Abstract
In this chapter I consider Newton’s use of the Baconian label experimentum crucis in his famous 1672 paper on Light and Colors. I take it to be a sort of ‘signpost’, or methodological clue, which, properly understood, can help us to assess the kind of ‘empiricist’ commitment that may be ascribed to Newton. In order to dispel persistent misunderstandings, the first part of the chapter shows how our present understanding of crucial experiments has been shaped by nineteenth-century philosophers of science, as part of a characteristically anti-Baconian methodology. It also shed light on the particularly ambiguous character of Newton’s methodological legacy. In the remaining parts of the paper, muting these retrospective overtones, I show what crucial instances, or crucial experiments, really meant for Bacon, and for his heirs, in order to elucidate Newton’s usage in the light of its actual context (chiefly, the one provided by Bacon, Descartes and Hooke). I argue that the crucial experiment in Newton’s 1672 paper is not devised to arbitrate between competing full-blown and empirically grounded theories, but rather to make the abstract structure of a new, and still unclear, phenomenon (namely: dispersion) entirely transparent. It functions as a ‘perceptual’ index rather than a judgmental criterion. Finally, I explain why the expression has been dropped in the published text of the 1704 Opticks. The ‘exhibiting’ function of the experimentum crucis is now taken over by a long and complex pattern of experiments. It is the whole complex composition of these optical experiments that is now ‘crucially’ exhibiting the abstract structure of refraction.
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Notes
- 1.
See, in this volume, the chapter by Marc Ratcliff.
- 2.
By contrast, the question of Newton’s relation to Locke cannot be framed in this way. Newton’s philosophical and methodological convictions were already well rooted when he became acquainted with Locke at the time of the publication of the Essay in 1690.
- 3.
The role of Bacon’s writings on the constitution of Descartes’ reflections on method is certainly underestimated, and a thorough comparison between the Regulae and De Augmentis scientiarum would help clarifying the extent of this influence. Huygens’ works also contain frequent praises of Bacon’s method of natural histories: for instance, in 1668 he recommended that the newly founded Académie Royale des Sciences should follow “Verulamius’s design” (see Huygens 1888–1950, vol. XIX, 268).
- 4.
Newton (1958).
- 5.
Laudan (1981a).
- 6.
See Newton’s “First rule for the Study of Natural Philosophy” in Book III of the Mathematical principles of natural philosophy: “no more causes of natural things should be admitted than are both true and sufficient to explain the phenomena” (Newton 1999, 794).
- 7.
Laudan (1981b).
- 8.
Reid (2002), 121.
- 9.
See his influential The life of Sir Isaac Newton: Brewster (1832), esp. 334sq., where the sterility of Bacon’s method is denounced.
- 10.
Jevons (1892), 508.
- 11.
- 12.
See Koyré (1965b) or William Whewhell’s comments on the hypotheses non fingo: “this is in reality a superstitious and self-destructive spirit of speculation. Some hypotheses are necessary in order to connect the facts which are observed, some new principle of unity must be applied to the phenomena, before induction could be applied.” (Whewell 2001b, 183).
- 13.
See, for instance, this classical statement of the hypothetico-deductive method in Huygens’ Preface to his Traité de la Lumière: “au lieu que les géomètres prouvent leurs propositions par des principes certains et incontestables, ici les principes se vérifient par les conclusions qu’on en tire; la nature de ces choses ne souffrant pas que cela se fasse autrement. Il est possible toutefois d’y arriver à un degré de vraisemblance, qui bien souvent ne cède guère à une évidence entière. Savoir lorsque les choses qu’on a démontrées par ces principes supposés se rapportent parfaitement aux phénomènes que l’expérience a fait remarquer; surtout quand il y en a un grand nombre, et encore principalement quand on se forme et prévoit des phénomènes nouveaux qui doivent suivre des hypothèses qu’on emploie, et qu’on trouve qu’en cela l’effet répond à notre attente.” (Huygens 1992, 48).
- 14.
Descartes was a pure deductivist regarding the first principles of physics (the laws of motion are directly deduced from our innate ideas of God’s immutability, and they would hold in any possible world). However, when one comes to the particular physics of this actual world, the method actually applied by Descartes was hypothetico-deductive, as can be seen in parts 3 and 4 of his Principles of Philosophy. See especially Descartes (1985a), book IV, § 205, 289–90 where Descartes uses the cipher model to account for the kind of moral certainty achievable by the hypothetical method. On this dual aspect of Cartesian methodology, see Hamou (2002).
- 15.
