Synthese

pp 1–19 | Cite as

Constraining (mathematical) imagination by experience: Nieuwentijt and van Musschenbroek on the abuses of mathematics

S.I.: Use & Abuse of Maths

Abstract

Like many of their contemporaries Bernard Nieuwentijt (1654–1718) and Pieter van Musschenbroek (1692–1761) were baffled by the heterodox conclusions which Baruch Spinoza (1632–1677) drew in the Ethics. As the full title of the EthicsEthica ordine geometrico demonstrata—indicates, these conclusions were purportedly demonstrated in a geometrical order, i.e. by means of pure mathematics. First, I highlight how Nieuwentijt tried to immunize Spinoza’s worrisome conclusions by insisting on the distinction between pure and mixed mathematics. Next, I argue that the anti-Spinozist underpinnings of Nieuwentijt’s distinction between pure and mixed mathematics resurfaced in the work of van Musschenbroek. By insisting on the distinction between pure and mixed mathematics, Nieuwentijt and van Musschenbroek argued that Spinoza abused mathematics by making claims about things that exist in rerum natura by relying on a pure mathematical approach (type 1 abuse). In addition, by insisting that mixed mathematics should be painstakingly based on mathematical ideas that correspond to nature, van Musschenbroek argued that René Descartes’ (1596–1650) natural-philosophical project (and that of others who followed his approach) abused mathematics by introducing hypotheses, i.e. (mathematical) ideas, that do not correspond to nature (type 2 abuse).

Keywords

René Descartes (1596–1650) Early eighteenth-century Dutch Republic Bernard Nieuwentijt (1654–1718) Pure versus mixed mathematics Baruch Spinoza (1632–1677) Pieter van Musschenbroek (1692–1761) 

Notes

Acknowledgements

Research for this paper was funded by the Vrije Universiteit Brussel under the form of a Research Professorship. Parts of this essay were delivered at the international workshop ‘The Uses and Abuses of Mathematics in Early Modern Philosophy’ which took place in Budapest on 10 March 2015. I am grateful to its audience for feedback. I am also indebted to the Special Collections Department at Leiden University Library for permission to quote from material in their care, to Ronald Desmet, Koen Lefever, and Jip Van Besouw for comments on an earlier version of this essay, to the editors of this special issue for their encouragement and hard work, and to the two anonymous referees of this journal for valuable feedback.

