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approach to geometrical manipulations. With respect to the tri-
angle,
Ethics
says, for example: «The affects [emotions like dejec-
tion, pride, envy] follow as necessarily from the said emotions, as
it follows from the nature of a triangle, that the three angles are
equal to two right angles»
118
.
To briefly summarize the above discussion, there are then two
different aspects to the use of “geometry” in both Spinoza and
Vico. To restate the aspect that was just pointed out, for Spino-
za, geometrical constructions and the way such constructions are
arrived at, were imbued with metaphysical significance. Far from
being an idiosyncratic, mystical view of phenomena, the inter-
connections between geometry and higher level structures were
for Spinoza part and parcel of a single and unified (monist) reali-
ty. The same cannot be said for Vico who accorded geometry,
together with “arithmetic” forming mathematics, a key position
in his theory of knowledge, but also insisting on its conditions of
possibility, boundaries, and epistemological separateness, both
with respect to metaphysics and physical reality
119
.
The other aspect which has been dealt with in greater detail
above because it bears a more direct relationship to the literary
structure of Vico’s “Elements”, is the
geometric method /deductive
logic
. Spinoza’s
Ethics
can be seen as having, by design, as points
of departure, terms of reference in vogue at the time; the work is
not devoted to re-invent these concepts in a fresh foundational
framework, but rather, for argument’s sake assume them as giv-
en
120
, and take them to their logical conclusion
121
. Set against this
structural characteristic of
Ethics
, the contrast with Vico’s “Ele-
ments” becomes evident: it is not inferences from already known
first principles that Vico is preoccupied with, but the discovery
and enunciation of such first principles in the first place
122
. These
“axioms” or
degnità
, in fact, have every right to be called “ele-
ments” in the formal sense of fundamental constituents rather
than merely derived, subordinate components, perhaps even
more so than the products of deductive logic
123
.