uided in our discovery of the
true and the false, solely by the light of our natural understanding.
And the truths we discover are not temporary fabrications of the human
mind, but eternal truths about the nature of things. Perhaps no other
single aspect of Spinoza's philosophy distinguishes Spinoza from the
medievalists as thoroughly as does his use of the geometrical order of
exposition; and no other single aspect, perhaps, justifies as
thoroughly Spinoza's claim to rank with the moderns if not even the
contemporaries.

The geometer's method of starting with definitions and axioms and
proceeding from proposition to proposition especially appealed to
Spinoza, apart from the fact that geometry was an ideal science,
because, for Spinoza, the essence of logical method consists in starting
out with ideas that are of utter simplicity. Then, if the ideas are
understood at all, they can only be clearly and distinctly understood.
The absolutely simple we can either know or not know. We cannot be
confused about it. And ideas which are clearly and distinctly understood
are, according to Spinoza, necessarily true. Such unambiguously simple
and therefore necessarily true ideas Spinoza believed his definitions
and axioms expressed. Furthermore, if we gradually build up the body of
our science by means of our initial simple ideas, justifying ourselves
at every step by adequate proof, our final result will necessarily be as
firmly established and as certainly true as the elementary ideas we
started with. The reliability of this whole procedure more than
compensates for its tediousness--a defect Spinoza expressly recognizes.

Unfortunately, however, there are other defects in the geometrical
method when it is applied to philosophy, far more serious than its
tediousness,--defects, moreover, Spinoza apparently did not recognize.
Even though the geometrical method is preeminently scientific, it is
hardly a form suitable for philosophy. The Euclidean geometer can take
it for granted that the reader understands what a line or plane, a solid
or an angle is. For formality, a curt definition is sufficient. But the
philosopher's fundamental terms and ideas are precisely those in need of
most careful and elaborate elucidation--something which cannot be given
in a formal definition or axiom. Also, in the geometrical form, the
burden of the author's attention is shifted from the clarification of
the propositions to the accurate demonstration of