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Empress vs. Spider-Man: Margaret Cavendish on pure and applied mathematics

  • S.I. : Use & Abuse of Maths
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The empress of Margaret Cavendish’s The Blazing World dismisses pure mathematicians as a waste of her time, and declares of the applied mathematicians that “there [is] neither Truth nor Justice in their Profession”. In Cavendish’s theoretical work, she defends the Empress’ judgments. In this paper, I discuss Cavendish’s arguments against pure and applied mathematics. In Sect. 3, I develop an interpretation of some relevant parts of Cavendish’s metaphysics and epistemology, focusing on her anti-abstractionism and what I call her ’assimilation’ view of knowledge. In Sects. 4 and 5, I use this to develop Cavendish’s critiques of pure and applied mathematics, respectively. These critiques center on the claims that mathematics purports to describe non-beings, that nature is infinitely and irreducibly complex, and, perhaps most originally, that mathematical thinking (like other formal methods in philosophy) deforms the subject of representation, not just the object.

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  1. This paper owes much to discussions with a lively Cavendish reading group, organized by Marcy Lascano and Lewis Powell, and with the wonderful audience at the New Narratives in Philosophy conference at Duke University (April 14–17, 2016), organized by Andrew Janiak and Marcy Lascano. I am especially grateful to Marcy Lascano, Alan Nelson and Jon Shaheen for discussion and comments, and to two anonymous referees at Synthese.

  2. Abbreviations are: Poems and Fancies (PF), Philosophical Letters (PL), Philosophical and Physical Opinions (PPO), Observations upon Experimental Philosophy (OEP), The Blazing World (BW), Grounds of Natural Philosophy (G). OEP is ed. Eileen O’Neill. (2001). Cambridge: Cambridge University Press. Page numbers are from first editions, which are available online (e.g. at Early English Books Online), except OEP. I have modernized capitalization and spelling as O’Neill has done in OEP, described at OEP xlvi.

  3. Cavendish suggests that the various beast-men “each followed such a profession as was most proper for the nature of their species”, but she does not say anything much more specific to tie the characters to their targets. Cavendish describes lice in a different and likely unrelated context in BW as “terrible Creatures” who feed on beggars and “instead of thanks, do reward them with pains, and torment them for giving them nourishment and food”. Jon Shaheen pointed out to ME that the lice-men “measure all things to a hairs-breadth”, and lice are, after all, often found in hair. In conversation, Sarah Hutton suggested the Royal Society as a target for the spidermen, pointing out that that in the Novum Organum, Francis Bacon compares “rationalists” or “dogmatists” to spiders, who “make cobwebs out of their own substance” and experimentalists to ants, who “only collect and use” (Book I, Aphorism 95). And spiders, of course, spin webs in geometrical patterns. Sarasohn writes that in this section Cavendish uses “parody to figuratively demolish an institution she viewed as dangerous, useless, and deluded into thinking that its experimental program could rival and confine the works of nature” (1). An anonymous referee suggests that while the spider-men represent mechanical philosophers, Cavendish’s attacks on the lice-men are aimed at the scholastic curriculum, which counts mathematics as an art, and helpfully points out that Cavendish’s anti-mathematics and anti-abstractionism echo some of the anti-scholastic rhetoric of her day. On Cavendish’s attitude toward and visit to the Royal Society, see Sarasohn (pp. 31–34).

  4. In the more general parlance of the time, “geometricians” refers to both pure and applied geometers, but measurement is clearly part of their task. See, e.g. the introduction to the English version of Burgersdijk’s Logic: “Let the geometricians then be confined to their circles and measures, the arithmeticians to their numbers...”

  5. Cavendish, like a number of her contemporaries, frequently refers to other worlds, e.g. G 234. These worlds differ from nature in more and less fundamental ways, and are something in between actual parts of nature and possible worlds, in that she seems to think that it is epistemically possible that they exist, but their primary function is to allow her to make claims about how our world might have been.

