Atoms and the ‘Analogy of Nature’: Newton’s Third Rule of Philosophizing

  • J. E. McGuire
Chapter

Abstract

As in the case of ancient atomism, the revival of atomistic doctrines in the seventeenth century gave rise to questions regarding the existence and properties of primordial entities. With their insistent emphasis on sensory experience as a foundation of physical knowledge, the English experimental empiricists were faced with various epistemological problems. The majority, such as Robert Hooke and Henry Power, believed that atoms could in principle be observed: hence their problem was not the nature of knowledge of the microscopic, but rather how our knowledge could be extended into that realm.1 Thinkess such as Henry More and Ralph Cudworth tended to the view that, even if we could observe atoms, it would not add to our knowledge of first principles.2 Newton, and to some extent Locke, were confronted with a more difficult problem. Simply stated it is this: are there justificatory principles by which to sanction inferences from what is observable to what in principle is unobservable? If the basis of natural knowledge is strictly confined to what is actually or possibly observable, how can any claims be established about the nature and existence of atoms? The following study will refer to these questions as the problem of transduction;3 moreover it will be concerned primarily to analyse Newton’s use of the phrase ‘the analogy of Nature’. In its best known context that phrase appears in the Rules of Philosophizing prefixed to the third Book of the Principia in 1713.

