Biancani on Scientiae Mediae
We can witness the recent surge of interest in the controversy over the scientific status of mathematics among Jesuit Aristotelians around 1600. Following the lead of Wallace, Dear, and Mancosu, I propose to look into this controversy in more detail. For this purpose, I shall focus on Biancani’s discussion of scientiae mediae in his dissertation on the nature of mathematics. From Dear’s and Wallace’s discussions, we can gather a relatively nice overview of the debate between those who championed the scientific status of mathematics and those who denied it. But it is one thing to fathom the general motivation of the disputation, quite another to appreciate the subtleties of dialectical strategies and tactics involved in it. It is exactly at this stage when we have to face some difficulties in understanding the point of Biancani’s views on scientiae mediae. Though silent on the problem of scientiae mediae, Mancosu’s discussions of the Jesuit Aristotelians’ views on potissima demonstrations, mathematical explanations, and the problem of cause are of utmost importance in this regard, both historically and philosophically. I will carefully examine and criticize some of Mancosu’s interpretations of Piccolomini’s and Biancani’s views in order to approach more closely what was really at stake in the controversy.
- Biancani, G. (Blancanus, Josephus). (1615a). De Mathematicarum Natura Dissertatio. Bologna. Available at http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?dir-bian.
- Laird, W. R. (1983). The Scientiae Mediae in Medieval Commentaries on Aristotle’s posterior analytics. Ph.D. Dissertation, University of Toronto.Google Scholar
- Laird, W. R. (1997). Galileo and the mixed sciences. In D. A. Di Lisca, et al. (Eds.), Method and order in renaissance philosophy of nature (pp. 253–270). Aldershot: Ashgate.Google Scholar
- Livesey, S. J. (1982). Metabasis: the interrelationship of the sciences in antiquity and the middle ages. Ph.D. Dissertation, UCLA.Google Scholar
- Livesey, S. J. (1989). Theology and science in the fourteenth century. Leiden: E.J. Brill.Google Scholar
- Lohr, C. H. (1999). Aristotelian theories of science in the renaissance. Sciences et religions: de Copernic a Galilee, 1540–1610, 17–29.Google Scholar
- Maddy, P. (1997). Naturalism in mathematics. Oxford: Oxford University Press.Google Scholar
- Mancosu, P. (1996). Philosophy of mathematics and mathematical practice in the seventeenth century. Oxford: Oxford University Press.Google Scholar
- Park, W. (2009). The status of Scientiae Mediae in the history of mathematics: Biancani’s case. Korean Journal of Logic, 12(2), 141–170.Google Scholar
- Piccolomini, A. (1547). Commentarium de Certitudine Mathematicarum Disciplinarum, Romae. Available at http://nausikaa2.mpiwg-berlin.mpg.de/digitallibrary/sevlet/Scaler?pn.
- Putnam, H. (1979). Mathematics, matter and method: Philosophical papers (Vol. 1, 2nd ed.). Cambridge: Cambridge University Press.Google Scholar
- Quine, W. V. O. (1980). From a logical point of view (2nd ed.). Cambridge: Harvard University Press.Google Scholar
- Steiner, M. (1975). Mathematical knowledge. Ithaca, NY: Cornell University Press.Google Scholar
- Steiner, M. (1998). The applicability of mathematics as a philosophical problem. Cambridge, MA: Harvard University Press.Google Scholar
- Westman, R. S. (1986). The Copernicans and the churches. In D. C. Lindberg, R. N. Numbers (Eds.), God and nature (pp. 76–113). Berkeley: University of California Press.Google Scholar