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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