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Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions

Published online by Cambridge University Press:  22 November 2016

GIULIANO MORI
GIULIANO MORI*
Affiliation:
Institute for Advanced Study, School of Historical Studies, 1 Einstein Drive, Princeton, NJ 08540, USA. Email: giulianomori@yahoo.com.au; gmori@ias.edu.
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Abstract

This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the ‘subtlety’ commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be ‘naturalized’.

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Research Article
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The British Journal for the History of Science , Volume 50 , Issue 1 , March 2017 , pp. 1 - 21
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Copyright © British Society for the History of Science 2016 

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References

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26 Cf. inter alia Romano, op. cit. (20), pp. 132, 159; Williams, op. cit. (20), p. 60.

27 Cf. Bacon, op. cit. (5), pp. 540–541; Francis Bacon, Novum Organum, in WFB, vol. 1, pp. 70–365, 281.

28 Cf. Bacon, op. cit. (5), pp. 576–577.

29 Cf. Boethius, , ‘De Sancta Trinitate’, in Moreschini, Claudio (ed.), De consolatione philosophiae, Opuscula theologica, Munich: K.G. Saur, 2000, pp. 165–181, esp. 168–169CrossRefGoogle Scholar.

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31 Cf. Valla, op. cit. (18), fols. a iiiv, a ivr.

32 Cf. Fine, op. cit. (18), fol. 60v. Cf. also Axworthy, op. cit. (19), pp. 37, 40. The characteristic medietas of mathematical objects was also frequently underlined in contexts different from that of the quaestio de certitudine mathematicarum. Ramus, for instance, assigned mathematics an intermediate position between dialectics and the world. In this way, departing from the third dialectic judgement it would have been possible to arrive at mathematics, and through mathematics to analyse nature. Besides, at the same time, it was also possible to arrive at dialectics from mathematics since the mathematical study constituted the first stage of the process of liberation of the intellect, which was to be fully achieved only through dialectics. Cf. Goulding, op. cit. (11), pp. 23–24.

33 Cf. Fine, op. cit. (16), fol. AA 2r. Cf. also Axworthy, op. cit. (19), pp. 44–45, 49.

34 Cf. inter alia Romano, op. cit. (20), p. 155.

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46 Cf. Francis Bacon, Translation of the ‘De principiis atque origininbus’, in WFB, vol. 5, pp. 459–500, 462 (original: Francis Bacon, De principiis atque originibus secundum fabula cupidinis et coeli …, in WFB, vol. 3, pp. 79–118, 81).

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50 Cf. Urbach, op. cit. (6), pp. 125 ff.

51 Bacon, Translation, op. cit. (46), p. 479 (original: Bacon, De principiis, op. cit. (46), p. 97). Cf. also Francis Bacon, Thema Coeli, in WFB, vol. 3, pp. 769–780, 773; Bacon, op. cit. (5), p. 644.

52 Francis Bacon, Translation of the ‘Thema Coeli’, in WFB, vol. 5, pp. 547–559, 550 (original: Bacon, op. cit. (51), p. 772).

53 Bacon, op. cit. (52), p. 556 (original: Bacon, op. cit. (51), p. 778).

54 ‘Harmonize facts with Plato's philosophy’. Angelini, op. cit. (39), p. 269.

55 Cf. De Pace, op. cit. (39), pp. 9, 341; Goulding, op. cit. (11), pp. 14–15.

56 Cf. inter alia Ramus, op. cit. (14), pp. 20, 74.

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59 [Melanchthon], op. cit. (17), fols. B4v–B5v.

60 Cf. Mancosu, op. cit. (40), p. 12.

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64 Cf. Williams, op. cit. (20), p. 77.

65 Cf. Goulding, op. cit. (11), p. 170.

66 Francis Bacon, Translation of the ‘Novum organum’, in WFB, vol. 4, pp. 37–248, 167–168 (original: Bacon, op. cit. (27), p. 281).

67 Bacon, op. cit. (66), p. 24 (original: Bacon, op. cit. (27), p. 136).

68 It is interesting to remark, in this regard, that, in line with the Elizabethan suspicion towards Machiavellian subtlety, the serpent in Genesis 3:1 is described in the King James Bible as ‘more subtil than any beast of the field’, while the Vulgate simply had ‘callidior cunctis animantibus terrae’.

