Newton's Training in the Aristotelian Textbook Tradition: From Effects to Causes and Back

I am somewhat suspicious of using the term ‘Aristotelian’ here. Any tradition is modified as different authors interpret it. However, these authors “take the principal concepts and divisions of their natural philosophy from Aristotle's books”. See Reif Patricia , “The textbook tradition in natural philosophy”, Journal of the history of ideas, xxx (1969), 17–32, pp. 19–20. The Aristotelian tradition was not a monolithic whole. For a recent account of the tradition and its variety from Antiquity to the seventeenth century see Leijenhorst Cees Lüthy Chrostoph Thijssen Johannes (ed.), The dynamics of Aristotelian natural philosophy from Antiquity to the seventeenth century (Leiden, Boston and Cologne, 2002).

Near the end of the seventeenth century, the textbook mode of exposition became more and more popular. Direct reading of the Aristotelian text correspondingly began to decline. It was during the seventeenth century that the philosophical textbooks really began to dominate the teaching of the subject in most formal courses in institutions of higher learning. See Schmitt Charles B. , “The rise of the philosophical textbook”, in Schmitt Charles B. (ed.), The Cambridge history of Renaissance philosophy (Cambridge, 1988), 792–804, p. 801.

See Schmitt Charles B. , Aristotle and the Renaissance (Cambridge, MA, and London, 1983), 3, 108.

See Mamiani Maurizio , “To twist the meaning: Newton's regulae philosophandi revisited”, in Buchwald Jed Z. Cohen I. Bernard (ed.), Isaac Newton's natural philosophy (Cambridge, MA, and London, 2001), 3–14.

Mamiani , op. cit. (ref. 4), 4.

I admit that the brute fact that these books were present in Newton's library does not by itself constitute evidence that these books contributed to Newton's conception of natural philosophy.

See Leijenhorst Cees , The mechanisation of Aristotelianism: The late setting of Thomas Hobbes' natural philosophy (Leiden, Boston and Cologne, 2003), 8.

See Hintikka Jaakko Remes Unto , The method of analysis, its geometrical origin and its general significance (Dordrecht and Boston, 1974), 107–8; Westfall Richard , Never at rest: A biography of Isaac Newton (Cambridge, 1980), 377–81; and Dear Peter , Discipline and experience: The mathematical way in the Scientific Revolution (Chicago and London, 1995), 240. McGuire and Tamny have a rather different explanation: They claim that “Newton probably became familiar with the method of analysis and synthesis in a philosophical context” from Thomas Hobbes's Elements of philosophy (1656). See McGuire James E. Tamny Martin (ed.), “Commentary”, in Certain philosophical questions: Newton's Trinity notebook (Cambridge, 1983), 24. Hobbes indeed discusses the synthetical and analytical method as respectively preceding from and ascending to causes (especially in chap. 6 of Of method). The conjecture of McGuire and Tamny can be consistent with my findings. See Hobbes Thomas , Elements of philosophy (London, 1656), and Leijenhorst , op. cit. (ref. 7).

See Crombie Alistair C. , Styles of scientific thinking in the European tradition: The history of argument and explanation especially in the mathematical and biomedical sciences and arts (London, 1994), 283. In an accompanying footnote Crombie refers to the Opticks but not to the Principia. See ibid., 716n.

For a recent account and further references see Guicciardini Niccolò , “Analysis and synthesis in Newton's mathematical work”, in Cohen I. Bernard Smith George E. (ed.), The Cambridge companion to Newton (Cambridge, 2002), 308–38.

Guicciardini , op. cit. (ref. 10), 311.

Guicciardini , op. cit. (ref. 10), 317.

Guicciardini , op. cit. (ref. 10), 319. See especially Guicciardini Niccolö , Reading the Principia: The debate on Newton's mathematical methods for natural philosophy from 1687 to 1736 (Cambridge, 1999), 17–38.

Guicciardini , op. cit. (ref. 13), 38.

From a purely logical point of view this mathematical account of analysis-synthesis is incompatible with Newton's conception of analysis as discovering causes, and synthesis as assuming these causes to explain phenomena (see 3.1). In the mathematical tradition analysis means reasoning from what is sought to what is known and conversely for synthesis. In Newton's view analysis is reasoning from what is known, the effect, to what is sought, the cause, and conversely for synthesis.

