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Vico’s Ring


formed by his epistemic commitments, that is, the tree-tiered

taxonomy of knowledge, which internally was made to cohere

with ultimate truth-preservation in the form of «scientia intui-

tiva». If our thesis is correct, a comparable state of affairs should

obtain and be observable in Spinoza’s approach to natural sci-



. To that end we will examine certain Spinoza letters that

deal with physics, on the one hand, and chemistry, on the other




With respect to physics, our reading will focus on

Letter 12

. In

it Spinoza performs a “thought experiment” of an (incompressi-

ble) fluid, such as water, flowing in a channel bounded by two

circles; the channel is formed, in plan view as shown in Spinoza’s

own diagram, by a large outer circle, and an inset smaller circle,

and the fluid flows parallel to the circles. However, the key fea-

ture of the channel is that the inner circle is eccentrically placed

so that the width of the channel is not constant but varies con-



. The main point or argument of this “experiment” is

that the continuously variable size of the channel entails that as

«all the inequalities of the space lying between two circles […]

exceed any number, [so] do all the variations of the speed of

matter moving through that area», thus demonstrating the reality

of «infinity»



Letter 12

is also called the “Letter on the Infinite”,

of which this physical setup is given as the actual proof. How

then may Spinoza’s surrounding exposition of «the infinite»

throw light on his epistemic approach to the «interpretation of

Nature»? Spinoza sets the tone and agenda right from the begin-

ning of the letter in terms of his epistemic system, into which we

are merely inserting his nomenclature:

[…] there is the failure to distinguish between [3


kind of knowledge:]

that which we can apprehend only by the intellect and not by the imag-

ination, and [1


kind:] that which can also be apprehended by the im-

agination. […] I answer that we conceive quantity in two ways: [3


kind:] abstractly or [1


kind:] superficially, as we have it [1


kind:] in