ABSTRACT
Something that is missing from Aristotle’s syllogistic-at least, if is to be considered as offering a general theory of reasoning-is that it assigns no special place to mathematical reasoning. This is odd on a number of counts. One is that Plato set great store by arithmetic in the educational programme sketched in Republic. The discussion of this in Book VII leaves no doubt about its importance in training the mind of a future philosopher. However, at least since the time of Pythagoras the study of numbers and calculation had been regarded as belonging to a different intellectual domain from either poetry or the arts of disputation. The division of intellectual labour that eventually fossilised into the programmes of the trivium and quadrivium in the medieval universities of Europe treated grammar, logic and rhetoric as falling under the study of words, while arithmetic, geometry, astronomy and music fell under the study of numbers. But the origins of this dichotomy undoubtedly lie in the ancient world.
