PETER REAR * JESUIT MATHEMATICAL SCIENCE AND THE RECONSTITUTION OF EXPERIENCE IN THE EARLY SEVENTEENTH CENTURY I AN ‘EXPERIMENT’ in modern science is often contrasted with simple ‘experience’ by claiming that the former involves the posing of a specific question about nature which its outcome is to answer, whereas the Iatter does nothing more than supply items of fact regarding phenomena, and is not designed to judge matters of theory or interpretation. Thus it has been pointed out that pre-modern, scholastic uses of ‘experience’ in natural philosophy tend to take the form of selective presentation of instances which illustrate conclusions generated by abstract philosophizing, and not the employment of such material as a basis for testing these conclusions. ‘Experiment’ became a characteristic feature of natural philosophy only in the seventeenth century.’ In its broadest terms this picture must be accepted, but enough is left out in the analysis of the nature of ‘experiment’ to obscure understanding of its historical emergence. The science-textbook definition of experiment fails to capture the reality of the new conceptions of the seventeenth century: Robert Hooke’s term ‘experimentum crucis’, so signally adopted by Newton, was certainly intended to pick out an aspect of Bacon’s teaching suitable to the notion of ‘experiment’ as a test of hypotheses, but Boyle’s ‘experimental histories’, also indebted to Bacon, had no immediate purpose beyond the mere collection of facts.’ The ‘experiments’ of the Accademia de1 Cimento were frequently designed to test hypotheses or decide between alternatives,3 but the empirical work of the Accademia’s Florentine forebear, Galileo, seems at *Department of History, Corndl University, McGraw Hall, Ithaca. NY 14853-4601. U.S.A. Received 12 January 1986. ‘See, for instance, Charles B. Schmitt, ‘Experience and Experiment: A Comparison of Zabarella’s View with Galileo’s in De mo0Z, Shrdies in fire Renaissance 16 (1969), 80- 138; Paolo Rossi, ‘The Aristotelian6 and the Moderns: Hypothesis and Nature’, Annali dell’lstifutu e Muse0 di St&a delta Sciema di Firenze 7 (1982). fasc.1. 3-27, both of which look particularly at Zabarella as a representative Aristotelian. *Robert Hooke, Microwaphia (London, 1665: facsimile edn. New York: J3over, 1%2), p. 54; the term seems to derive %rn Elafon’s ‘i&a& cruds’. ‘See W. E. Knowles Middleton, The Experimenters: A Study of the Accademia del Cimento (Baltimore: Johns Hopkins University Press, 1971). S&d. H&t. Phil. Sci,, Vol. 18. No. 2, pp. 133 - 175, 1987. 0039- 3681/87 $3.00 f 0.00 Printed in Great Britain. Pergamon Journals Ltd. 133 134 Studies in History and Philosophy of Science least partly to have been directed towards establishing premises for formal scientific demonstrations, a quite different function.’ As a novel feature of the Scientific Revolution, ‘experiment’ is not easily characterized. The problem is really one of determining how the seventeenth century reconstructed the pre-existing concept of ‘experience’ to fit new ends. I have argued elsewhere’ that ‘experience’ as an element of scholastic natural philosophical discourse took the form of generalized statements about how things usually occur; as an element of characteristically seventeenth-century, non-scholastic natural philosophical discourse it increasingly took the form of statements describing specific events. The former were associated with the commentary as the typical literary genre, the latter with the research report exemplified by countless contributions to the Philosophical Tramactions by the early Fellows of the Royal Society. For the scholastic natural philosopher, writing his commentaries on Aristotle, the grounding in experience of the physical facts debated in his discussions was guaranteed by their generality as experiential statements - ‘heavy bodies fall’ is a statement to which all could assent, through common experience embodied in authoritative texts. If experiential statements referred to singular events, however, and if evidential weight attached to that singularity, as in the case of contrived experiences using special apparatus, this kind of common assent by which to establish their truth could not be anticipated. The new ‘experience’ of the seventeenth century, therefore, established its legitimacy in historical reports of events, often citing witnesses. The singular experience could not be evident, but it could provide evidence. The development of the idea of ‘experiment’ as an arbiter of hypotheses, therefore, formed only one aspect of the change in the nature and function of experience in the Scientific Revolution. More fundamental was the emergence of the discrete experience as the primary empirical component of natural philosophy. Although no simple