  Stephen Toulmin once observed that `it has never been customary for
philosophers to pay much attention to the rhetoric of mathematical debate'.
Might the application of Toulmin's layout of arguments to mathematics remedy
this oversight?
  Toulmin's critics fault the layout as requiring so much abstraction as to
permit incompatible reconstructions. Mathematical proofs may indeed be
represented by fundamentally distinct layouts. However, cases of genuine
conflict characteristically reflect an underlying disagreement about the nature
of the proof in question.
