This account of the achievements of medieval science should not be thought of as
claiming that no significant basic advances in scientific methodology were made in the seventeenth century. One such advance was Galileo’s assertion of the importance of
abstraction and idealisation. Galileo accounted for the behaviour of falling bodies by
describing how free fall would work in a vacuum, and then explaining the actual behaviour
of falling bodies as resulting from this account modified by the effects of the medium in
which the actual bodies we encounter are travelling. Such idealisations may rarely or never
occur in the actual world, and hence cannot simply be derived from experience or produced
by experiment; they were however necessary for the development of Newton’s physics.
Another advance was Pascal and Fermat’s formulation of the mathematics of probability,
an entirely new departure the results of which are now essential to every science.7 A
clearer grasp of the value of a piecemeal approach to scientific problems, that does not
attempt to give a universal theory as an explanation for phenomena, was also important for
scientific progress.