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
