NIEUWENTIJT, BERNARD

(b. Westgraftdijk, North Holland, 10 August 1654; d. Purmerend, North Holland, 30 May 1718)

mathematics, philosophy.

Bernard was the son of Emmanuel Nieuwentijt, minister at Westgrafidijk, and Sara d’ImbIevilie. Although he was expected to enter the ministry, he chose instead to study natural sciences. On 28 February 1673 he was enrolled as a student in medicine at Leiden University; later in the year he was also enrolled at Utrecht University; where he studied law and defended his medical thesis in 1676 [I]. He then settled as a medical practitioner in Purmerend. On 12 November 1684 he married. Eva Moens, the widow of Philips Munnik, a naval captain in the service of the Dutch States-General.. He was elected a member of the city council and became a burgomaster of Purmerend. As a youth Nieuwentijt was influenced by Cartesianism and he acquired, a thorough knowledge of mathematics and natural philosophy. In 1695–1700 he was engaged in a controversy with Leibniz and his school on the foundations of calculus. On 12 March 1699 he married his second wife, Elisabeth Lams, the daughter of Willem Lams, burgomaster of Wormer.

Nieuwentijt became famous in his home country and abroad because of the publication of two lengthy works. One [6] was originally published in Dutch in 1714; according to [12] it was reedited in 1717, 1720, 1725, 1741, and 1759; editions with other dates are incidentally found in various libraries (1715, 1718, 1730; see [13]). The work was translated, into English by J. Chamberlayne in 1718 [6a]; a fourth edition (1730) is mentioned. It was also translated into French by P. Noguez [6h]; this translation was published in 1725 (Paris), 1727 (Amsterdam), and 1760 (Amsterdam-Leipzig). A German translation by W.C. Baumann appeared in 1732 and another by J.A. von Segner in 1747 [6c], The second of his two works [8] was posthumously published in Dutch, in 1720; it was published, again in. 1741 and 1754; and. was translated into French (1725) and English (1760). Nieuwentijt’s portrait, painted by D, Valkenburg, is in the University of Amsterdam; the portrait in his 1714 publication [6] was engraved by P. van Gunst.

The title of Nieuwcntijt’s Analysis infinitorum [3] reminds the historian of the title of Leibniz’ article of 1686, “De geometria recondita et analysi indivisibilium.” Nieuwentijt’ [3] was the first Comprehensive book on “analysis infinitorum.” By L. Euler’s Introductio in analysin infinitorum, analysis became the name of a mathematical discipline. To this field Nieuwentijt contributed little more than the name. What is surprising, however, is the erudite scholarship of a small-town physician who, except for limited university study, does not seem to have cultivated many learned colleagues. Nieuwentijt’s work reveals his full acquaintance with the mathematics of his period and a remarkable self-reliance.

Nieuwentijt rejected Leibniz’ approach to analysis. He did not admit infinitesimals of higher order. Nieuwentijt’s method consists, in modern terms, in adjoining to the real field an element e with e²=0.. Leibniz’ answer [9] to Nieuwentijt’s objections [2] (see also [4]) was not convincing. Nieuwentijt’s objections, however, may have contributed to improving the insight into higher-order differentials. It is disappointing that he did not sufficiently appreciate Leibniz’ integral calculus.

His 1714 publication [6], of about 1,000 pages, was intended to demonstrate the existence of God by teleological arguments. Never before had this been tried on such a scale, and none among Nieuwentijt’s numerous imitators equaled his completeness. It is not clear, however, whether or to what degree he depended on William Derham, whose Physica-Theology[10] (see also [II]) appeared almost simultaneously. Nieuwentijt may have known of Derham’s lectures of 1711–1712, which were the nucleus for the work.

It is an old idea that nature, by its purposiveness, betrays the existence of a creator; Nieuwentijt, however, was one of the first who, rather than relying on a few examples, reviewed the whole of natural sciences to show in detail how marvelously things fitted in the world. His work [6] looks like a manual of up-to-date science and as such it may have contributed to the propagation of knowledge. On the other hand, by the abundance of its argumentation, it is tiring reading and full of platitudes. Its fundamental shortcoming is its static world picture and its lack of any trace of the oncoming evolutionary ideas. Its background philosophy, however, is remarkably sound. Nieuwentijt opposed both chance and necessity as explanatory principles of nature. He preferred empiricist above rationalist arguments. Natural laws have, according to Nieuwentijt, factual rather than rational truth, and as such they must have been ordained by a lawgiver.

