In Advice to a Young Scientist, P.B. Medawar
defines four different kinds of experiment: the Kantian,
Baconian, Aristotelian, and the Galilean.
Mathematics has always participated deeply in the first three
categories but has somehow managed to avoid employing the Galilean
model.
`` (the Baconian experiment) is the consequence of `trying things out' or even of merely messing about.''
``(the) Galilean Experiment is a critical experiment -- one that discriminates between possibilities and, in doing so, either gives us confidence in the view we are taking or makes us think it in need of correction.,,