Home > axiomatics, geometry, history of mathematics, miwhpm, philosophy of mathematics > Paolo Mancosu – Axiomatics and purity of methods: On the relationship between plane and solid geometry

Paolo Mancosu – Axiomatics and purity of methods: On the relationship between plane and solid geometry

The Montreal Inter-University Workshop on the History and Philosophy
of Mathematics presents:
Paolo Mancosu (UC Berkeley):
Axiomatics and purity of methods: On the relationship between plane
and solid geometry
With a commentary by Michael Hallett (McGill).
Thursday, April 19, 2012
Salle W-5215, Pavillon Thérèse-Casgrain (455 Boul. René-Lévesque),
UQAM. 2:00-4:30pm
Abstract:
Traditional geometry concerns itself with planimetric and stereometric
considerations, which are at the root of the division between plane
and solid geometry. To raise the issue of the relation between these
two areas brings with it a host of different problems that pertain to
mathematical practice, epistemology, semantics, ontology, methodology,
and logic. In addition, issues of psychology and pedagogy are also
important here.
In this talk (which is based on joint work with Andy Arana), my major
concern is with methodological issues of purity. In the first part I
will give a rough sketch of some key episodes in mathematical practice
that relate to the interaction between plane and solid geometry. In
the second part, I will look at a late nineteenth century debate (on
"fusionism") in which for the first time methodological and
foundational issues related to aspects of the mathematical practice
covered in the first part of the paper came to the fore. I conclude
this part of the talk by remarking that only through an axiomatic and
analytical effort could the issues raised by the debate on "fusionism"
be made precise. The third part of the talk focuses on Hilbert’s
axiomatic and foundational analysis of the plane version of Desargues’
theorem on homological triangles and its implications for the
relationship between plane and solid geometry. Finally, building on
the foundational case study analyzed in the third section, in the
fourth section I point the way to the analytic work necessary for
exploring various important claims on "purity", "content" and other
relevant notions.
For more information, please contact:Gregory Lavers (Concordia),
Mathieu Marion (UQÀM), Jean-Pierre Marquis (UdM), Dirk Schlimm
(McGill).
Website: http://www.cs.mcgill.ca/~dirk/workshop

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