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specifi cally to attack the importation into medicine of methods and ideas
that he associates with ‘philosophy’, by which he here means speculative
theories about such topics as the constitution of the human body. For good
measure he insists that if one were to engage in that study, the proper way
of doing so would be to start from medicine.
Medicine provides particularly striking examples of second-order
debates parallel to those in mathematics: indeed in the Hellenistic period
the disagreements among the medical sects were as much about methods
and epistemology as they were about medical practice. But other fi elds too
exhibit similar fundamental divisions between competing approaches. In
music theory, Barker has explored the analogous disputes fi rst between
practitioners on the one hand, and theoretical analysts on the other, and
then, among the latter, between those who treated musical sound in geo-
metrical terms, as an infi nitely divisible continuum, and those who adopted
an analysis based rather on arithmetic. 11 F u r t h e r a fi eld I may simply remark
that the methods and aims of historiography are the subject of explicit
comment from Herodotus onwards. His views were criticized, implicitly,
by his immediate successor Th ucydides, who contrasts history as enter-
tainment with his own ambition to provide what he calls a ‘memorial for
eternity’ (1 21). But to achieve that end depended, of course, on the critical
evaluation of eyewitness accounts, as well as an assumption that certain
patterns of behaviour repeat themselves thanks to the constancy of human
nature.
With the development of both the practice and the teaching of rhetoric –
the art of public speaking – goes a new sense of what it takes to persuade an
audience of the strength of your case – and of the weakness of your rivals’
position. Both the orators and the statesmen deployed a rich vocabulary of
terms, such as apodeiknumi , epideiknumi and cognates, to express the claim
that they have proved their point, as to the facts of the matter in question, as
to the guilt or innocence of the parties concerned, or as to the benefi ts that
would accrue from the policies they advocated.
Yet that very same vocabulary was taken over fi rst by Plato and then
by Aristotle to contrast what they claimed to be strict demonstrations on
the one hand with the arguments that they now downgraded as merely
plausible or persuasive, such as were used in the law courts and political
assemblies – and this takes us back to mathematics, since it provides the
essential background to the claims that some, but not all, mathematicians
made about the strictest mode of demonstration that they could deliver.11 Barker 1989 , 2000.