imself carried by his mathematical technique beyond
the assumptions of a metaphysical physics he abandoned the field of
physical astronomy and confined himself to the development of his
mathematical expressions.

In other fields Greek science analyzed with varying success and critical
skill only the conceptions found in the experience of their time and
world. Nor did Greek thought succeed in formulating any adequate method
by which the ultimate concepts in any field of science were to be
determined. It is in Aristotle's statement of induction and the process
of definition that we appreciate most clearly the inadequacy of their
method. This inadequacy lies fundamentally in Aristotle's conception of
observation which, as I have already noted, implies the recognition of
an individual, that is, an object which is an embodied form or idea. The
function of knowledge is to bring out this essence. The mind sees
through the individuals the universal nature. The value of the
observation lies, then, not in the controlled perception of certain data
as observed facts, but in the insight with which he recognizes the
nature of the object. When this nature has been seen it is to be
analyzed into essential characters and thus formulated into the
definition. In Aristotle's methodology there is no procedure by which
the mind can deliberately question the experience of the community and
by a controlled method reconstruct its received world. Thus the natural
sciences were as really fixed by the conceptions of the community as
were the exact sciences by the conceptions of a Euclidian geometry and
the mathematics which the Greeks formulated within it. The individual
within whose peculiar experience arises a contradiction to the
prevailing conceptions of the community and in whose creative
intelligence appears the new hypothesis which makes possible a new
heaven and a new earth could utilize his individual experience only in
destructive skepticism. Subjectivism served in ancient thought to
invalidate knowledge not to enlarge it.

Zeller has sketched a parallelism between the ideal state of Plato and
the social structure of the medieval world. The philosopher-king is
represented by the Pope, below him answering to the warrior class in the
Platonic state stands the warrior class of the Holy Roman Empire, who in
theory enforce the dictates of the Roman curia, while at the bottom in
both communities stand the mass of the people bound to obedience