In the refined version of the method, however, prediction and antediction of known phenomena need to be complemented by some sort of ‘independent or collateral support’ in order to answer the classical objection that a conjecture may be a pure fiction constructed in an ad hoc manner in order to account for a given set of phenomena. For example, the conjecture should be able to explain or predict unexpected or foreign phenomena, or empirical data which were not included among the data set which the hypothesis had originally been devised to explain. The fact that the ‘attractive force’ hypothesis not only accounts for the astronomical phenomena for which it has been devised, but can also be used for explaining the tides, or the precession of equinoxes, or the variation of the pendulum at different places on the earth is a good example of such ‘consilience of inductions’ (to borrow Whewell’s formula). See Laudan (1981c), 128sq.; Whewell (2001a), 101.
- 16.
Reid (2002), 82. Reid quotes Hartley (1749), vol. I, 15–6: “Thus we admit the key of a cypher to be a true one when it explains the cypher completely and the decipherer judges himself to approach to the true key, in proportion as he advances in the explanation of the cypher; and this without any direct evidence at all. And as the false and imperfect keys which turn up to the decipherer in his researches, prepare the way for the discovery of the true and complete one, so any hypothesis that has so much plausibility, as to explain a considerable number of facts, helps us to digest these facts in proper order, to bring new ones to light, and to make experimenta crucis for the sake of future Inquirers. The rule of false affords an obvious and strong instance of the possibility of being led, with precision and certainty, to a true conclusion from a false position”. In Hartley’s view it is therefore quite clear that the experimentum crucis comes as a judgmental criterion at the end of a trial and error hypothetical procedure. See also Hartley (1749), vol I, 347.
- 17.
Here is how Pierre Duhem characterizes this eliminative procedure: “Do you wish to obtain from a group of phenomena a theoretically certain and indisputable explanation? Enumerate all the hypotheses that can be made to account for this group of phenomena; than, by experimental contradiction eliminate all except one; the latter will no longer be a hypothesis, but will become a certainty” (Duhem 1954, 188).
- 18.
Jevons (1892), 518–9.
- 19.
Jevons is quite explicit on the fact that a crucial experiment is not simply a concerted experiment designed to pick out one causal explanation against possible others. It must also be an effective refutation of a full-blown concurrent theory: “Pascal’s experiment of causing a barometer to be carried to the top of the Puy-de-Dôme has often been considered as a perfect experimentum crucis, if not the first distinct one on records; but if so we must dignify the doctrine of nature’s abhorrence of a vacuum with the position of a rival theory. A crucial experiment must not simply confirm one theory but must negative another, it must decide a mind that is in equilibrium as Bacon says.” (Jevons 1892, 519).
- 20.
See in this volume the contribution by Siegfried Bodenmann (Chap. 6).
- 21.
In fact the experiment is not a complete refutation of the corpuscular theory of light, but only of the way refraction was usually modeled in this theory, in terms of small range attractive forces directed toward the denser medium at the separating line between two mediums. See Duhem (1954), and for a more nuanced view: Sabra (1981), 315–317.
- 22.
See Bacon (2004), “The first book of Aphorisms” 105, 162–3.
- 23.
Ibid., “The second book of Aphorisms” 20, 261.
- 24.
Ibid, “The second book of Aphorisms” 19, 261: “…if we do not yet possess good and true notions of simple natures, how can the Exclusive process be put right?”
- 25.
Ibid, “The second book of Aphorisms” 36, 319–321.
- 26.
The proposed crucial experiment—an observation made in the Panama Strait—is, on Bacon’s own admission, only partly decisive: “Now a decision for or again this seems safe provided that we assume that the Earth is stationary. But if the Earth turns, it could well be that the different rates of rotation of Earth and sea (in point of speed or impetus) produce a violent piling up of the waters or high tide, followed (when the waters can stand no more accumulation) by a falling back or ebb.” (ibid., 323) Bacon will examine the question of the motion of the Earth in a next example of crucial instances.
- 27.
Bacon gives no less than ten examples which cover a large range of ‘disputed’ questions in early modern natural philosophy and cosmology: two are concerned with the nature and cause of the tides; two with the motion of the earth (diurnal and annual), the others touch on gravity, magnetism, the nature of the corporeal substance of the moon, projectile motion, explosion of gunpowder, the fleeting nature of the flame (ibid., 320–339).
- 28.
See Hesse (1964).
- 29.
Hooke (1665), The Preface, g1.
- 30.
See Descartes’s Discourse on the Method (Part Six): “I must also admit that the power of nature is so ample and so vast, and these principle so simpe and so general, that I notice hardly any particular effect of which I do not know at once that it can be deduced from the principles in many different ways; and my greatest difficulty is usually to discover in which of these ways it depends on them. I know no other means to discover this than by seeking further observations [French: experiences] whose outcome vary according to which of these ways provides the correct explanation.” (Descartes 1985, 144; Descartes 1969–78, vol. VII, 64–65). For Descartes, the need for crucial experiments is related to the fact that the particular phenomena of nature are, so to speak, under-determined by the general laws of motion and collision. They crucially depend on certain initial conditions (the distribution of parcels of matter of various sizes and motions in the plenum). Under other conditions, the same general laws would have produced different phenomena.