Few authors have explicitly labelled Newton's reasoning abductive. See e.g. Smith George E. , “The methodology of the Principia”, in Cohen Smith (ed.), op. cit. (ref. 10), 31–70.

Newton's Principia for instance contained the synthetical method of ultimate ratios as well as the analytical method of fluxions. See Guicciardini , op. cit. (ref. 10), 320–4, and especially Guicciardini , op. cit. (ref. 13), 39–98.

See Westfall , op. cit. (ref. 8), 81–82. Students read Aristotle's Physica, De caelo, and De anima. See especially Allen Phyllis , “Scientific studies in the English universities of the seventeenth century,” Journal of the history of ideas, x (1949), 219–53, p. 220. For a general survey see Costello William T. , The scholastic curriculum at early seventeenth-century Cambridge (Cambridge, MA, 1958).

McGuire Tamny (eds), op. cit. (ref. 8).

Westfall , op. cit. (ref. 9), 84.

Vossius Gerardus Ioannis , Rhetorices contractae, sive partitionum oratorium, Libri V (Oxford, 1631).

McGuire Tamny (eds), op. cit. (ref. 8), 19.

Magirus Johannes , Physiologiae peripetaticae, libri sex cum commentariis (Canterbury, 1619; quotation from 1642 edn). Magirus's treatment of the doctrine of the causes can be found in “Librum I: De natura deque naturalium principiis, affectionibus & accidentibus”, ibid., 1–56. For Magirus's discussion on efficient and final causes, see ibid., 21–25.

Ibid., 26–56.

Ibid., 9, 21.

McGuire Tamny (eds), op. cit. (ref. 8), 15–17.

Magirus , op. cit. (ref. 23), 1.

Stahl Daniel , Axiomata philosophica, sub titulis XX (Cambridge, 1645).

McGuire Tamny (eds), op. cit. (ref. 8), 18.

Stahl , op. cit. (ref. 28), 60ff.

Ibid., 69.

Ibid., 76.

See Jardine Nicolas , “Epistemology of the sciences”, in Schmitt (ed.), op. cit. (ref. 2), 685–711, p. 686.

Dear , op. cit. (ref. 8), 27. Also see Randall John H. , “The development of scientific method in the school of Padua”, Journal of the history of ideas, i (1940), 177–206; Wallace William , Galileo's logic of discovery and proof: The background, content, and use of his appropriated treatises on Aristotle's Posterior Analytics (Dordrecht, Boston and London, 1992), 166–7.

See Jardine , op. cit. (ref. 2), 687–8.

Howell Samuel W. , Eighteenth-century British logic and rhetoric (Princeton, 1971), 13.

I will focus on the similarities in these works. This inevitably harms the content of these works. However, my aim is not to present these books in their full complexity, but to point to some representative features common to the Aristotelian tradition in which Newton was trained. We have to bear in mind that “beneath the umbrella of ‘Aristotelianism’ are a very large number of thinkers of very diverse orientation”. See Schmitt Charles B. , John Case and Aristotelianism in Renaissance England (Kingston and Montreal, 1983), 218. Those interested in a broader perspective I refer to Howell Samuel Wilbur , Logic and rhetoric in England, 1500–1700 (New York, 1961).

For a presentation of this work see Howell , op. cit. (ref. 36), 350–63.

See Harrison John , The library of Isaac Newton (Cambridge, 1978), 182.

Arnauld Antoine Nicole Pierre , Logica sive ars cogitandi (London, 1687), 386.

Ibid., 375.

Ibid., 375–6. Arnauld and Nicole point out that the greatest part discussed here concerning questions was taken from “a manuscript of the Deceas'd Descartes”.

Ibid., 375.

Ibid., 369.

Ibid., 369.

Ibid., 416. I will not insist on this point since these features also are present in the mathematical tradition.

For a presentation see Howell , op. cit. (ref. 36), 292–8. It is bound together with Edward Brerewood's Elementa logicae (edition of 1649). See Brerewood Edward , Elementa logicae (London, 1649), and Harrison , op. cit. (ref. 39), 110, 240. Since Brerewood does not add anything fundamental for my present purposes I will omit a presentation of it here.