References

  1. anon. [= Frans Kuyper] (1687). Korte en bondige weederlegging van het wiskunstig bewijs van B. D. Spinosa. S.l.: s.n.Google Scholar
  2. anon. [= Johannes Duijkerius] (1697 [1691]). Vervolg van ’t leven van Philopater. Groningen: Siewert van der Brug [= Aart Wolsgryn].Google Scholar
  3. anon. (1718). [Obituary for Bernard Nieuwentijt]. Maendelyke uitreksels, of Boekzael der geleerde wereld, Pt. 3 (pp. 744–747).Google Scholar
  4. anon. (1720). Catalogus variorum & insignium in omni doctrinarum genere librorum praecipue mathematicorum, quibus usus fuit, dum esset in vivis vir clarissimus & sagissimus Bernardus Nieuwentyt M.D. & urbis Purmurendanae consul & c. Amsterdam/Purmerend: Joannes Oosterwyk/Cornelis Hoogendorp.Google Scholar
  5. anon. (1762). Bibliotheca Musschenbroekiana, sive catalogus librorum. Lugduni Batavorum: Per S. et L. Luchtmans.Google Scholar
  6. Adam, C., & Tannery, P. (Eds.) (1897–1909). Oeuvres de descartes (Vol. 11). Paris: Leopold Cerf.Google Scholar
  7. Bayle, P. (1697). Dictionnaire historique et critique (Vol. 2). Rotterdam: Reiniers Leers.Google Scholar
  8. Bots, J. (1972). Tussen Descartes en Darwin, Geloof en natuurwetenschap in de achttiende eeuw in Nederland. Assen: Van Gorcum & Comp. N.V.Google Scholar
  9. Boyle, R. (1772 [1744]). The works of the honourable Robert Boyle (Vol. 6) (T. Birch, Ed.). London: W. Johnston e.a.Google Scholar
  10. Corneanu, S. (2011). Regimens of the mind: Boyle, Locke, and the Early Modern cultura animi tradition. Chicago/London: The University of Chicago Press.CrossRefGoogle Scholar
  11. Curley, E. (1986). Spinoza’s geometric method. Studia Spinozana, 2, 151–169.Google Scholar
  12. de Pater, C. (1979). Petrus van Musschenbroek (1692–1761), Een newtoniaans natuuronderzoeker. Ph.D dissertation, Utrecht University. Utrecht: Elinkwijk.Google Scholar
  13. de Pater, C. (1995). ’s Gravesande on moral evidence. In M. F. Fresco, L. Geeraedts, & K. Hammacher (Eds.), Frans Hemsterhuis (1721–1790), Quellen, philosophie und rezeption (pp. 221–242). Münster/Hamburg: LIT Verlag.Google Scholar
  14. Douglas, A. X. (2015). Spinoza and Dutch Cartesianism: Philosophy and theology. Oxford: Oxford University Press.CrossRefGoogle Scholar
  15. Ducheyne, S. (2014a). W. J. ’s Gravesande’s appropriation of Newton’s natural philosophy. Part II: Methodological Issues, Centaurus, 56, 97–120.Google Scholar
  16. Ducheyne, S. (2014b). W. J. ’s Gravesande’s appropriation of Newton’s natural philosophy. Part I: Epistemological and Theological issues, Centaurus, 56, 31–55.Google Scholar
  17. Ducheyne, S. (2014c). Celeberrimus Atheismi patronus praecedentis saeculi: Petrus van Musschenbroek’s anti-Spinozism unveiled. Lias, Journal of early modern intellectual culture and its sources, 41, 173–197.Google Scholar
  18. Ducheyne, S. (2015). Petrus van Musschenbroek and Newton’s vera stabilisque Philosophandi methodus. Berichte zur, Wissenschaftsgeschichte, 38, 279–304.CrossRefGoogle Scholar
  19. Ducheyne, S. (2016). Petrus van Musschenbroek (1692–1761) on the scope of physica and its place in philosophy. Asclepio, Revista de historia de la medicina y de la ciencia, 68, article number: 123.Google Scholar
  20. Ducheyne, S. (2017). Curing pansophia through eruditum nescire: Bernard Nieuwentijt’s (1654–1718) epistemology of modesty. HOPOS, 7 (in print).Google Scholar
  21. Freudenthal, H. (1955). Nieuwentijt und der teleologische Gottesbeweis. Synthese, 9, 454–464.CrossRefGoogle Scholar
  22. Garrett, A. V. (2003). Meaning in Spinoza’s method. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  23. ’s Gravesande, W. J. (1717). Oratio inauguralis de matheseos, in omnibus scientiis, praecipue in physicis, usu, nec non de astronomiae perfectione ex physica haurienda. Lugduni Batavorum: Apud Samuelem Luchtmans.Google Scholar