Nieuwentijt felt that rationalism led to Spinozism and other kinds of atheism. A more methodical struggle against rationalism was fought in his second major work [8]. This is, indeed, a methodology of science which surprises by a seemingly modern view. In fact it is nothing but a philosophy of common sense, and this explains why it fell into oblivion amid more sophisticated philosophies. In this work [8] Nieuwentijt arrived at a clear distinction between what he called ideal and factual mathematics, and at the insight that both avail themselves of the same formal methods, that all ideal statements are conditional, and that the ultimate criterion for factual statements is corroboration by experience. Nieuwentijt distinguished himself from the British empiricists by his closeness to mathematics and exact sciences. Although his influence in philosophy was negligible, his position as a methodologist was unique up to modern times.

BIBLIOGRAPHY

1. Disputatio medica inauguralis de obstructionibus, 8 Feb. 1676, Ultraiecti.

2. Considerationes circa analyseos ad quantitates infinitè parvas applicatae principia, et calculi differentialis usum in resolvendis problematibus geometricis (Amsterdam, 1694).

3. Analysis infinitorum, seu curvilineorum proprietates expolygonorum natura deductae (Amsterdam, 1695).

4. Considerationes secundae circa calculi differentialis principia; et responsio ad virum nobilissimum C. G. Leibnitium(Amsterdam, 1696).

5. “Nouvel usage des tables des sinus au moyen de s’en servir sans qu’il soit nécessaire de multiplier et de diviser,” in Journal litéraire, 5 (1714), 166–174.

6. Het regt gebruik der wereltbeschouwingen ter overtuiginge van ongodisten en ongelovigen, aangetoont door…(Amsterdam, 1714).

6a. The Religious Philosopher, or the Right Use of Contemplating the Works of the Creator:(I) In the Wonderful Structure of Animal Bodies,(II)In the Formation of the Elements,(III) In the Structure of the Heavens, Designed for the Conviction of Atheists, trans. by J. Chamberlayne, 3 vols.(London, 1718).

6b. L’existence de Dieu démontrée par les merveilles de la nature, en trois parties, où l’on traite de la structure des corps de lrsquo;homme, des élémens, des astres et de leurs divers effets, trans. by P. Noguez (Paris, 1725).

6c. Rechter Gebrauch der Weltbetrachtung zur Erkenntnis der Macht, Weisheit und Güte Gottes, auch Überzeugung der Atheisten und Ungläubigen, trans. by J. A. v. Segner (Jena, 1747).

7. “Brief aen den Heer J. Bernard, zynde een antwoord op de Aenmerkingen van den Heer Bernard, omtrent de werelt-beschouwingen, in de Nouv. de la Repub. 1716, 252,” in Maandelijke Uittreksels, of Boekrael der Geleerde Werelt(1716), 673–690.

8. Gronden van zekerheid of de regte betoogwyze der wiskundigen so in het denkbeeldige als in het zakelijke: ter weerlegging van Spinosaas denkbeeldig samenstel; en ter aanleiding van eene sekere sakelyke wysbegeerte, aangetoont door … (Amsterdam, 1720).

9. G. G. L. [Leibniz], “Responsio ad nonnullas difficultates, a Dn. Bernardo Nieuwentijt circa methodum differentialem seu infinitesimalem motas,” in Acta eruditorum 1695, pp. 310–316.

10. William Derham, Physico-Theology, or a Demonstration of the Being and Attributes of God From His Works of Creation (London, 1713).

11. William Derham, Astro-Theology, or a Demonstration of the Being and Attributes of God From a Survey of the Heavens (London, 1715).

12. Nieuw Nederlandsch Biographisch Woordenboek, 6 (1924), 1062–1063.

13. A. J. J. Van der Velde, “Bijdrage tot de bio-bibliographie van Bernard Nieuwentyt (1654–1718),” in Bijdragen en Mededelingen Koninklijke Vlaamsche Academic van Taal- en Letterkunde 1926, 709–718.

14. E. W. Beth, “Nieuwentyt’s Significance for the Philosophy of Science,” in Synthese, 9 (1955), 447–453.

15. H. Freudenthal, “Nieuwentijt und der teleologische Gottesbeweis,” in Synthese, 9 (1955), 454–464.

16. J. Vercruysse, “La fortune de Bernard Nieuwentyd en France au 18e siècle et les notes marginales de Voltaire,” in Studies on Voltaire and the 18th Century, 30 (1964), 223–246.

17. J. Vercruysse, “Frans onthaal voor een Nederlandse apologeet: Bernard Nieuwenty—1654–1718,” in Tijdschrift van de Vrije Universiteit te Brussel, 11 (1968–1969), 97–120.

Hans Freudenthal