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Berkeley and the Primary Qualities: Idealization vs. Abstraction

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Abstract

In the First of the Three Dialogues, Berkeley’s Hylas, responding to Philonous’s question whether extension and motion are separable from secondary qualities, says:

What! Is it not an easy matter, to consider extension and motion by themselves, . . . Pray how do the mathematicians treat of them?

After some introductory comments I propose to contrast Philonous’s (Berkeley’s) answer to this question, with an alternative, arguing for the following. (1) A distinction, Berkeley would accept should be made between abstraction as Berkeley conceives it in The Introduction to the Principles of Human Knowledge and idealization, exemplified by Galileo’s ignoring friction in formulating the law of free-fall. (2) Idealizations, being neither sensible objects nor Platonic forms, illustrate the way mathematically inclined natural philosophers of the time would treat some sensible objects. (3) Therefore one puzzle Berkeley raises, whether extension can exist without color or tactile qualities, disappears. (4) So too can the resemblance puzzle be easily avoided, that is how ideas (taken here to be sensible objects) can resemble what’s in principle insensible. Lastly I suggest this way of developing Hylas’s above remark is consistent with, though not requiring, Berkeley’s idealist metaphysics.

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Notes

  1. Robert Boyle, “Origin of Forms and Qualities,” in Selected Papers of Robert Boyle, ed. M. A. Stewart, 20–21. Whether Boyle thought elementary ‘corpuscles’ were in principle insensible is doubtful. He often just calls them invisible, meaning not visible to unaided vision, rather than necessarily non-discernible by sense. I comment on this below. See also New Experiments Hay exhibits, http://library.brown.edu/exhibit/items/show/36.

  2. Locke takes primary qualities as “those utterly inseparable from the Body.” Locke, An Essay Concerning Human Understanding, 2, 8, 9, 134. ed. Peter H. Nidditch, (Oxford: Oxford University Press, 1975). As a reviewer noted Locke likely meant that we can’t imagine a material object that lacked, say, extension or bulk, nor could we think that dividing the object till its parts were imperceptible would cause them to lack some extension or bulk. (See below)

  3. Berkeley notes three types of ideas; ideas of sense, of imagination, and of reflection on the mind’s operations. PHK 1. The first includes immediate sensible ideas, colors, sounds, tastes, etc., and mediate objects of sense, generally physical objects which are congeries of the former.

  4. I take “archetypes” to mean what sensible objects for us would be for God, who, though lacking sense organs, communicates ideas of sense to us.

  5. A point Berkeley makes against what he takes to be Locke’s conception of abstract general ideas.

  6. E.g., The diagonal of a square is commensurable with its sides. They both containing a certain number of M;V: [minima visibilia], Berkeley’s Notebooks, Notebook B #258. Works 1. See also Zoltan Szabo,“Berkeley’s Triangle,” History of Philosophy Quarterly, 12, 1 (1995): 41–63, and Douglas M. Jesseph, Berkeley’s Philosophy of Mathematics, (Chicago: University of Chicago Press, 1993).

  7. The question whether classical geometry requires a commitment to the infinite divisibility of finite extension is somewhat controversial. See discussion in Thomas Heath; Euclid, The Thirteen Books of the Elements, Vol.1, (Books I and II) translated by Sir Thomas Heath, (New York, Dover: 1956), 267–268.

  8. And in the Analyst, a late work, Berkeley writes: “Whether the diagrams in a geometrical demonstration are not to be considered as signs, of all possible finite figures, of all sensible and imaginable extensions or magnitudes of the same kind.” Berkeley, The Analyst, [1734] edited A. A. Luce, in Works , vol. 4, op. cit., query 6, 96. (my italics) The problem however concerns constraints on the extension of “same kind.” For example, are the instances meant to be Euclidean figures?

  9. Galilei Galileo, Two New Sciences, (1638), trans. Stillman Drake, with History of Free Fall (1989), Combined Edition, (Toronto: Wall and Emerson, 2000), 161–162. Isaac Newton, Principia Mathematica, (1686) 1st edition, trans. Andrew Motte (1729), revised Florian Cajori, (Berkeley: University of California Press, 1962), 5.