  24. ’s Gravesande, W. J. (1720–1721). Physices elementamathematica, experimentis confirmata, sive introductio adphilosophiam Newtonianam (Vol. 2). Lugduni Batavorum: ApudPetrum & Balduinum Janssonium vander AaGoogle Scholar
  25. ’s Gravesande, W. J. (1734). Orationes duae, Prima De vera, & nunquam vituperata philosophia... Altera De evidentia.... Lugduni Batavorum: Apud Samuelem Luchtmans.Google Scholar
  26. ’s Gravesande, W. J. (1742\(^{2}\) [1720-1721]). Physices elementa mathematica experimentis confirmata, sive introductio ad philosophiam Newtoniam (Vol. 2). Leidae: Apud Johannem Arnoldum Langerak, Johannem et Hermannum Verbeek.Google Scholar
  27. Hall, A. R. (1982). Further Newton correspondence. Notes and Records of the Royal Society of London, 37, 7–34.CrossRefGoogle Scholar
  28. Israel, J. I. (1996). The banning of Spinoza’s work in the Dutch Republic (1670–1678). In W. van Bunge & W. Klever (Eds.), Disguised and overt Spinozism around 1700. E. J. Brill: Leiden/New York/Köln.Google Scholar
  29. Israel, J. I. (2001). Radical enlightenment: Philosophy and the making of modernity, 1650–1750. Oxford: Oxford University Press.CrossRefGoogle Scholar
  30. Jorink, E. (2009). Honouring Sic Isaac, or, exorcising the ghost of Spinoza: Some recent remarks on the success of Newton in the Dutch Republic. In S. Ducheyne (Ed.), Future perspectives on Newton Scholarship and the Newtonian Legacy (pp. 23–34). Brussels: Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten.Google Scholar
  31. Jorink, E. (2010). Reading the Book of Nature in the Dutch Golden Age, 1575–1715. Leiden: Brill.CrossRefGoogle Scholar
  32. Jorink, E., & Zuidervaart, H. (2012). The miracle of our time, How Isaac Newton was fashioned in the Netherlands. In E. Jorink & A. Maas (Eds.), Newton and the Netherlands, How Isaac Newton was fashioned in the Dutch Republic (pp. 13–65). Amsterdam: Leiden University Press.CrossRefGoogle Scholar
  33. Kernkamp, G. W. (1936). De Utrechtsche Universiteit 1636–1936 (Vol. 2). Utrecht: A. Oosthoek’s uitgevers maatschappij.Google Scholar
  34. Klever, W. N. A. (1988). Letters to and from Neercassel about Spinoza and Rieuwertsz. Studia Spinozana, 4, 329–340.Google Scholar
  35. Klijnsmit, A. J. (1991). Spinoza en Verwer: Een zeventiende-eeuws meningsverschil over de grondslagen van de wetenschap. In J. Noordegraaf & R. Zemel (Eds.), Accidentia: Taal-en letterkundige oefeningen voor Jan Knol (pp. 9–20). Amsterdam: Stichting Neerlandistiek VU.Google Scholar
  36. Mancosu, P. (1996). Philosophy of mathematic and mathematical practice in the seventeenth century. Oxford/New York: Oxford University Press.Google Scholar
  37. More, H. (1679). Opera omnia (Vol. 2). Londoni: J. Macock sumptibus J. Martyn & Gualt. Kettilby.Google Scholar
  38. Nadler, S. (2006). Spinoza’s Ethics: An introduction. Cambridge: Cambridge University Press.Google Scholar
  39. Nagel, F. (2008). Nieuwentijt, Leibniz, and Jacob Hermann on infinitesimals. In U. Goldenbaum & D. Jesseph (Eds.), Infinitesimal differences: Controversies between Leibniz and his contemporaries (pp. 199–214). Berlin: Walter de Gruyter.Google Scholar
  40. Nieuwentijt, B. (1694). Considerationes circa analyseos ad quantitates infinite parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus gemetricis. Amstelaedami: Apud Joannem Wolters.Google Scholar
  41. Nieuwentijt, B. (1695). Analysis infinitorum, seu curvilineorum proprietates ex polygonorum natura deductae. Amstelaedami: Apud Jooannem Wolters.Google Scholar
  42. Nieuwentijt, B. (1696). Considerationes secundae circa calculi differentialis principia, & Responsio ad Virum Nobilissimum G.G. Leibnitium. Amstelaedami: Apud Jooannem Wolters.Google Scholar
  43. Nieuwentijt, B. (1718), The religious philosopher: Or, the right use of comtemplating the works of the creator (Vol. 2) (J. Chamberlayne, Trans.). London: J. Senex and W. Taylor.Google Scholar
