Thomas Harriot and Atomism: A Reappraisal

For considerations of the religious difficulties confronting the revival of atomism see, for example, Westfall R. S. , Science and religion in seventeenth-century England (New Haven, 1958); and Sailor D. B. , “Moses and atomism”, Journal of the history of ideas, xxv (1964), 3–16. The philosophical problems have not been granted the analysis they deserve but for indications see van Melsen Andrew G. , From atomos to atom: The history of the concept atom (New York, 1960); Dijksterhuis E. J. , The mechanisation of the world picture , trans, by Dikshoorn C. (Oxford, 1961); Zubov V. P. , “Zur Geschichte des Kampfes zwischen dem Atomismus und dem Aristotelismus im 17 Jahrhundert (minima naturalia und mixtio)”, in Harig G. (ed.), Sowjetische Beitrage zur Geschichte der Naturwissenschaft (Berlin, 1960), 161–91; and Boas Marie , “The establishment of the mechanical philosophy”, Osiris , x (1952), 412–451.

A number of thinkers who come into this category, Fracastoro, Cardano, Telesio, Patrizi, Bodin, van Helmont, Sennert and others, are dealt with in Lasswitz K. , Geschichte der Atomistik vom Mittelalter bis Newton (2 vols, Hamburg and Leipzig, 1890).

Robert Boyle shows his awareness of two of the major problems: The possibility of void space, and whether matter is infinitely divisible or not, in Some specimens of an attempt to make chymical experiments useful to illustrate the notions of the corpuscular philosophy, in Works (6 vols, London, 1772), i, 355. If we take just the problem of void space we can see that both Descartes and Hobbes denied the possibility of vacua, giving their, assent to many of the arguments raised against it by Aristotle. See Descartes R. , Principles of philosophy: Second part, of the principles of material things, Principles IV-XX, in The philosophical works , trans, by Haldane E. S. and Ross G. R. T. (2 vols, Cambridge, 1968), i, 254–64; and Hobbes Thomas , The elements of philosophy, the first section, concerning body, pt II, chs vii and xxvi, in The English works , ed. by Molesworth William Sir (11 vols in 12, London, 1839–45), i, 97 and 414–25. Pierre Gassendi managed to reject all Aristotelian influence but had to go to great pains to establish his own theory which did allow the existence of void spaces. See Gassendi P. , Syntagma philosophicum, Bk II, in Opera omnia (6 vols, Lyon, 1658; repr. Stuttgart - Bad Cannstatt, 1964), i, 179–228.

See Shirley J. W. (ed.), Thomas Harriot, Renaissance scientist (Oxford, 1974). This includes an extensive bibliography of secondary sources, pp. 169–74.

North John , “Thomas Harriot and the first telescopic observations of sunspots”, in Shirley , op. cit. (ref. 4), 129–57. For accusations of plagiarism against Descartes, see the article on Harriot in Biographia britannica: Or, the lives of the most eminent persons who have flourished in Great Britain and Ireland… (6 vols, London, 1747–66), iv, 2542. Harriot also anticipated the sine law of refraction before Snell and Descartes; see Shirley J. W. , “An early experimental determination of Snell's Law”, American journal of physics, xix (1951), 507–8. For a brief general survey of Harriot's achievements, see Rosen Edward , “Harriot's science: The intellectual background”, in Shirley, op. cit. (ref. 4), 1–15.

Kargon R. H. , Atomism in England from Harriot to Newton (Oxford, 1966).

ibid., 24.

ibid., 36.

ibid., 42.

Ibid ., 26. Kargon has failed to notice that Harriot's conception of atoms as non-extended mathematical points, which he discusses on p. 25, is completely incompatible with atoms having “magnitude” and “shape”: P. 26. Furthermore, here and elsewhere Kargon proceeds as though there were no significant differences between Democritus and Epicurus. However, it is now clear that Democritus tried to develop a theory of mathematically indivisible atoms, while Epicurus was content to make them merely physically indivisible. See Furley D. J. , “Indivisible magnitudes”, in Two studies in the Greek atomists (Princeton, 1967), 3–158, esp. pp. 79–103.