  10. Ennan McMullin, “Galilean Idealization,” Studies in the History and Philosophy of Science, 16, 3, (1985): 247–273.

  11. Onora O’Neill, Towards Justice and Virtue, (Cambridge: Cambridge University Press, 1996), 40–41. A reviewer gives this case; to cover an apparently square field with ten foot sides with cloth one would need approximately 100 square feet of cloth. That is to treat it as flat for computational purposes. Then you might snip off or add material.

  12. Alan Nelson, “Micro-Chaos and Idealization in Cartesian Physics,” Philosophical Studies, 77 2/3, (1995): 377–391.

  13. Jesseph, 33.

  14. Jesseph 75, refers to PHK 131 where Berkeley claims denying the infinite divisibility of finite extensive segments doesn’t destroy what’s useful in geometry. Jesseph writes:

    “This is a shift from zealous revisionism [of the Notebooks] to a brand of instrumentalism which treats geometric theorems as false when taken as perceived lines and figures in a proof, but true and useful when applied to the solution of practical problems.”

    But neither practical nor theoretical geometry require assuming theorems are true. Euclidean geometry is equally useful (or not) for theoretical purposes, e.g., proving theorems, or practical reasons, e.g. computing the diagonal of a table top

  15. A reviewer comments on the contradiction between the Euclidean view that any line segment being capable of bisection entails its infinite divisibility, and the fact that no actual segment is in fact infinitely divisible. Berkeley attempts to finesse the problem in PHK 127 by equating the claimed infinite divisibility of a finite segment, say an inch, with the true claim that every finite perceived segment can be increased in length. The former, Berkeley believes, is a sign of the latter. But classical geometry simply asserts (via a construction with straight edge and compass) that line segments can be bisected. So, yes, in a diagram we could call a line 1000 ft, (although it’s an inch) construct the bisector, and label each segment 500 ft. For a practical bisection, say of a two by four, we do the best we can.

  16. George Berkeley, The Analyst (1734), Works vol. 4.

  17. If we identify sounds, for example, as Hylas suggests, with “motions in the air,” the mathematization of sound might be possible. Philonous, however, finds the identity incoherent. (1 181). As he does identifying colors with light rays (1 187).

  18. Newton, (Cajori) Principia, 40–42.

  19. Galileo, Two New Sciences, 161–162.

  20. Newton, (Letter to Bently) writes: “It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact.” published online, 2007. Source: 189.R.4.47, ff. 7–8, Trinity College Library, Cambridge, UK.

  21. See Downing, “Berkley’s Philosophy of Science,” in The Cambridge Companion to Berkeley, ed. Kenneth Winkler, Cambridge: Cambridge University Press (2005): 230–266.

    254–255, and her “Siris and the Scope of Berkeley’s Instrumentalism,” in The Cambridge Companion to Berkeley, ed. Kenneth Winkler, Cambridge: Cambridge University Press .(2005): 279–300. Also see her “Berkeley’s Case Against Realism in Dynamics,” (1995) in Robert Muehlmann (ed.), Structural, Interpretative, and Critical Essays, Penn State, 197–214. In addition, see Garber, “Locke, Berkeley, and Corpuscular Scepticism,” in Berkeley, Critical and Interpretive Essays, ed. Colin Turbayne, (Minneapolis: U of Minnesota Press, 1982), 174–79. Margaret Wilson, arguing against Garber, claims that in PHK 60–66 Berkeley isn’t defending an instrumentalist interpretation of the “inner constituents of things.” Margaret Wilson, Ideas and Mechanism, (Princeton: Princeton University Press, 1999), 243–257. I think this is correct in the sense that taking “inner constituents of things” to refer to what Berkeley thinks perceivable in principle, then he could countenance useful correlations–though not strict causes—between inner structure and surface properties.

  22. On the history of the kinetic theory of gasses see Eric M. Rogers, Physics for the Inquiring Mind, (Princeton: Princeton University Press, 1960), Chapter 25.

  23. See the discussion in Gabriel Moked, Particles and Ideas, Bishop Berkeley's Corpuscularian Philosophy, (Oxford: Clarendon Press, 1988), 27–30.

  24. A reviewer’s phrase.

  25. Presumably Berkeley would have no difficulty with Ptolemaic devices, e.g., epicycles, equants, etc. used purely instrumentally to predict planetary orbits. In dynamics he notes the parallelogram of forces as a fictional but useful device to compute resultant forces (DM 18).

