Abstract
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.
This chapter was originally published as Park (2009). An earlier version was read at the international conference on “The Classical Model of Science” held at Amsterdam in 2007.
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Notes
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“In accordance with their understanding of Aristotle, the commentators all sought to keep the terms of premises and conclusions within the same subject genus. For most of them this meant that a mathematical proof in a mixed science is quia, not propter quid, since it is not made through the proximate, necessarily physical cause of the composite predicate’s adhering in the composite subject. And when a mathematical middle term proved a mathematical predicate of a physical subject, the proof was usually considered quia through the remote cause. Only Zabarella and, in a more limited way, Aquinas, allowed for propter quid mathematical demonstrations in the mixed sciences.” (Laird 1997, pp. 259–260).
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- 3.
Clavius provides us with a clear example of this way of comparing the three disciplines: “Because the mathematical disciplines discuss things that are considered apart from any sensible matter—although they are themselves immersed in matter—it is evident that they hold a place intermediate between metaphysics and natural sciences, if we consider their subjects, as is rightly shown by Proclus. For the subject of metaphysics is separated from all matter, both in the thing and in reason; the subject of physics is in truth conjoined to sensible matter, both in the thing and in reason; when, since the subject of the mathematical disciplines is considered free from all matter-although it[i.e., matter] is found in the thing itself-clearly it is established intermediate between the other two.” (Clavius, “In disciplinas mathematicas prolegomena” in Opera mathematica, Vol. 1, p. 5; requited from Dear 1995, p. 37).
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Park, W. (2018). Biancani on Scientiae Mediae. In: Philosophy's Loss of Logic to Mathematics. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-95147-8_12
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