  6. There is a lot more to be said about this argument and about Cavendish’s account of place and motion. If my reading here is right, then it shouldn’t apply only to transferred motion, but should entail that whenever a body loses or gains motion (whatever that means for Cavendish), it loses or gains bulk. Cavendish does indeed imply at PL 445 that a thing’s motion “hath a material being”.

  7. But see OEP 253, where Cavendish writes that “whatsoever has neither form, figure, nor quality, is no body”. Even there, though, Cavendish writes that the principle of form is innate and inherent self-motion, which is identical with matter.

  8. Cavendish is aware of the tension here with the view that all motion is self-motion; see OEP 27.

  9. For details of and arguments for Cavendish’s matter theory, see, e.g., James (pp. 220–230), O’Neill (pp. iiv–vix) and Cunning (Ch. 2).

  10. For more detailed studies of Cavendish’s epistemology, see James (1999), Michaelian (2009) and Boyle (2015). Their interpretations don’t always agree with mine. For example, Michaelian thinks that when Cavendish says that all action of nature are perceptive, she means that “acting is always a matter of figuring, that acting always has this in common with perception” (41). But as I’ve argued, not all perception is patterning, for Cavendish, and her claim that all the actions of nature are perceptive means that motion and especially directed motion cannot occur unless one body somehow registers facts about the other body. Boyle is especially useful on the variety of ways Cavendish uses “perception” and “knowledge”, and Michaelian on self-knowledge.

  11. Detlefsen (2007, p. 173) and Lascano (in correspondence) point out that Cavendish does posit classes or species of things, and relates them to order [e.g. “Nature is necessitated to divide her Creatures into Kinds and Sorts, to keep Order and Method” (G 166)]. This is true, and it is also true that Cavendish frequently appeals to explanations in terms of shared properties or forms. It is still true that, in other places (and sometimes in the same places) Cavendish provides arguments against explanations in terms of shared properties or forms, inspired by her reductionist materialism.

  12. There are still such explanations in the late Grounds (e.g. G 186–9, 203, 211), but the Grounds is a revision of the much earlier Philosophical and Physical Opinions. In the OEP, Cavendish denies that spherical figures are any more perfect than other figures, or are the “principle out of which all other figures are made” (OEP 204).

  13. Although her use of ‘exact’ and ‘perfect’ do not always indicate geometrical exactness or regularity. When Cavendish denies an exact or perfect figure to nature as a whole, she means that nature cannot be circumscribed or limited (PL 520). When she suggests that finite parts are in a sense imperfect (PL 439–440), she usually means that they are dependent on the rest of nature, as in her arguments against atomism (PL 437). Perfection in creatures tends to mean adequacy to their forms, as in her discussions of animal development.

  14. Cunning argues that Cavendish has an imagistic account of ideas, and that “Cavendish is committed to the view that our very best mathematical reasoning is a matter of reasoning through imagistic figures” (23). He then constructs an anti-mathematical argument for Cavendish along the lines of Locke, Berkeley and Hume, so that mathematical reasoning involves using particular imagistic ideas with a more general application. I am less sure that Cavendish thinks that ideas are imagistic in the first place, but Cunning’s account is welcome, since Cavendish does not provide a very explicit story about how it is that we have general ideas in the face of her strong anti-abstractionism. Cunning also points out that, given this imagistic account of ideas, if Cavendish does allow that there are legitimate mathematical demonstrations, she “would need to explain...the way in which our ideas of the truths of logic and mathematics incorporate a sense of the necessity of those truths” given that we do not encounter those necessities in our experience (27).

  15. Katherine Brading helpfully suggested that the understanding of figure that Cavendish exhibits in these passages is a topological rather than a geometrical one.

  16. PPO 3. Compare to Hobbes, De Corpore VII 7: “NUMBER is. One and One, or One One and One, and so forwards; namely One and One make the Number Two, and One One and One, the Number Three; and so are all other Numbers made; which is all one as if we should say, Number is Unities”.

