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Vico’s Ring


clidean geometry, and other comparable forms of mathematical reasoning.

Interestingly, Fletcher, in his review of J. R. Goetsch,

Vico’s Axioms,

brought a

modern result into the discussion, namely K. Gödel’s

incompleteness theorem

(1931) (A. Fletcher,

Book Reviews

, in «NVS», 14 (1996), pp. 86-90, p. 89). It

stunned the mathematical community by showing that the deductive system is

unable to produce every true statement, or viewed vice versa, that not every

true statement could be proved within the system (see D. R. Hofstadter,


Escher, Bach: an Eternal Golden Braid

, New York, Vintage Books, 1980, pp. 15-

24, 82-102). This observation is of course anachronistic, in a strict sense;

however, it is not without basis altogether as far as the early modern era is

concerned. As the philosopher of logic, J. Hintikka, remarked: «This kind of

reaction [divorcing logic from mathematics] to Gödel’s incompleteness result

is not a peculiarity of twentieth-century philosophers. It is in reality part and

parcel of a long tradition which goes back at least to Descartes» (Id.,

The Prin-

ciples of Mathematics Revisited

, Cambridge, Cambridge University Press, 1998, p.

89). As Spinoza studies have suggested, Spinoza presupposed



as a result of which «it turns out that his


exhibits the

defining properties of the universe it describes. That is to say, the



«that the conception of which does not need the conception of another thing

from which it must be formed» (E-I, def. 3. Th. C. Mark,

Ordine Geometrica


cit., pp. 283-284; see also M. Hooker,

Deductive Character of Spino-

za’s Metaphysics


cit., pp. 30, 301, on “incompleteness” in


). For further

philosophical implications of Gödel’s incompleteness theorem, see e.g. E.


Il mito del sistema completo,

in «Teoria», 2005, 2, pp. 183-190.

In Vico’s case, the question of completeness/incompleteness is of another

sort. To follow Hintikka’s terminology, it has to do with so-called




Principles of Mathematics

, cit., pp. 91-95), of which Hintikka said:

«This notion is definable completely independently of any axiomatization of

the underlying logic, and hence independently of all questions of deductive

completeness» (


, p. 95). An echo of Vico’s aspiration of descriptive com-

pleteness (whether fully realized or not) is detectable in statements of readers

such as: «the penchant for generalizing and turning every insight into a “prin-

ciple”» (D. R. Kelley,

Vico’s Road


cit., p. 17), and: «Vico reverses Occam’s

sense of the economy of thought. We find not Occam’s razor, but Vico’s

magnet. Principles are multiplied and as many as possible are drawn into the

presentation of a given point» (D. Ph. Verene,

Vico’s Science of Imagination

, Itha-

ca-London, Cornell University Press, 1981, p. 106).


As V. Hösle remarked: «Die Frage nach dem Ursprung der Axiome hat

Vico nicht beantwortet (Vico did not answer the question of the origin of the

axioms)» (Id.,


, cit., p. CXIII).