Jacquot Jean , “Thomas Harriot's reputation for impiety”, Notes and records of the Royal Society of London, ix (1952), 164–87, pp. 178 and 182. See also idem, “Harriot, Hill, Warner and the new philosophy”, in Shirley , op. cit. (ref. 4), 107.28.

Harriot Thomas , A briefe and true report of the new found land of Virginia (London, 1588).

Harriot Thomas , Artis, analyticae praxis, algebraicis nova methodo resolvendas (London, 1631).

Presumably the editors had as much trouble with his papers as later scholars. See Tanner R. C. H. , “The study of Harriot's manuscripts, I: Harriot's will”, History of science, vi (1967), 1–16.

For a complete list of these extensive remains see the bibliography in Shirley , op. cit. (ref. 4), 166–8.

British Library, Add. MS. 6782b, f. 362r-374v; and Add. MS. 6785b, f. 436–7. See also Harley B. L. MS. 6002, f. 2–10 for a clearer copy.

B. L. Harley MS. 6002, f.10. Presumably it is the haphazard, inchoate and illegible nature of Harriot's papers which has prevented their publication.

B. L. Harley MS. 6002, f. 5r. For a full examination of Zeno's arguments see Lee H. D. P. , Zeno of Elea: A text with translation and notes (Cambridge, 1936); and Vlastos Gregory , “Zeno of Elea”, in The encyclopaedia of philosophy (8 vols, New York, 1967), viii, 376–7.

B. L. Add. MS. 6782b, f. 362 (Harley MS. 6002, f. 6v).

B.L. Add. MS. 6782b, f. 363r. (Harley MS. 6002, f. 7r).

B.L. Add. MS. 6782b, f. 364.

B.L. Add. MS. 6782b, f. 367, 368.

B.L. Add. MS. 6782b, f.365.

See Jacquot , “Harriot's reputation”, op. cit. (ref. 11), for an account of Torporley. We will be considering Torporley again later.

Ibid ., 166–7 and passim; and Shirley J. W. , “Sir Walter Ralegh and Thomas Harriot”, in Shirley , op. cit. (ref. 4), 16–35, pp. 23–27.

The phrase is quoted by Aubrey John , Brief lives , ed. by Clark Andrew (2 vols, Oxford, 1898), i, 286; and Wood Anthony à , Athenae oxonienses, 3rd ed., ed. by Bliss P. (6 vols, London, 1813–20), ii, col. 301.

Kristeller P. O. , “Paduan Averroism and Alexandrism in the light of recent studies”, in Renaissance thought II: Papers on humanism and the arts (New York, 1965), 111–18, p. 117.

Jacquot , “Harriot's reputation” (ref. 11), 179.

Glanvill Joseph , Scire/i tuum nihil est: Or, the author's defence of the vanity of dogmatizing etc. (London, 1665), 60. For a further denunciation of “Aristotelian atheism” see Tillotson John , The works…, 3rd ed. (London, 1701), 11–13.

See ref. 26 above.

See Harriot's letter to Theodore de Mayerne (his doctor) in B.L. Add. MS. 6789, f.446v.; letter from Lower to Harriot, 6 February 1610, Add. MS. 6789, f.427-8; and his will, which is transcribed in Stevens Henry , Thomas Harriot, the mathematician, the philosopher, and the scholar… (London, 1900), 193–203.

B.L. Add. MS. 6788, f.493r. exnihilo nihil fit uno nihil aliud duobus nihil tertium Tribus quodlibet.

Sion College MS. ARC L40. 2/E10., f.82r (copy at f.88r).

If Harriot's epitaph is to be relied upon, he seems to have been a devout believer in the concept of the Trinity, for he is described as: “Dei Trini—unius cultor piisimus.” See Stevens , op. cit. (ref. 31), 142.

Bruno Giordano , De innumerabilibus immenso et infigurabili; seu de universo et mundis libri octo (Frankfurt, 1591); and De l'infinito universo et mondi (London, 1584).