69 Cf. Tertullian, Adversus Hermogenem, in PL, vol. 2, cols. 219–262, 222A; Tertullian, Adversum Marcionem, in PL, vol. 2, col. 481B; Tertullian, Adversus Valentinianos, in PL, vol. 2, cols. 263–558, 543A.

70 Cf. Augustine, Contra Academicos, in PL, vol. 32, cols. 908–938, 919, 916, 937.

71 Thomas Aquinas, Scriptum super Sententiis, Book 4, d. 43, q. 1, a. 1, qc. 1 ad 2, in Corpus Thomisticum, automato translatum a Roberto Busa.

72 Cf. Boethius, op. cit. (30); Boethius, De geometria, in PL, vol. 63, cols. 1299–1364, 1353. Cf. also [Girolamo Cardano], De libris propriis eorumque ordine, et usu …, in HCO, vol. 1, pp. 55–150, 143. Such notion can also be traced in many of the humanist reformers, cf. for instance Fine, op. cit. (18), fol. 61v.

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74 Cf. [Cardano], op. cit. (73), pp. 1–2. Concerning Cardano's notion of subtilitas cf. also Ingegno, Alfonso, Saggio sulla filosofia di Cardano, Florence: La Nuova Italia, 1980, pp. 212–213 Google Scholar; Magnard, Pierre, ‘La notion de subtilité chez Jérôme Cardan’, in Baldi, Marialuisa and Canziani, Guido (eds.), Girolamo Cardano: Le opere, le fonti, la vita, Milan: Franco Angeli, 1999, pp. 159–167, 159–160Google Scholar.

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77 Cf. [Cardano], op. cit. (73), p. 410.

78 Cf. [Cardano], op. cit. (73), p. 409.

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83 Cf. Bacon, op. cit. (27), p. 228.

84 Bacon, op. cit. (66), pp. 199 (original: Bacon, op. cit. (27), p. 314).

85 Cf. Francis Bacon, Sylva Sylvarum: Or a Natural History, in WFB, vol. 2, pp. 325–680, 602–603.

86 Bacon, op. cit. (4), p. 332.

87 Francis Bacon, Translation of the ‘Cogitationes de natura rerum’, in WFB, vol. 5, pp. 419–439, 419 (original: Francis Bacon, Cogitationes de natura rerum, in WFB, vol. 3, pp. 15–35, 15).

88 Cf. [Cardano], op. cit. (73), p. 411.

89 Bacon, op. cit. (44), p. 371 (original: Bacon, op. cit. (5), pp. 577–578).

90 Bacon, op. cit. (44), p. 411 (original: Bacon, op. cit. (5), p. 621).

91 Francis Bacon, Translation of the ‘Historia vitae et mortis’, in WFB, vol. 5, pp. 213–335, 263 (original: Francis Bacon, Historia vitae et mortis …, in WFB, vol. 2, pp. 101–226, 154).

92 Bacon, op. cit. (4), p. 285.

93 Bacon, op. cit. (27), p. 191.

94 It is interesting in this regard to consider the perceived vicinity between magic and some mathematical practices in Elizabethan England. Cf. Zetterberg, J. Peter, ‘The mistaking of “the mathematicks” for magic in Tudor and Stuart England’, Sixteenth Century Journal (1980) 11, pp. 83–97, 86, 88, 95–96CrossRefGoogle Scholar.

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96 Bacon, op. cit. (66), p. 49 (original: Bacon, op. cit. (27), p. 158).

97 Bacon, op. cit. (66), p. 51 (original: Bacon, op. cit. (27), pp. 160–161).

98 Bacon, op. cit. (44), p. 371 (original: Bacon, op. cit. (5), p. 578). Cf. also Rees, op. cit. (5), p. 407.

99 Bacon, op. cit. (66), p. 162 (original: Bacon, op. cit. (27), p. 275).

100 Cf. Giglioni, op. cit. (7), pp. 136–137.

101 Cf. Bacon, op. cit. (27), p. 201.

102 Bacon, op. cit. (66), p. 126 (original: Bacon, op. cit. (27), p. 235).