  26. Hume, citing Berkeley as the source of the point, argues “an extension, that is neither tangible or visible, cannot possibly be conceived.” David Hume, Enquiry Concerning Human Understanding, (1774) ed. Selby-Bigge, revised P. H. Nidditch, (Oxford: Clarendon Press, 1995) 54. See also Daniel Flage, “Berkeley’s Epistemic Ontology": Canadian Journal of Philosophy, 34, 1 (2010.): 25–60.

  27. Edwin McCann, “Locke’s Distinction between Primary Primary Qualities and Secondary Primary Qualities,” in Lawrence Nolan, ed. Primary and Secondary Qualities, (Oxford: Oxford University Press, 2011), 176.

  28. Michael Jacovides, “Locke on Primary and Secondary Qualities,” in The Cambridge Companion to Locke’s Essay Concerning Human Understanding, ed. Lex Newman, (Cambridge: Cambridge University Press, 2007) 109. Robert Boyle writes at times as if the ultimate parts of matter were in fact Euclidean. For example:

    For a figure of the portion of matter may either be one of the five regular solids treated of by geometricians, or some determinate species of solid figures as that of a cone, cylinder, &c., [also irregular shapes] . . . And as the figure so the motion of one of these particulars . . .as (besides straight) circular, elliptical, parabolical, hyperbolical,and I know not how many others . . . Boyle, “About the Excellency and Grounds of the Mechanical Hypothesis,” (1674) in Selected Philosophical Papers of Robert Boyle, ed. M.A., Stewart, (Indianapolis: Hackett, 1991). 232–233. But Boyle, as far as I can tell, doesn’t claim the material corpuscles are a priori insensible though he often calls them invisible. In an edition of The Excellencies of Robert Boyle, ed. J .J. Macintosh, Boyle notes—in support of corpuscularianism—that, as revealed in a microscope, “minute grains of sand” have size and shape, like a “rock or a mountain.” (Toronto: Broadview, 2008), 234. Much like Locke’s example of dividing a piece of wheat.

  29. Locke, 2.8.9 135.

  30. On this contrast see also Peter Ansty, John Locke &Natural Philosophy, (Oxford: Oxford University Press, 2011), Ch. 2. Also Margaret Wilson, Ideas and Mechanism, (Princeton: Princeton University Press, 1999), 244–245.‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬

  31. Catherine Wilson, The Invisible World, (Princeton: Princeton University Press, 1995), 244–245, Berkeley PHK 60. See also Margaret Wilson, 247.

  32. Locke, 165.

  33. Ken Winkler, discussing Locke’s view of physics, writes: “By a mathematical physics I mean a physics that makes essential use of mathematics in formulating its essential claims, and in deriving other claims—explanations or predictions of particular facts for example—from them.” Winkler, “Locke’s Defense of Mathematical Physics,” in Contemporary Perspectives on Early Modern Philosophy, ed. Paul Hoffman, David Owen, (Peterborough: Broadview Press, 2008), 241. Yet though Locke uses the model of geometrical deduction in the passage quoted, it’s not clear he meant premises in corpuscularian explanations take a mathematical form.

  34. Also see Andrew Wayne, “Expanding the Scope of Explanatory Idealization,” Proceedings of the Philosophy of Science Association, 78, 5 Part I. (2010): 830–841.

  35. As Leibniz in the New Essays (1704–6) takes “abstraction” to be “what mathematicians do when we are to “consider perfect lines and uniform motions . . . although matter . . . always provides some exception.” (Quoted by Martha Bolton, “Primary and Secondary Qualities in the Phenomenalist Theory of Leibniz,” in Nolan ed., 205).

  36. He would also have to accept what have been called “bridge principles,” or “correspondence rules,” for example, identifying the temperature of a gas with the mean kinetic energy of its molecules. This identity would be pragmatically useful and I believe no more a problem for him than mass-points for Newton.

  37. He did have important criticisms of Newton’s examples in the Principia meant to distinguish absolute from relative motion (DM 59,60; PHK 110, 111).

  38. See Walter Ott, Causation and Laws of Nature in Early Modern Philosophy. nOxford: Oxford University Press, 2009).

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Brook, R. Berkeley and the Primary Qualities: Idealization vs. Abstraction. Philosophia 44, 1289–1303 (2016). https://doi.org/10.1007/s11406-016-9778-8

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