Smith Samuel , Aditus ad Logicam (London, 1613), 97.

Ibid., 111.

Ibid., 112. These translations are mine. I have opted for a free translation (without doing harm to the original content).

Ibid., 113.

Ibid., 116.

Ibid., 154.

Howell , op. cit. (ref. 36), 29.

Ibid., 39.

Quoted from ibid., 36.

Quoted from ibid., 39.

Wallis John , Institutio logicae (Oxford, 1687), 212–13.

See Howell , op. cit. (ref. 36), 40–41; and Wallis , op. cit. (ref. 58), 215–17. As we have seen, Arnauld and Nicole also stressed the importance of clear and evident axioms and principles.

Newton Isaac , The Principia: Mathematical principles of natural philosophy, transl, by Cohen I. Bernard Whitman Anne (Berkeley, Los Angeles and London, 1999), 382. The part continues: “It is to these ends that Books 1 and 2 are directed, while in Book 3 our explanation [explicationem Systematis mundani] of the system of the world illustrates these propositions. For in Book 3, by means of propositions demonstrated mathematically in Books 1 and 2, we derive from celestial phenomena the gravitational forces by which bodies tend toward the Sun and toward the individual planets. Then the motions of the planets, the comets, the moon, and the sea are deduced from these forces by propositions that are also mathematical.” Ibid., 382.

Ibid., 415.

In the case of the motion of the Moon, Newton declared as follows: “I wished to show by these computations of the lunar motions that the lunar motions can be computed from their causes by the theory of gravity”, ibid., 869. In Book III, Proposition 24, Newton declared: “Hitherto I have given the causes of the motions of the moon and seas”, ibid., 839.

In the conclusion of his Experimental philosophy (London, 1664), 192, Henry Power used the expression “deducing the Causes of things”. I do not know in what way Power might have been important to Newton's idea of science. Newton owned a copy of the first edition, see Harrison , op. cit. (ref. 39), 221.

See Newton Isaac , Opticks or a treatise of reflections, refractions, inflections and colours of light (New York, 1979), 369.

Ibid., 404–5.

Newton , op. cit. (ref. 60), 943.

Ibid., 53.

Athanasios Raftapoulos calls the immediate cause a “property” and the highest level cause a “cause”. Raftopoulos Athanasios , “Newton's experimental proofs as eliminative reasoning”, Erkenntnis, 1(1999), 91–121, pp. 107–8.

Cohen I. Bernard (ed.), Isaac Newton's papers and letters on natural philosophy (Cambridge, 1978), 54. In the Opticks, immediately after the famous analysis-synthesis piece, Newton declares that he used the method of analysis to discover and prove the “original Differences of the Rays of Light in respect of their Refrangibility, Reflexibility, and Colour, and their alternate Fits of easy Reflection and easy Transmission, and the Properties of Bodies both opake and pellucid, on which their Reflexions and Colours depend” ( Newton , op. cit. (ref. 64), 405; for causal statements on these matters see e.g., ibid. , 57, 113, 119, 244). Thereafter he used the method of composition for explaining the phenomena arising from them (e.g., the rainbow).

Newton Isaac , The optical papers of Isaac Newton, i: The optical lectures 1670–1672, ed. by Shapiro Alan E. (Cambridge, 1984), 433; see also 525.

Ibid., 603.

Ibid., 523; for Newton's explanation of the rainbow, see ibid., 593–601.

McMullin Ernan , “The impact of Newton's Principia on the philosophy of science”, Philosophy of science, lxviii (2001), 279–310, esp. pp. 288–9.

Shapiro Alan E. , Fits, passions, and paroxysms: Physics, method, and chemistry and Newton's theories of colored bodies and fits of easy reflection (Cambridge, 1993), 23.

McMullin , op. cit. (ref. 73), 289.

Bernard Cohen I. , The Newtonian Revolution, with illustrations of the transformation of scientific ideas (Cambridge, 1980), 28, 37.

Cohen , op. cit. (ref. 76), 63.

Newton , op. cit. (ref. 60), 444.