This reference is presumably the one which Ethel Seaton alluded to in a lecture to the Elizabethan Literary Society in February 1933: See Singer D. W. , Giordano Bruno, his life and thought (New York, 1950), 68. It appears at B.L. Add. MS. 6788, f.67v and I am grateful to an anonymous referee for pointing it out to me.

Massa Daniel , “Giordano Bruno's ideas in seventeenth-century England” Journal of the history of ideas, xxxviii (1977), 227–42, p. 241.

B.L. Add. MS. 6785, f.310v.

See Singer , op. cit. (ref. 36), 26–45; and Yates F. A. , Giordano Bruno and the Hermetic tradition (London, 1964), 205–56.

B.L. Add. MS. 6789, f. 425–6.

Lower is referring to Kepler's De Stella nova in pede Serpentarii (Prague, 1606), see Gesammelte Werke, ed. by Caspar M. (19 vols, Munich, 1937–75), i, 151–292, p. 253.

Letter (now partially lost), dated 6 February 1610. See Rigaud S. P. , “Account of Harriot's astronomical papers”, in Supplement to Dr Bradley's miscellaneous works (Oxford, 1833), 43.

See Shirley J. W. , “The scientific experiments of Sir Walter Ralegh, the wizard earl, and the three magi in the Tower, 1603–1617”, Ambix , iv (1949), 52–66, p. 54; and Kargon , Atomism in England (ref. 6), 15–17.

Aubrey , op. cit. (ref. 26), i, 285–6; Wood , op. cit. (ref. 26), ii, 300.

de Fonblanque Edward , Annals of the House of Percy from the conquest to the opening of the nineteenth century (2 vols, London, 1887), ii, 626–30.

Bruno Giordano , De specierum scrutinio et lampade combinatoria Raymondi Lulli (Prague, 1588). For an account of Bruno's systems of memory see Tocco Felice , Le opere latine di Giordano Bruno (Florence, 1889 and Rome, 1963), 21–101; and Yates F. A. , The art of memory (London, 1966).

Fonblanque , op. cit. (ref. 45), ii, 333.

Bruno Giordano , De gl'heroici furori (Paris, 1585). There is some material of a cosmological interest in this but it is classified as one of the dialoghi morali in Opere italiane, ed. by Gentile G. and Spampanato V. (3 vols, Bari, 1927), ii, 309–519. For the extent of the research into Percy's library see Batho G. R. , “The library of the ‘wizard’ earl: Henry Percy ninth Earl of Northumberland (1564–1632)”, The library, 5th series, xv (1960), 246–61. It is perhaps worth adding that there is not one book by Bruno among the 515 books now known to have been in Ralegh's library, yet there are a number of books on natural philosophy, including works by Agrippa Scaliger Porta Della , and Patrizi . See Oakeshott Walter , “Sir Walter Ralegh's library”, The library, 5th series, xxiii (1968), 285–327.

Hill Nicholas , Philosophia epicurea, democritiana, theophrastica proposita simpliciter non edocta (Paris, 1607, and Geneva, 1619).

See Massa , op. cit. (ref. 37).

Kargon , Atomism in England (ref. 6), 14–15.

Aubrey , op. cit. (ref. 26), i, 319.

ibid., ii, 270.

See the article in Dictionary of national biography.

Although there is no record of Hill's birth date he was seventeen in 1587 when he matriculated at Oxford. Wood , op. cit. (ref. 26), ii, 86.

Aubrey , op. cit. (ref. 26), ii, 192.

Wood , op. cit. (ref. 26), ii, 86–7.

Letter from Isaac Walton dated 2 December 1680 in Aubrey , op. cit. (ref. 26), ii, 15.

Kargon , Atomism in England (ref. 6), 14. My arguments about the insubstantiality of the evidence relating Hill to Harriot have been inspired by my recollections of Hugh Trevor-Roper, “ Hill Nicholas (1570–1610), an English Campanella?”, a paper read at the Warburg Institute, University of London, in 1978. Unfortunately, this remains unpublished. A large part of this paper was devoted to a much fuller survey than the one given here and still pointed to the same conclusion—that there is no evidence which confirms an association between Hill and Harriot.