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Notes

  1. 1.
    For a detailed discussion of this approach with a full analysis of a range of texts see Laurens Laudan ‘The Clock Metaphor and Probabilism: The Impact of Descartes on English Methdoological Thought, 1650–65’, Annals of Science 22 (1966), 81–97. I am grateful to Charles B. Schmitt Laurens Laudan, Gerd Buchdahl and John Yolton for comments on an early draft of this paper. They are in no way responsible for its interpretatin.Google Scholar
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    See Henry More, Divine Dialogues (London, 1668)Google Scholar
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    Ralph Cudworth, The True Intellectual System of the Universe (London, 1678).Google Scholar
  4. 2c.
    In his study Philosophy, Science and Sense Perception (The Johns Hopkins Press, Baltimore, 1964), Maurice Mandelbaum has used the term ‘transdiction’ in designating this problem. To conform more with the usage of the terms ‘deduction’ and ‘induction’, I have decided to use the term ‘transduction’, i.e. ‘leading across’. In no way do I wish to imply thereby that the latter is a special type of ‘ inference’; rather, the term is used to designate a problem recognized in seventeenth-century natural philosophy.Google Scholar
  5. 4.
    Sir Isaac Newton, The Mathematical Principles of Natural Philosophy, translated by Benjamin Motte (London, 1729), vol. II, 203. I have altered the Latin of the statement of the rule in the interest of accuracy. The corresponding Latin is in the appendix to this paper. The original is found in Isaac Newton, Philosophiae Naturalis Principia Mathematica (Cambridge, 1713), 357.Google Scholar
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    Another such integral element is homogeneity. Though never explicitly stated by Newton, this is a fundamental presupposition lying behind his identification of a quantity of matter with its vis inertiae, a proportionality questioned by Roger Cotes in a letter of February 1711/2. See Joseph Edleston, Correspondence of Sir Isaac Newton and Professor Cotes (London, 1850), 65–66.Google Scholar
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    This is the received view as developed in the writings of Basil Willey, The Seventeenth-Century Background (London, 1934)Google Scholar
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    Benjamin Martin, Pilosophia Britannica: or a New and Comprehensive System of the Newtonian Philosophy (Reading, 1747), 1–42. In his first lecture, Martin discusses Newton’s four rules in some detail. Thus when ‘we take survey of the visible world’, we conclude that all bodies ‘consist of one and the same sort of Matter or Substance’. He concludes that ‘Matter, thus variously modified and configurated, constitutes an infinite variety of bodies, all of which are found to have the following common Properties ’.Google Scholar
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    George Adams, Lectures on Natural and Experimental Philosophy (London, 1794), vol. II. In a lengthy lecture entitled ‘In the method of Reasoning in Natural Philosophy’ Adams concludes his discussion of the history of method by analysing Newton’s first three rules. Of the third rule he says that it allows us ‘by analogy to extend our conclusion to all other bodies, and thus make it universa: a way of reasoning, that is agreeable to the harmony of things and to the old maxim ascribed to Hermes (p 134). For this maxim see note 40 below, on Maclurin. Adams is drawing on Maclaurin’s treatise.Google Scholar
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    William Nicholson, An Introduction to Natural Philosophy (London, 1805), vol. I. In his introduction he discusses intuition, demonstration, and probabilistic knowledge, saying of natural philosophy that it is based on analogy: ‘To give stability to this science, it is necessary to admit no probabilities, as first principles of analogy, but those which possess the strongest and most incontrovertible resemblance to truth. For this purpose, the following rules are adopted’: the first three rules are then quoted without comment.Google Scholar
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    William Whewell, On the Philosophy of Discovery (London, 1860), chapter XVIII, 181–200, section 14. Whewell is mainly concerned in this chapter with the notion of vera causa as discussed in Newton’s first rule. He points out, however, that the third rule’s conception of universal laws in inconsistent with the stricture of the fourth rule that a ‘law may be inaccurate’. See also Philosophy of the Inductive Sciences (London, 1840), vol. I, 416, where Whewell observes that the third rule is circular.Google Scholar
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    James Challis, ‘On Newton’s “Foundations of all Philosophy”‘, Phil. Mag. 26 (1863), 280–292. In this particular article Challis is attempting to base a theory of science on Newton’s third rule. These discussions are the most interesting in the literature I have examined. Most of these writers are concerned with the problem of generalizing properties of matter, rather than with Newton’s criterion for deciding essential qualities. Many other writers such as Halley, Stirling, Ferguson, Desaguilers, Wright and Worster mention or refer to the rule; these with the above references are more than sufficient to establish the widespread influence of this aspect of Newton’s methodology throughout the eighteenth and early nineteenth centuries. I am grateful to Laurens Laudan for the references to Condillac and Musschenbrock, and to Peter Heimann for calling attentinn to Higgins.Google Scholar
  27. 10a.
    This question is discussed with great vigour and in detail by James Hutton in his Dissertations on Different Subjects in Natural Philosophy (Edinburgh 1792), part III, ‘Physical Dissertations on the Powers of Matter and Appearance of Bodies’, and in his An Investigation of the Principles of Knowledge, and of the Process of Reason, From Sense to Science and Philosophy (Edinburgh, 1794), vol. II, section XII. Hutton makes it clear by referring to unnamed contemporaries that the problem of identifying matter with bodies or with some sort of unperceived theoretical enttty was a live issue in the late eighteenth century. His own position is unambiguous. Identifying matter with intensive powers he states: ‘Matter as a thing distinctly different from body has not been observed by us nor ever can be made the subject of our observation. Our immediate knowledge, or all external information comes necessarily from sensible and perceptible bodies, which being formed of matter must be distinctly different from it’, Dissertations, part III 306.Google Scholar
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    A similar distinction is made by the Newtonian Thomas Exley, Principles of Natural Philosophy: or, a New Theory of Physics, Founded on Gravitation, and Applied in Explaining the General Properties of Matter (London, 1829). Exley makes a distinction between ‘The theoretical constutution of matter’, section II, 6–45, and ‘The theoretical construction of bodies’. In Postulate I (p. 3) he states: ‘Let it be granted that an atom of matter consists of an indefinitely small sphere of repulsion, which is the central part of an indefinitely extended concentric sphere of attraction’; drawing on this postulate, Proposition I of section II states: ‘If matter be constituted, as in post. I., it will be capable of rest and motion, as will also the bodies consisting of such matter’. [Italics mine.] Exley’s distinction is really that between ordinary matter and ‘theoretical’ matter; since in Definition I of section I he defines matter as ‘that substance which we perceive by the senses’.Google Scholar