  44. Nieuwentijt, B. (1725\(^{4}\) [1715]). Het regt gebruik der wereltbeschouwingen, ter overtuiginge van ongodisten en ongelovigen aangetoont. Amsterdam: Joannes Pauli.Google Scholar
  45. Nieuwentijt, B. (1720). Gronden van zekerheid, of de regte betoogwyse der wiskundigen so in het denkbeeldige, als in het zakelyke: Ter wederlegging van Spinosaas denkbeeldige Samestel; en ter aanleiding van eene sekere sakelyke wijsbegeerte. Amsterdam: Joannes Pauli.Google Scholar
  46. Petry, M. (1979). Nieuwentijt’s criticism of Spinoza. Mededelingen vanwege het Spinozahuis (Vol. 15). Leiden: E. J. Brill.Google Scholar
  47. Petry, M. (1981). Kuyper’s analysis of Spinoza’s axiomatic method. In K. Cramer, W. G. Jacobs, & W. Schmidt-Biggemann (Eds.), Spinozas Ethik und ihre frühe Wirkung (pp. 1–18). Wolfenbüttel: Herzog August Bibliothek.Google Scholar
  48. Roux, S. (2010). Forms of mathematization (14th-17th centuries). Early science and medicine, 15, 319–337.CrossRefGoogle Scholar
  49. Sassen, F. (1959). Geschiedenis van de wijsbegeerte in Nederland tot het einde der negentiende eeuw. Amsterdam: Elsevier.Google Scholar
  50. Schliesser, E. (2012). Newton and Spinoza: On motion and matter (and God, of course). The Southern Journal of Philosophy, 50, 438–458.CrossRefGoogle Scholar
  51. Schliesser, E. (forthcoming). Spinoza and the philosophy of science: Mathematics, motion, and being. In M. della Rocca (Ed.), The Oxford Handbook of Spinoza. Oxford: Oxford University Press.Google Scholar
  52. Schuurman, P. (2010). ‘Thou Knowest not the Works of God’: Gisbertus Voetius (1589–1676) and John Locke on learned ignorance. Westminster Theological Journal, 72, 59–69.Google Scholar
  53. Serrurier, J. (1706). Oratio pro philosophia. Trajecti ad Rhenum: Ex officina Guillelmi vande Water.Google Scholar
  54. Spinoza, B. (2002). Complete works (M. L. Morgan, Ed. and intro., S. Shirley, Trans.). Hackett: Indianapolis/Cambridge.Google Scholar
  55. S., B. d. [= Spinoza, B.] (1677). Opera posthuma. S.l.: s.n.Google Scholar
  56. Steenbakkers, P. (1994). Spinoza’s Ethica from manuscript to print: Studies on text form and related topics. Assen: Van Gorcum.Google Scholar
  57. Steenbakkers, P. (2009). The geometrical order in the Ethics. In O. Koistinen (Ed.), The Cambridge companion to Spinoza’s Ethics (pp. 42–55). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  58. Van Besouw, J. (forthcoming). ’s Gravesande on the application of mathematics in physics and philosophy, Noctua.Google Scholar
  59. Van Besouw, J. (ms.). ’s Gravesande Essais de métaphysique: ‘Leibnizian’ considerations on God, goodness, and liberty as foundation of empirical science.Google Scholar
  60. van Blijenbergh, W. (1682). Wederlegging van de Ethica of Zede-Kunst, van Benedictus de Spinosa. Dordrecht: By de Weduwe van Jasper, en by Dirck Goris.Google Scholar
  61. van Bunge, W. (2001). From Stevin to Spinoza, An essay on philosophy in the seventeenth-century Dutch Republic. Leiden/Boston/Köln: E.J. Brill.Google Scholar
  62. van Bunge, W., Krop, H., Leeuwenburgh, B., Schuurman, P., van Ruler, H., & Wielema, M. (Eds.). (2003). Dictionary of seventeenth and eighteenth-Century Dutch philosophers (Vol. 2). Bristol: Thoemmes Press.Google Scholar
  63. van Bunge, L. (2012). Spinoza past and present, Essays on Spinoza, Spinozism, and Spinoza scholarship. Leiden/Boston: Brill.CrossRefGoogle Scholar
  64. Van Bunge, W. (2017). The waning of the Radical Enlightenment in the Dutch Republic. In S. Ducheyne (Ed.), Reassessing the Radical Enlightenment (pp. 178–193). Abington: Routledge.Google Scholar
  65. van der Wall, E. G. E. (2003). The religious context of the early Dutch Enlightenment: Moral religion and society. In W. van Bunge (Ed.), The early Enlightenment in the Dutch Republic (pp. 39–57). Leiden: Brill.Google Scholar
  66. Vandevelde, J. J. (1926). Bijdrage tot de bio-bibliographie van Bernard Nieuwentyt (1654\({\dagger }\) 1718). In Verslagen en mededelingen van de Koninklijke Vlaamse Academie voor Taal-en Letterkunde (pp. 709–718).Google Scholar