Perhaps trends are now changing. For a recent reaction against Bruno and the role of his brand of “Hermeticism” see Westman R. S. and McGuire J. E. , Hermeticism and the scientific revolution (Los Angeles, 1977).

Kepler , Gesammelte Werke (ref. 41), xvi, 172 (letter dated 13 July 1608).

Brucker J. J. , The history of philosophy from the earliest times to the beginning of the present century…(2 vols, London, 1791), ii, 515, 516.

Tiraboschi G. , Storia della letteratura italiana (9 vols in 13, Florence, 1805–13), vii, pt ii, 472.

Tocco , op. cit. (ref. 46), 327–31.

Olschki L. , Giordano Bruno (Bari, 1927), 12–14, 51–52. For a brief outline of this controversy together with a defence of Bruno see Greenberg S. T. , The infinite in Giordano Bruno (New York, 1978), 5–8.

Lasswitz , op. cit. (ref. 2), i, 399.

Michel Paul-Henri , The cosmology of Giordano Bruno (Paris/London, 1973), 140, 145.

Atanasijevic K. , The metaphysical and geometrical doctrine of Bruno, as given in his work De triplici minimo, trans, by Tomashevich G. V. (St Louis, 1972), 20, 94, 96, 24. It is worth saying that this work is actually very sympathetic towards Bruno, in spite of these judgements.

Lasswitz , op. cit. (ref. 2), i, 371, and 376; Michel , op. cit. (ref. 67), 145–6. See also de Santillana Giorgio , “De Bruno à Leibniz”, in Reflections on men and ideas (Cambridge, Mass., 1968), 284–98, p. 285.

Massa , op. cit. (ref. 37), has added his voice to Kargon's and Jacquot's to insist that Harriot believed in “the kind of atomism sustained by Bruno” (p. 241) and “adopted Bruno's views” (p. 242). Needless to say, the references Massa supplies do not support his contention.

Bruno , De triplici minimo , in Opera latine conscripta , ed. by Tocco F. and Vitelli H. (3 vols in 8, Florence, 1879–91), i, pt iii, 234.

Aristotle , Physics , 231a21–231b19. See also the pseudo-Aristotelian De insecabilibus lineis, 972a12. For Harriot's consideration of related matters see B.L. Add. MS. 6782b, f.362 (and Harley MS . 6002, f.6v), and f.374v.

Bruno , Opera (ref. 71), i, pt iii, 159–60. Cf. Aristotle, Physics, 231a20–231b6.

Bruno , Opera (ref. 71), i, pt iii, 160.

Ibid.

Michel , op. cit. (ref. 67), 146.

Michel Both , op. cit. (ref. 67), and Atanasijevic , op. cit. (ref. 68) attempt to do this. The latter even considers Bruno to be the precursor of Petronijevic, who has evidently developed a discrete or finitist geometry. I must acknowledge a debt to both these authors whose heroic efforts have helped me to find my way through Bruno's De minimo. However, I feel bound to say that both show a disconcerting tendency to gloss over the many untenable features of Bruno's thought, presumably in an attempt to show it in the best light.

I suppose Aubrey was so enthusiastic simply because he thought it would afford some amusement. See Aubrey , op. cit. (ref. 26), i, 321.

For modern editions of these works see Jonson Ben , The alchemist , ed. by Steane J. B. (London, 1967); and Shadwell Thomas , The virtuoso , ed. by Nicolson M. H. and Rodes D. S. (London, 1966).

For indications of the extent of Jonson's knowledge of alchemy, for example, see Duncan E. H. , “The alchemy in Jonson's Mercury vindicated”, Studies in philology, xxxix (1942), 625–37.

McPherson David , “Ben Jonson's library and marginalia: An annotated catalogue”, Studies in philology, lxxi (1974), Supplement, 1–106, p. 51. Jonson wrote in his copy: “Non lectore tuis opus est sed Appoline tuis” —a cryptic remark but fairly obviously disparaging.

