Munich Center for Mathematical Philosophy (MCMP)

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Talk: Yael Kedar (Tel Hai College)

Location: Ludwigstr. 31, ground floor, Room 021.

09.02.2023 at 16:00 


Propter quid demonstrations and the use of diagrams by Roger Bacon (C. 1220-1292)


In the Posterior Analytics 1.13 Aristotle introduces a distinction between two kinds of demonstrations: of the fact (quia), proving that a certain fact is necessarily true, and of the reasoned fact (propter quid), proving why a certain fact is necessarily true. Both demonstrations take a syllogistic form, in which the middle term links either two facts (in the case of quia demonstration) or a proximate cause and a fact (in propter quid demonstrations).
While Aristotle stated that all the terms of one demonstration must be taken from within the proper subject matter, he made an exception. Sometimes, when the subject-genera are not identical but the same in some qualified sense, the fact and the reasoned fact are instantiated by terms from different sciences, as when math provides the reason and another science will provide the empirical fact. This statement had been the subject of varying interpretations in the 13th century. Thomas Aquinas and Albert the Great, for instance, understood it to mean that a mathematical middle term could not provide real propter quid explanation of a natural fact, since the cause it provides is not proximate. Hence, such demonstrations ought to be considered quia. Roger Bacon, however, adhering to Grosseteste’s Posterior Analytics commentary, held not only that math can provide the middle term in propter quid demonstrations, but that it is the most appropriate middle term. Moreover, he replaced the propositions in these demonstrations with diagrams, thus producing geometrical arguments. In this paper, I focus on Bacon’s geometrical propter quid arguments, as applied in three case-studies: the heat caused by a free-falling body, the motion of the scale, and the contraction of water. Based on an analysis of these diagrams, I seek to uncover both Bacon’s theoretical justification for this practice, and his unique interpretation of the propter quid process, which reflects his understanding of scientific method in general and the relation between mathematics and philosophy of nature in particular.