Brackenridge Bruce , The key to Newton's dynamics, the Kepler problem and the Principia (Berkeley, 1995), 26. Hence a centripetal force is a necessary and sufficient condition for the area law. As Newton writes somewhat further: “Since the uniform description of areas indicates the center towards which that force is directed by which a body is most affected and by which it is drawn away from rectilinear motion and kept in orbit, why should we not in what follows use uniform description of areas as a criterion for a center about which all orbital motion takes place in free spaces?” (Newton, op. cit. (ref. 60), 449).

Newton , op. cit. (ref. 60), 446.

He further writes: “The more the law of force departs from the law there supposed, the more the bodies will perturb their mutual motions; nor can it happen that bodies will move exactly in ellipses while attracting one another according to the law here supposed, except by maintaining a fixed proportion of distances one from another. In the following cases, however, the orbits will not be very different from ellipses” ( Newton , op. cit. (ref. 37), 568).

Newton , op. cit. (ref. 60), 451.

De Gandt François , Force and geometry in Newton's Principia, transl. by Wilson Curtis (Princeton, 1995), 267.

Newton , op. cit. (ref. 60), 588–9.

Newton , op. cit. (ref. 60), 415; Newton , op. cit. (ref. 64), 369.

Cohen , op. cit. (ref. 76), 28, 37.

See Ducheyne Steffen , “Mathematical models in Newton's Principia: A new view of the ‘Newtonian Style’”, International studies in the philosophy of science, xix (2005), 1–19. This paper contains a critique of I. Bernard Cohen's “Newtonian Style”.

Smith , op. cit. (ref. 16).

Newton , op. cit. (ref. 60), 567–9.

Newton , op. cit. (ref. 60), 818, 819, 832, 840, 841, 845, 847, 864, 867.

Newton , op. cit. (ref. 60), 943.

Buchdahl Gerd , “Gravity and intelligibility: Newton to Kant”, in Butts R. E. Davis J. W. (ed.), The methodological heritage of Newton (Bristol, 1970), 74–102, esp. p. 81.

See especially Janiak Andrew , “Newton and the reality of force”, Journal of the history of philosophy (forthcoming).

Gingras Yves , “What did mathematics do to physics”, History of science, xxxix (2001), 383–416.

Iliffe Robert , “Abstract considerations: Disciplines and the incoherence of Newton's natural philosophy”, Studies in history and philosophy of science, Part A, xxxv (2004), 427–54, p. 439.

For a thorough account of Newton's concept and practice of unification see Ducheyne Steffen , “Newton's idea and practice of unification”, Studies in history and philosophy of science, Part A, xxxvi (2005), 61–78.

See Newton , op. cit. (ref. 60), 588–9.

See Shapiro Barbara , Probability and certainty in seventeenth-century England: A study of the relationships between natural science, religion, history, law, and literature (Princeton, 1983), 58.

See Van Leeuwen Henry G. , The problem of certainty in English thought 1630–1690 (The Hague, 1963). For a general discussion on the emergence of probability in the seventeenth century, see Hacking Ian , The emergence of probability: A philosophical study of early ideas about probability, induction and statistical inference (Cambridge, 1975); Popkin Richard , The history of scepticism from Erasmus to Spinoza (Berkeley, Los Angeles and London, 1979); and Shapiro , op. cit. (ref. 78).

See Hunter Michael , Science and society in Restoration England (Cambridge, 1981), 180; Hunter points to the “significant methodological differences” between the members. See also his Establishing the new science: The experience of the early Royal Society (Woodbridge, 1989), 207–8. The corresponding chapter (pp. 185–244) in Hunter's books is a reprint of the original paper: Wood Paul Hunter Michael , “Towards Solomon's House: Rival strategies for reforming the early Royal Society”, History of science, xxiv (1986), 49–108.

Glanvill Joseph , quoted in Van Leeuwen , op. cit. (ref. 99), 76.

Schmitt suggested that it could be argued that there was a significant Aristotelian component to Newton's thought. See Schmitt , op. cit. (ref. 3), 28, and op. cit. (ref. 2), 7. He did not provide a thorough elaboration of this and did not specify wherein this Aristotelian component consisted.

For a rough sketch on the preceding period see Schmitt , op. cit. (ref. 3), especially Chapter I.