Kargon's opinion has been noted above, ref. 51. See also Harrison C. T. , “The ancient atomists and English literature of the seventeenth century”, Harvard studies in classical philology, xiv (1934), 1–79, p. 5; Massa , op. cit. (ref. 37), 229; and Jacquot J. , “Harriot, Hill, Warner…” (ref. 11), 113.

In our introductory section.

Galilei Galileo , Two new sciences, including centers of gravity and force of percussion , trans, with introduction and notes by Drake Stillman (Madison, Wis., 1974), 19 (59). The page reference in brackets is to the Edizione Nazionale of Le opere (20 vols, Florence, 1890–1909), vol. viii.

ibid., 28 (67), 39 (77).

ibid., 15(54).

ibid., 39(77).

B.L. Add. MS. 6782b, f.369r (and Harley MS. 6002, f.9v). If Harriot was influenced by Bruno he would have had a solution (of a sort) to draw upon. See Bruno , Opera (ref. 71), i, pt iii, 228–9. Once again, it is hard to imagine Harriot or any mathematician taking Bruno seriously.

Galileo , op. cit. (ref. 84), 28–33 (68–72). On “Aristotle's wheel” see the pseudo-Aristotelian Mechanical problems. This is available in translation in Aristotle, Minor works, trans, by Hett W. S. (London, 1963), 343–7.

Galileo's essential agreement with Aristotle here has been forcefully argued in Smith A. Mark , “Galileo's theory of indivisibles: Revolution or compromise?”, Journal of the history of ideas, xxxvii (1976), 571–88.

See above, ref. 20.

B.L. Add. MS. 6782b, f.371r (Harley MS. 6002, f.10).

B.L. Harley MS. 6002, f.9.

Galileo , op. cit. (ref. 84), 46 (83).

ibid., 40–41 (78–79).

B.L. Harley MS. 6002, f.9.

B.L. Add. MS. 6785b, f.436. Cf. Galileo , op. cit. (ref. 84), 47 (85).

B.L. Harley MS. 6002, f.4. This particular jotting only occurs in the copy of Harriot's papers and cannot be found in the original papers. A note tells us, however, that it was found “on a loose paper of Mr Hariots”.

Patrizi Francesco , Nova de universis philosophia (Ferrara, 1591), f.67r.

Bruno , Opera (ref. 71), i, pt i, 151. See Michel , op. cit. (ref. 67), 132–3.

Patrizi , op. cit. (ref. 99), f.66r-67r. For a similar argument in Bruno see Michel , op. cit. (ref. 67), 133.

Patrizi , op. cit. (ref. 99), f.67v. For a fuller consideration of Patrizi's arguments about divisibility see my “Francesco Patrizi and the concept of space” (M.Phil. thesis, University of Leeds, 1977), 120–8.

Bruno , Opera (ref. 71), i, pt iii, 229. Bruno's minima are spherical in shape and these build up to form all other bodies. The smallest triangle, for example, must consist of three minima in a triangular configuration. Similarly, the smallest circle is composed of one minimum, but the next possible circle must consist of seven minima (six contiguous about the central one) and the next possible circle must consist of nineteen minima (twelve contiguous about six, contiguous about one) and so on. See ibid., i, pt iii, 189–90.

Fonblanque , op. cit. (ref. 45), ii, 627 and 629. It is not clear why the work appears twice on the list. It may simply be that there were two copies. However, one of them is listed under the heading “books in quarto” and the other not, yet then was only one edition of the work which was in quarto (Ferrara, 1587). It should be pointed out that this work is a very insignificant piece, consisting merely of a series of definitions and expositions from de puncto, de linea, de linea recta, and so on, through to de triangulis rectilineis. There is no discussion here of a finitis geometry.

On Bruno's anti-Aristotelianism see, for example, Michel , op. cit. (ref. 67), 21, 41 44, and passim; Yates , op. cit. (ref. 39), 251–2. On Patrizi's see Brisca L. M. , “L retorica di Francesco Patrizi o del platonico antiaristotelismo”, Aevum , xxv (1952), 434–61; and Henry J. , “Francesco Patrizi da Cherso's concept of spac and its later influence”, Annals of science, xxxvi (1979), 549–75, pp. 559–60.