  17. Cavendish does allow that rational matter has a more “general perception” than sensitive matter; it can “judge better of objects than the sensitive, as being more knowing; and knows more, because it has a more general perception, because it is more subtle and active” (OEP 143–144, see also OEP 39, 180). But when Cavendish writes that something is “general” she does not mean that it has a general or universal application, but that it comprehends a greater part of a whole: “[the rational] can more easily make a united perception, than the sensitive; which is the reason the rational parts can make a whole perception of a whole object, whereas the sensitive makes but perceptions in part, of one and the same object” (PL 141). The perception of reason is also more “general” in time, since the rational retains the past actions of the sensitive parts (OEP 145).

  18. In an interesting and more detailed study on the order and disorder of nature, Detlefsen (2007) argues that it is as wrong, albeit tempting, to read Cavendish as claiming that in order to explain order among nature’s parts, nature as a whole must guide, “from the top-down, all the parts in their causal interactions” to explain why those interactions are orderly (170). What I say here is not an endorsement of this reading; it does not imply that nature has some causal power or knowledge, over and above the causal power and knowledge of its parts, that is required to maintain order. The power and knowledge of nature as a whole may be nothing more than the power and knowledge of the sum of its parts, but it may still be necessary to appeal to power and knowledge of the whole to explain order. Moreover, the reading I am offering here agrees with Detlefsen that “there are true disorders independent of the human perspective” (177). But I am less sure that there are true disorders when nature is considered as whole, given (the many) passages like PL 280, which suggest that for Cavendish, as for Spinoza, nature can be considered as natura naturata or natura naturans.

  19. A number of scholars have explored aspects of Cavendish’s reliance on nature’s wisdom and addressed the role of teleology in Cavendish’s system. See Detlefsen, Lascano (9-11), Boyle, Walters (83-85), Cunning (70-96), Broad (50-51). Cunning contrasts also highlights some of Cavendish’s arguments against alternative explanations of order; for example, Pythagoras’s numbers or laws of nature (90-91).


Works by Cavendish

  • Grounds of natural philosophy. London (1668).

  • The blazing world. London (1666).

  • Observations upon experimental philosophy. In E. O’Neill (Ed.), Cambridge: Cambridge University Press (2001).

  • Poems and fancies. London (1653).

  • Philosophical letters. London (1664).

  • Philosophical and physical opinions. London (1663).

Works by others

  • Bacon, F. (2000). Th New Organon. IN L, Jardine & M. Silverthorne (Eds.) Cambridge: Cambridge University Press.

  • Broad, J. (2004). Women philosophers of the seventeenth century. Cambridge: Cambridge University Press.

  • Boyle, D. (2015). Margaret Cavendish on perception, self-knowledge, and probable opinion. Philosophy Compass, 10(7), 438–450.

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  • Cunning, D. (2016). Arguments of the philosophers: Cavendish. Oxford: Routledge.

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  • Detlefsen, K. (2007). Reason and freedom: Margaret Cavendish on the order and disorder of nature. Archiv für Geschichte der Philosophie, 89, 157–191.

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  • Hutton, S. (1996). In dialogue with Thomas Hobbes. Women’s Writing, 4, 421–432.

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  • James, S. (1999). The philosophical innovations of Margaret Cavendish. British Journal for the History of Philosophy, 7(2), 219–244.

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  • Lascano, M. (unpublished manuscript). The world and our place in it: Early modern women philosophers.

  • Michaelian, K. (2009). Margaret Cavendish’s ppistemology. British Journal for the History of Philosophy, 17(1), 31–53.

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  • Walters, L. (2014). Margaret Cavendish: Gender, science and politics. Cambridge: Cambridge University Press.

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Peterman, A. Empress vs. Spider-Man: Margaret Cavendish on pure and applied mathematics. Synthese 196, 3527–3549 (2019).

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