum for Philosophy at the London School of Economics.