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    Tullio Gregory, ‘Studi sull’Atomismo de Seicento. David van Goorle e Daniel Sennert’, Giornale Critico della Filosofia Italiana, Fasc I (1966), 44–63; W. Subow, ‘Zur Geschichte des Kampfes zwischen dem Atomismus und dem Aristotelismus im 17. Jahrhundert (Minima naturalia und Mixtio)’, in N. A. Figurowski et al., Sowjetische Beiträge zur Geschichte der Naturwissenschaft (Berlin, 1960), 161–191Google Scholar
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    David J. Furley, Two Studies in the Greek Atomists (Princeton 1967) 24. The sentence is from Furley’s translation of Epicurus’s Letter to Herodotus. Furley’s treatment of the use of analogy in the atomic theory of Epicurus is important and throws light on Gassendi’s though.Google Scholar
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    The translation is mainly based on Dialogues concerning Two New Sciences, translated by Henry Crew and Alfonso De Salvo (New York, Dover Publications, n. d.), 40–41. I have also consulted Thomas Salisbury’s translation, Mathematical Discourese and Demonstrations touching Two New Sciences (London, 1665), 33. I am grateful to James MacLachlan of the University of Toronto for calling my attention to this passage.Google Scholar
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    Isaac Newton, Optice: sire de Reflexionibus, Refractionibus, Inflexionibus & Coloribus Lucis (London 1706), 171. A similar distinction between and a use of, these verbs is found in Descartes’s Regulae which Newton probably knew. In Rule XII we find him saying while dis cussing the properties of magnets: ‘Sed insuper ut quaestio sit perfecta, volumus illam omnimo determinari, adeo ut nihil amplius quaeratur, quam id quod deduci potest ex datis.’ (Italics mine.) Œuvres de Descartes, edited by Charles Adam and Paul Tannery (Paris, 1908), vol. X, 431. Also in Rule XII we find: ‘ . primo diligenter colligit illa omnia quae de hoc lapide habere potest experimenta, ex quibus deinde deducere conatur qualis necessaria sit naturam simplicium mixtura ad omnes iilos ’. There is no doubt that there are abundant scholastic precedents for this usage. Like Newton, Descartes is clearly not using ‘deduce’ in the sense of ‘formally deduce’. It is not unlikely that Newton was influenced by Descartes, since both were more concerned with the mode of establishing principles rather than with their explictt verification. A similar observation has been made of Galileo with respect to establishing principles by E. McMullin. See his Introduction in Galileo, Man of Science (Basic Books, New York, 1967), 13.Google Scholar
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    Locke, 3.6.12, p. 213. Surprisingly, Locke scholars have scarcely commented on his adherence to the chain of being. A. S. Pringle-Pattison has a short footnote reference to it in his edition of An Essay concerning Human Understanding (Oxford, 1924), 341–342. What he says follows almost entirely A. C. Fraser’s footnote comment in his edition reproduced by Dover (New York, 1959), vol. II, 380–381. Both fail to see how these ideas provide part of the general framework of Locke’s Essay, and content themselves with saying that they are ‘more comprehensive speculation than is usual with him’, Fraser, op. cit., 380.Google Scholar
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    John Theophilus Desaguliers: The Newtonian System of the World the Best Model of Government: an Allegorical Poem (London, 1728). Nehemiah Grew in his Cosmologia Sacra: or a Discourse of the Universe as it is the Creature and Kingdom of God (London, 1701) also connects nature, religion, government and society by the use of analogy and Providnntialism. The New England Divine Jonathan Edwards writing early in the eighteenth century in developing his theory of reality from Newton’s doctrine of gravitation and the Cambridge Platonist doctrines of God and space, makes analogical connections which echo Cheyne. See his Dissertation on the End For which God Created the World, in Works (New York, 1881), vol. II, 201f. In Images and Shadows of Divine Things (Yale, 1948), the moral and religious worlds are reflected in the physical world. He holds like Cheyne that just as the planets are attracted to the sun so minds are attracted to God by ‘moral gravity’ or love.Google Scholar
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    See Chapter 5. Though Newton had a notion of the conservation of matter, with respect to momentum it was not independent of active principles. The former had to be periodicalyy ‘recruited’. The sensibility of Newton’s thought regarding conservation seems to hark back to the ‘biological’ thought of such thinkers as Power and Glisson who moved from the material to the immaterial, partly because they had no conscious notion of a ‘state’ of matter. With respect to both matter and motion Robert Hooke had a relatively clear notion of conservation: ‘Both these Powers I take to be the immediate Product of the Omnipotent Creato, and immutable in themselve, without a like command of the same Power; and always to act in a regular and Uniform Geometrical or Mechanical Method; which Method by diligent Observation and curious Scrutiny may by natural and artifical Means be discovered, and, as I conceive, reduced under certain Rules, and Geometrically demonstrated.’ Robert Hooke, Postumous Works (London, 1705), 73. Hooke derived his ideas on conservation from Genesis, pp. 97, 172, 175. For him matter and motion are appearances of one ‘POWER’.Google Scholar
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    But he also conceived micro-particles as having properties different from gross bodies. There is also a strong possibility that Newton may have conceived the particles of his later aethereal medium to be noninertial. In all three editions of the Principia, definition I, which is concerned with the notion of the quantity of matter (mass), seems to contrast ponderable bodies with the aether; for Newton says that he has ‘no regard in this place to a medium, if any such there is, that freely pervades the interstices between the parts of bodies’. This conjecture is strengthened by Newton’s observation in the intended letter to Hartsoeker (op. cit., note 138) of ‘a power seated in (an immaterial) a substance in wch bodies move & flote without resistence & which has therefore no vis inerttae ’. There is furthermore a curious inconsistency in Newton’s thought, displayed not only in the difference between these speculations and the third rule, but in the rule itself. In the remarks to the rule he speaks of ‘The extension, hardness, impenetrability, and vis inertiae of the whole’, resulting ‘from the extension, hardness, impenetrability, mobility and vis inertiae of the parts: and thence we conclude the least particles of all bodies to be all extended, and hard, and impenetrable, and moveable, and endow’d with their vires inertiae’. Not only does this commit the fallacy of composition, but the reasoning is evidently circular since the qualities of bodies are held to be known through experience alone. In any event, the possibiltty of micro-entities different from gross bodies occurred to Newton as early as 1663 in his Questiones quaedam Philosophiae (U. L. C. Add. 3996). He states there four possible positons ‘Off yt first mater’, namely: ‘Whither it be mathematicall points: or Mathematicall points & parts: or a simple entity before division indistinct: or individuals i.e. Attomes’ (Folio 88r). Newton rejects the other positions and argues for Gassendist-like atoms, which he associates with Henry More’s notion of ‘indiscerpible’ parts (Folio 89).Google Scholar
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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • J. E. McGuire
    • 1
  1. 1.Department of History and Philosophy of ScienceUniversity of PittsburghUSA

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