answer can be expected as to how this came about, aspects of the process can be found within the pre-established traditions of the mathematical sciences as practiced by members of what has long been regarded as a bastion of reaction - the Jesuit order.” The shift to a more modern concept of experience among Jesuit mathematicians may not typify ‘See notes 39 and 40 below. ‘Peter Dear, ‘Totius in v&o. Rhetoric and Authority in the Early Royal Society’, Isis 76 (1985), 145 - 161. ‘The assumption that the Jesuits played the part of reactionary Aristotelians seems largely to have stemmed from their role in Galileo’s condemnation. Recent reassessments arc beginning to change that picture: see e.g. Gabriele Baroncini, ‘L’Insegnamento della filosofia naturale nei collegi italiani dei Gesuiti (1610- 1670): un esempio di nuovo aristotelismo’, La ‘rutio st~diontm’: Modelli culturali e pratiche educative dei Gesuiti in Italia tra Cinque e Seicento, Gian Paolo Brizzi (cd.) (Roma: Bulzoni Editore, 1981), pp. 163 - 215; William A. Wallace, Galileo and his Sowwes. The Heritage of the ColIegio Ramono in Galileo’s Science (Princeton: Princeton University Press, 1984); and subsequent references below. Mafhematical Science and fhe Reconsfitution of Experience 135 this seventeenth-century phenomenon as a whoIe, but it impinges directly on the implications of moving from a scholastic to a characteristically early- modern natural philosophical framework. As such, it encapsulates an important aspect of the Scientific Revolution. Ii The importance of the mathematicaI disciplines in the Jesuit college curriculum of this period is weIl-known.7 In effect, the Jesuits had transplanted the medieval quadrivium, comprising the headings of arithmetic, geometry, astronomy and music, from the propaedeutic place (after the trivium) which it occupied in the medieva1 university to the second or third year of the three-year philosophy course, to be taught alongside either physics or metaphysics.’ The pattern varied from college to college, and over time, but by the early seventeenth century the mathematical disciplines held a prominent position in the courses of study offered by the Jesuits at the larger coheges, and in the ideal curricuIum enshrined in the 1599 Ratio studiorum The main constraint appears to have been an insufficient number of competent teachers to go around,” but this was not a problem at the major colleges, and ‘The fundamental work of Francois de Dainville on this issue includes La nu&rnce de I’humanisme moderne and La gdographie des humanktes (both Paris: Beauchesne, 1940), and articles collected in Dainville, L ‘l?ducation des J&uites XVI’- XWIc si&les (Paris: Editions de Minuit, 1978). ‘For a general account of Jesuit mathematical education see, in addition to the previous note, John L. Heilbron, Electricity in the I7th and I8th Centuries. A Study in Early Modern Physics (Berkeley etc.: University of California Press, I979), pp. IOI- 114. See aIso Camille de Rochemonteix, Un coffage de J&.&s aux XVII’ et XVIII’ s&k Le coflpge Henri IV de La FWhe, 4 vols (Le Mans: Leguicheux, 1889), especially vol. 4, pp. 27 and 32. Essays on the quad&al disciplines in the Middle Ages may be found in The Seven Liberal Arts in the Middle Ages, David L.-Wagner (ed.) (Bloomington: Indiana University Press, 1983). ‘Francois de Dainville. ‘L’Enseignment des mathtmatisues darts Ies colI&aes J&suites de Prance du XVI’au XVIII’ sit&‘, Revue-d’histoire des sciences 7 (1954), 6-21,109- 123; Giuseppe Cosentino, ‘Le matematiche nella ‘Ratio Studiorum’ della Compagnia di Gesu’, M&el/atreu Sforica Ligure II.2 (1970), 171-213; idem, ‘L’lnsegnamento de& matematiche nei collegi GcsuiticI neil’ltaha settentrionale: Nota introduttiva’, P&s& 13 (1971), 205-217; for comprehensive listings and biographical entries of mathematicians in the colleges see Karl Adolf Franz Fischer, ‘Jesuiten Mathematiker in da deutschen Assistenz bis 1773’, Archivum Historicurn Societutis Iesa 47 (1978), 159- 22~3; idem, ‘Jesuiten Mathematiker in der franziisischen und italienischen Assistenz bis 1762, bzw. 1773’, ibid. 52 (1983, 52-92; idem, ‘Die Jesuiten- mathematiker des nordostdeutschen Kulturgebietes’. Archives internationales d’histoire des sciences No.112 (1984). i24- 162. “‘Cf. Heilbron, Electricity, pp. 102 - 103. 136 Studies in History and Philosophy of Science altogether the Jesuits were quite successful in producing practitioners and writers in the mathematical sciences during the seventeenth century.” The prime mover in establishing these subjects in the curriculum, Christopher Clavius, had a great influence on the style and attitudes manifest in subsequent Jesuit mathematical writing.‘* Clavius’s textbooks formed the standard introduction to the quadrivial disciplines for