54 research outputs found
A Note on the Title of Walter Burley' s On the Purity of the Art of Logic
Philotheus Boehner suggested in 1955 that the puzzling title of Walter Burley's treatise "On the Purity of the Art of Logic" was an indication of Burley's intention to rid logic of what he regarded as Ockhamist contaminations. A closer look, however, shows that this conjecture cannot be right. We argue that Burley's title is simply an allusion to a phrase in Avicenna, and go on to explain why this explanation was not realized before
Parts, Wholes, and Quantity in Euclid’s Elements
This paper develops a novel methodology, combining history of mathematics,
philology, philosophy of mathematics, and logic. We develop a formal logical
treatment of Euclid’s Elements , in which set theory plays no role, but the
logic of part and whole does. We first consider a controversy about the nature
of Euclid’s Elements Book II. For Euclid, the part-whole relation plays roles
that are now played by arithmetic operations. This shows one crucial
limitation of the controversial interpretation of this text as geometrical
algebra. Returning to the beginning, we present a formal language for stating
Propositions 1 through 10 (omitting 7) and proofs of them. Surprisingly, this
has never been done (except for one recent approach, which differs from ours
in an essential way). We conclude by sketching several significant ways in
which this project can be further develope
- …