[SydPhil] 2014 HPS Research Seminar Series

[Debbie Castle]

Unit for History and Philosophy of Science
2014 Research Seminar Series
PLEASE NOTE NEW COMMENCEMENT TIME 4PM APPROX FINISH TIME 6PM

SCIENCE MEETING ROOM 450, 4TH FLOOR CARSLAW BUILDING, CAMPERDOWN CAMPUS
MONDAY
10TH MARCH

KATHERINE DUNLOP
(University of Texas)
"Arithmetic and Geometry in Poincaré's Science and Hypothesis"
It is usually supposed that Poincaré's Science and Hypothesis contains a unified view of mathematics and physical science.  But its defense of a role for intuition in arithmetic does not fit well with the conventionalism Poincaré advocates elsewhere in the book.  After bringing out the conflict, I argue that the most usual way of resolving it does not succeed.  That is to suppose the sciences are arranged in a hierarchy such that arithmetic is presupposed by geometry, which is presupposed by mechanics, etc.  On the usual reading, Poincaré takes arithmetic to depend on an a priori intuition which underlies the notion of natural number (and with it the principle of mathematical induction), and is thereby seen to underlie all science.  In contrast, I maintain that Poincaré conceives mathematical reasoning as a general type, of which the justification of arithmetical notions is just one instance, distinct from its application to geometry.  The sense in which intuition is foundational for all science is that it helps us to decide on conventions, by showing them to be appropriate in light of our experience.  So Poincaré's account of arithmetic has a place in his overall view of science, just a different place than is usually supposed.
Hope you can make it.



Debbie Castle
Administration Officer
Unit for History and Philosophy of Science
Room 441, Carslaw Building F07| THE UNIVERSITY OF SYDNEY   NSW  2006
T: + 61 2  9351 4226 E: debbie.castle at sydney.edu.au
Office Open: Monday Tuesday and Wednesday

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