Home > epistemology, geometry > 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

Paolo Mancosu, Département de philosophie, Université de Californie à Berkeley

Axiomatics and purity of methods: On the relationship between plane and
solid geometry.

Suivi d’un commentaire par Michael Hallett (McGill)

Jeudi 19 avril 2012, de 14h 00 à 16h30
Salle W-5215
Pavillon Thérèse-Casgrain
455, boulevard René-Lévesque est, Montréal

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.

Pour plus d’information, contacter : Mathieu Marion (UQAM),
marion.mathieu@uqam.ca

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