Vico’s Ring
49
stration
109
can be better appreciated when seen in the light of
modern mathematical thinking. As seen above, Vico was focused
on geometrical/mathematical entities by their
dimensionality
. This
seemingly self-evident and self-explanatory concept, however, is
highly complex in itself, and it is only recently that it received
mathematically rigorous formulation
110
.
In connection with describing geometrical demonstration, Vi-
co used terminology common to geometrical method such as
“elements” and “postulates”
111
. It might even be justified to say
that he had more grounds to use such terminology in connection
with geometric demonstration than those that reserve it for the
geometric method since it involves the initial, crucial moment(s)
of establishing the terms of reference for any subsequent exer-
cise of deductive logic, in other words, ontology comes first,
epistemology second
112
.
It has been said that Vico «had little use and less aptitude for
the niceties of geometry»
113
. It is true, Vico made a number of
references to the commonplace staples of geometry, circle, trian-
gle, angle, among which the circle, as noted above, became a fa-
vorite symbol of closure and completeness. However, he was
never tempted to violate his own dictum: «The geometrical
method applies only to measures and numbers. All other topics
are quite incapable of it»
114
. In this particular respect, it would
appear very difficult to find common ground between Vico’s at-
titude with Spinoza’s, of which Shmueli said: «The whole thrust
of Spinoza’s epistemological endeavors is to show that the sci-
ence of mathematics is able to arrive at a certitude in all spheres
of reality»
115
. Vico’s use of the triangle as an example is a case in
point: «Now, every triangle has angles equal to two right angles.
[...] because I recognize this property of it, it can also be the ar-
chetype of other triangles for me»
116
. While Vico derives the con-
cept of invariance (that is, 180
°
as the sum of the angles), the
discussion does not venture beyond the ambit of geometry
sui
generis
117
.
On the other hand, Spinoza takes a deeply philosophical