63 / 298
Vico’s Ring
63
111
For example, at the beginning of
Liber metaphysicus
, Chapter II, he
points out that «the synthetic method (that is, by means for forms) […] pro-
ceeds from the smallest elements to the infinite by means of its own postu-
lates, and in doing so, it shows the mode of composing the elements in ac-
cordance with which the truths which it demonstrates are formed; and the
reason that it shows the mode of composing elements is that man has within
himself the elements which it shows» (G. Vico,
On the Most Ancient Wisdom of
the Italians,
cit., p. 39).
112
The distinction made here between geometric method and demonstra-
tion may be helpful in reconciling the views of E. McMullin (
Vico’s Theory of
Science,
cit.) and L. Pompa in his comment (
Comment on Professor McMullin’s Pa-
per
, in
Vico and Contemporary Thought,
cit., pp. 90-93). As noted above,
McMullin could not find strict deductive logic in a geometric mold in Vico’s
“Elements”; on the other hand, Pompa insisted that «[i]t is important, […] to
look not at the validity of the arguments, but at the intended form, and here,
[…] all Vico’s terminology would go to suggest that he thought of them as
deductive». In a certain way, both McMullin and Pompa are correct: from a
formal deductive logic point of view modelled after common geometrical
practice, the arguments do not seem to be valid, but at the same time, Vico’s
choice of form or terminology is on target when seen at operating at the
deeper level of
demonstration.
The distinction may also be expressed in another
way. Vico’s “Elements” could be understood as a kind of “primary” axiomat-
ics in that they aim at elucidating the theoretical foundations, in contrast to
“secondary” axiomatics that take their fundamental constituents as already
present and accepted (this distinction is adapted from E. Kleinert,
Studien zu
Struktur und Methode der Mathematik
, Leipzig, Leipziger Universitätsverlag,
2012, p. 46). Seen in this light, Vico’s “Elements” deserve to be treated as
something more than «witty conceit».
113
D. R. Kelley,
Vico’s Road
, cit., p. 16.
114
Statement in the
Second Response
, see
On the Most Ancient Wisdom of the
Italians
, cit., p. 181. Vico made the same point already in
De ratione
: «But,
whenever the subject matter is unsuited to deductive treatment, the geomet-
rical procedure may be a faulty and captious way of reasoning» (G. Vico,
On
the Study Methods of Our Time
, cit., p. 22). C. Vasoli’s comments are pertinent
here: «[I]l Vico poteva negare che il metodo geometrico […] si estendesse ad
ogni ambito e dominio del sapere e potesse valere fuori di quel mondo di
«linee» e di «numeri» per il quale era stato costruito; e, soprattutto, che potesse
aver presa sulla realtà concreta degli eventi e della storia umana, sempre do-
minio del «probabile» (Vico could deny that the geometrical method […] ex-
tended to every area and domain of knowledge, and could be valid beyond the