64 / 298
Horst Steinke
64
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).
115
E. Shmueli,
The Geometrical Method, Personal Caution, and the Idea of Toler-
ance
, 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
all
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).
116
Liber metaphysicus
, Chapter II;
On the Most Ancient Wisdom of the Italians
,
cit., p. 49.
117
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.
118
Ibid.
, 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.
119
As is well-known, this is the major topic of
Liber metaphysicus.
120
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).
121
As A. V. Garrett observed: «There is a kind of bootstrapping going on
throughout the
Ethics
» (Id.,
Meaning in Spinoza’s Method
, cit., p. 116, footnote
45).
122
See a detailed discussion of Vico’s “axioms” in P. Cristofolini,
La
Scienza nuova
di Vico,
cit., pp. 77-109.
123
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-