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Horst Steinke


world of «lines» and «numbers» for which it was constructed; and, above all,

that it could be imposed on the concrete reality of events and human history

which are always the domain of «the probable»)» (Id.,

Note sul “metodo” e la

“struttura” della Scienza nuova prima

, cit., p. 26).


E. Shmueli,

The Geometrical Method, Personal Caution, and the Idea of Toler-


, cit., p. 204; Viljanen agrees with this assessment: «[T]his, […] strongly

suggests that Spinoza regards the mathematical standard as the correct one,

because through it the true formal character of the world can be pinned

down. Given Spinoza’s tendency to think about


things through the model

provided by geometrical objects, it is quite understandable that his doctrine of

causality has much in common with the idea of the formal cause» (italics in

the original) (Id.,

Spinoza’s Geometry of Power


cit., p. 44).


Liber metaphysicus

, Chapter II;

On the Most Ancient Wisdom of the Italians


cit., p. 49.


At other times, Vico uses geometrical terms, such as “line” and “acute”

(angle) in a metaphorical way, but does go no further (G. Vico,

On the Study

Methods of Our Time

, cit., p. 24; see commentary in D. De Cesare,

Sul concetto di

metafora in G. B. Vico

, in «BCSV», XVI, 1986, pp. 325-334, pp. 329-330.



, Part IV, Proposition LVII, Note. A detailed discussion of various

forms of triangles in terms of Spinoza’s theory of emotions can be found in

V. Viljanen,

Spinoza’s Geometry of Power


cit., pp. 151-155, which includes sever-

al drawings of triangles to illustrate Spinoza’s concepts. In Part II, Proposition

VIII, Note, Spinoza uses the circle and intersecting lines to «illustrate» the

Proposition regarding «the ideas of particular things, or of modes». His philo-

sophical concepts relating to attributes, laws, formal essence, and modes find

their counterparts in this geometrical construction. See St. Büttner,

Ein “Kreis”

voller Missverständnisse. Philologische Miszelle zu einem geometrischen Beispiel in Spinozas

Ethik, in «Studia Spinozana», 12, 1996, pp. 185-194, p. 189.


As is well-known, this is the major topic of

Liber metaphysicus.


According to E. M. Curley: «[I]t is not true that we must first have a

firm grasp of Spinoza’s initial assumptions before we can understand what

follows them» (Id.,

Behind the Geometrical Method

, cit., p. 52).


As A. V. Garrett observed: «There is a kind of bootstrapping going on

throughout the


» (Id.,

Meaning in Spinoza’s Method

, cit., p. 116, footnote



See a detailed discussion of Vico’s “axioms” in P. Cristofolini,


Scienza nuova

di Vico,

cit., pp. 77-109.


Parenthetically, the difference that is being argued can also be given

expression in terms of aspects of their “logic”. In the case of Spinoza, the is-

sue is the consistency and completeness of deductive logic employed in Eu-