  67. van Musschenbroek, P. BPL, codex 240, n\(^{\circ }\) 1–67, Special Collections Department, Leiden University Library, The Netherlands.Google Scholar
  68. van Musschenbroek, P. (1723). Oratio de certa methodo philosophiae experimentalis, Dicta publice A. D. xiii. Septemb. Trajecti ad Rhenum: Apud Guilielmum Vande Water.Google Scholar
  69. van Musschenbroek, P. (1726). Epitome elementorum physico-mathematicorum, conscripta in usus academicos. Lugduni Batavorum: Apud Samuelem Lugtmans.Google Scholar
  70. van Musschenbroek, P. (1731). Oratio de methodo instituendi experimenta physica. In id., Tentamina experimentorum naturalium captorum in Academia del Cimento (Vol. xlviii). Lugduni Batavorum: Apud Joan. Et Herm. Verbeek.Google Scholar
  71. van Musschenbroek, P. (1739\(^{2}\) [1736]). Beginsels der natuurkunde. Leyden: Samuel Luchtmans.Google Scholar
  72. van Musschenbroek, P. (1741\(^{2}\) [1734]). Elementa physicae conscripta in usus academicos. Lugduni Batavorum: Apud Samuelem Luchtmans.Google Scholar
  73. van Musschenbroek, P. (1744). The elements of natural philosophy, Chiefly intended for the use of students in universities (Vol. 2) (J. Colson, Trans). London: Printed for J. Nourse at the Lamb without Temple-Bar.Google Scholar
  74. van Musschenbroek, P. (1748). Institutiones logicae, Praecipue comprehentes artem argumentandi. Lugduni Batavorum: Apud Samuelem Luchtmans et filium.Google Scholar
  75. van Ruler, J. A. (1995). The crisis of causality, Voetius and Descartes on God, nature and change. Leiden/New York/Köln: E. J. Brill.Google Scholar
  76. Verbeek, T. (1988). René Descartes et Martin Schoock: La querelle d’Utrecht. Paris: Les impressions nouvelles.Google Scholar
  77. Verbeek, T. (1993). From ‘Learned Ignorance’ to Scepticism: Descartes and Calvinist Orthodoxy. In R. H. Popkin & A. J. Vanderjacht (Eds.), Scepticism and Irreligion in the Seventeenth and Eighteenth Centuries (pp. 31–45). Leiden/New York/Köln: E. J. Brill.Google Scholar
  78. Vermij, R. H. (1987). Bernard Nieuwentijt als experimentator. Tijdschrift voor geschiedenis der geneeskunde natuurwetenschappen, wiskunde en techniek, 10, 81–89.Google Scholar
  79. Vermij, R. H. (1988). Bernard Nieuwentijt en de physico-theologie. Documentatieblad werkgroep Achttiende eeuw, 20, 215–229.Google Scholar
  80. Vermij, R. H. (1989). Religion and mathematics in seventeenth-century Holland: The case of Bernard Nieuwentijt. In Ä. Bäumer & M. Büttner (Eds.), Science and Religion/Wissenschafts und Religion, Proceedings of the Symposium of the XVIIIth International Congress of History of Science at Hamburg-Munich, 1–9 August 1989 (pp. 152–158). Buchum: Universitätsverlag Dr. N. Brockmeyer.Google Scholar
  81. Vermij, R. H. (1991). Secularisering en natuurwetenschap in de zeventiende en achttiende eeuw: Bernard Nieuwentijt. Amsterdam: Rodopi.Google Scholar
  82. Vermij, R. H. (2003). The formation of the Newtonian philosophy: The case of the Amsterdam mathematical amateurs. British Journal for the History of Science, 36, 183–200.CrossRefGoogle Scholar
  83. Vermij, R. H. (2011). The light of nature and the allegorisation of science on Dutch frontispieces around 1700. In E. Jorink & B. Ramakers (Eds.), Art and science in the early modern Netherlands, Series: Netherlands yearbook for history of art (Vol. 61, pp. 209–237). Zwolle: WBOOKS.Google Scholar
  84. V., A. [=Adriaen Verwer] (1683). ‘t Mom-aensicht der atheistery afgerukt, Of de wederlegging der Zedekunst van Benedictus de Spinoza. Amsterdam: Wilhelmus Goeree.Google Scholar
  85. Verwer, A. (1698). Inleiding tot de christelyke Gods-geleertheid. Amsterdam: Jan Rieuwertz.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Philosophy and Moral Sciences, Centre for Logic and Philosophy of ScienceVrije Universiteit BrusselBrusselsBelgium

Personalised recommendations