- 31.
See Robert Hooke’s A Discourse of Earthquakes, in Hooke (1705), 330. See also On Comets and Gravity, in ibid., 173. This Hookian usage of the terms analysis and synthesis is rather unorthodox. Hooke insisted on the demonstrative aspect of Baconian induction, and for that reason he gave the name ‘synthesis’ to the regressive process that goes from effect to causes, which is more ordinarily designated as ‘analysis’ (see for example the very last pages of Newton’s Opticks (Newton 2007, 404–406). On the other hand the ‘analytical’ method, which for Hooke goes from causes to effects, is conjectural. It is a method “wherein from an hypothesis being supposed or a premeditated design, all the phaenomena of the subject will be a priori foretold, and the effects naturally follow as proceeding from a cause so and so qualified and limited. And in truth the synthetic way by experiments observations, etc. will be very slow if it be not often assisted by the Analytick, which proves of excellent use, even tho’ it proceed by a false supposition, for that the discovery of a Negative is one way of restraining and limitating an affirmative.” (Hooke 1705, 330).
- 32.
- 33.
Hooke (1705), 331.
- 34.
Hooke (1665), 34.
- 35.
The phrase ‘experimenta crucis’ appears in another interesting context, in the Discourse of Earthquakes (Hooke 1705, 352). Discussing the much debated question of the shape of the earth (prolated spheroid or oblong), Hooke suggested several observations and trials necessary to prove the hypothesis he favors, that the shortest diameter of the earth is that of the axis of rotation. These trials are “direct and positive and may be truly call’d experimenta crucis according to the Lord Verulam”. Hooke mentions the use of “clocks, kept under or near the aequinoxial, but whose time had been adjusted to the time by the sun or star at much greater latitude” in order to “assess the true gravity of the earth considered simply without the composition of the vertiginous movement”, and—“a much more difficult experiment, but yet much more positive and convincing than any other”—“the measuring of the quantity of a degree of latitude upon the earth in two places very much differing in latitude.”
- 36.
- 37.
See Worrall (2000).
- 38.
Newton (1958), 50–51.
- 39.
Newton (1959–1977), vol. I, 96–7.
- 40.
Newton (1959–1977), vol. I, 113: Hooke to Oldenburg, 15 Feb. 1671/2.
- 41.
Ibid. p. 114.
- 42.
In a provocative passage of his methodological discussion of the Lecture on Earthquakes (circa 1686–1687) Hooke gave Newton’s Principia as an example of his own ‘analytical method’: “An instance of which kind [the analytical method] I designed some years since to have given this Honourable Society in some of my Lectures upon the motions and influences of the Caelestial Bodies if it had been thought fit; but I understand the same thing will now be shortly done by Mr. Newton in a Treatise of his now in the press.” (see supra footnote 34).
- 43.
Newton (1959–1977), vol. I, 173: Newton to Oldenburg, 11 June 1672.
- 44.
Ibid., 174.
- 45.
- 46.
Newton (1959–1977), vol. I, 169 (English translation De Beer; Latin text: 164).
- 47.
In a recent essay, Dana Jalobeanu also argued that there is a distinctively Baconian outlook in Newton’s first paper on color. She suggested however that Newton gave to crucial experiments “a dogmatic twist of which neither Bacon nor Hooke could have approved” (Jalobeanu 2014, 62).
- 48.
- 49.
- 50.
- 51.
See Newton (1704), book I, in part I, prop. II, exper. 6, 45sq.
- 52.
Laymon (1978).
- 53.
Lohne (1968), 189–90.
- 54.
- 55.
See Schaffer (1989).
- 56.
This is not to say that Newton’s methodology is not evolving. See Ducheyne (2012), especially chapter 5, where it is argued that Newton had to realize in the Opticks that the “rather extremist methodological position” (Guicciardini 2009, 21 quoted by Ducheyne 2012, 199) defended in his earlier writings was untenable, especially his claim that the science of colors could be made ‘mathematical’.
- 57.
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Hamou, P. (2018). Experimentum crucis: Newton’s Empiricism at the Crossroads. In: Bodenmann, S., Rey, AL. (eds) What Does it Mean to be an Empiricist?. Boston Studies in the Philosophy and History of Science, vol 331. Springer, Cham. https://doi.org/10.1007/978-3-319-69860-1_4
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