Cf. above, ref. 72.

Galileo , op. cit. (ref. 84), 35 (73).

B.L. Add. MS. 6782b, f.362 (Harley MS. 6002, f.6v).

Galilei Galileo , Discorso intorno alle cose che stanno in su l'acqua o che in quella si muovono (Florence, 1612), in Opere (ref. 84), vi, 63–140. For a discussion of the chronological development of Galileo's atomism see Shea W. R. , “Galileo's atomic hypothesis”, Ambix, xvii (1970), 13–27. This must be supplemented, for an adequate treatment of Two new sciences, by Le Grand H. E. , “Galileo's matter theory”, in Butts R. E. and Pitt J. C. (eds), New perspectives on Galileo (Dordrecht, 1978), 197–208.

Galileo , Opere, iv, 105.

Postil to Benedetto Castelli's Errori di Giorgio Coresio, in Galileo , Opere, iv, 281, postil 23.

di Grazia Vincenzo , Considerazioni sopra il discorso di Galileo (Florence, 1613), in Galileo , Opere, iv, 416–17.

Galileo , Two new sciences (ref. 84), 33 and 42 (72 and 80).

ibid., 47–48 (85–86).

Il Saggiatore, in Opere , iv, 213–372. For an exposition of the atoms as described in this work see Shea , op. cit. (ref. 109), 17–22.

Galileo's attempt to explain condensation and rarefaction, which he believes to be a bonus of his account, is distinctly problematic, for example. In fact, it is no better than the Aristotelian account it purports to supersede. Two new sciences (ref. 84), 57 (95–96).

Torporley Nathaniel , A synopsis of the controversie of atoms (B. L. Birch MS. 4458, f.6, and copy f. 7–8), repr. in Jacquot , “Harriot's reputation” (ref. 11), 183–6.

Torporley Nathaniel , Corrector analyticus artis posthumae Thomae Hariote…(Sion College MS. ARC L 40.2/E.10), ff. 7–12. This is reprinted as an appendix to Halliwell J. O. (ed.), A collection of letters illustrative of the progress of science in England from the reign of Queen Elizabeth to that of Charles the second (London, 1841), 109–16.

The extended title includes these promises. The work is discussed in Stevens , op. cit. (ref. 31), 172–6.

Stevens , op. cit. (ref. 31), 172, 176.

Jacquot , “Harriot's reputation” (ref. 11), 186.

Aristotle , Physics, 216b31–217a11.

Letter to Kepler in Kepler, Gesammelte Werke (ref. 41), xv, 367–8. And BL. Add. MS. 6789, f.210; see also f.253.

Kepler , op. cit. (ref. 41), xvi, 32.

Ibid ., 172–3. It is worth remarking that in this letter Harriot cites his compatriot William Gilbert as someone else who defends the concept of the vacuum. This is true but Gilbert only believed in an extramundane vacuum (not interparticulate vacua) and was not an atomist. See Kelly Suzanne , The De mundo of William Gilbert (Amsterdam, 1965), 34–35. Clearly Harriot's theory of refraction is an interesting concept and may well repay further study. As far as I know there is no other discussion beyond that in these letters. It seems likely, therefore, that once again Harriot became aware of insuperable difficulties. For example, there must surely have been numerous reflections of light in the incident medium before ever reaching the refracting medium. I am grateful to an anonymous referee for this suggestion. Furthermore, Torporley makes an equally cogent objection (see next ref.). Interestingly Isaac Beeckman proposed the same explanation for refraction in November 1627; see de Waard C. (ed.), Journal tenu par Isaac Beeckman de 1604 à 1634 (4 vols, The Hague, 1939–53), iii, 28.

Jacquot , “Harriot's reputation” (ref. 11), 185.

Kargon , Atomism in England (ref. 6), 24.

ibid., 26.

Jacquot , “Harriot's reputation” (ref. 11), 182.

B.L. Add. MS. 6782b, f.369 ( Harley MS . 6002, f.9v).