Poincaré's philosophy of mathematics
Abstract
The primary concern of this thesis is to investigate
the explicit philosophy of mathematics in the work of
Henri Poincare. In particular, I argue that there is
a well-founded doctrine which grounds both Poincare's
negative thesis, which is based on constructivist
sentiments, and his positive thesis, via which he retains
a classical conception of the mathematical continuum.
The doctrine which does so is one which is founded on
the Kantian theory of synthetic a priori intuition.
I begin, therefore, by outlining Kant's theory of the
synthetic a priori, especially as it applies to mathematics.
Then, in the main body of the thesis, I explain how the
various central aspects of Poincare's philosophy of
mathematics - e.g. his theory of induction; his theory
of the continuum; his views on impredicativiti his
theory of meaning - must, in general, be seen as an
adaptation of Kant's position. My conclusion is that
not only is there a well-founded philosophical core to
Poincare's philosophy, but also that such a core provides
a viable alternative in contemporary debates in
the philosophy of mathematics. That is, Poincare's
theory, which is secured by his doctrine of a priori
intuitions, and which describes a position in between
the two extremes of an "anti-realist" strict constructivism
and a "realist" axiomatic set theory, may indeed be
true.
Type
Thesis, PhD Doctor of Philosophy
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.