8. To pan (“The all”). The Homeric term to pan
(τό πα̃ν) occurs several times in Aristotle's De caelo,
sometimes reinforced by to holon (τό ὅλον; the Whole),
and its meaning is a near-synonym for the leading term
ouranos (“Heaven,” “World”). However, in Physica,
Book 4, Ch. 5, at the end of the essay on topos, to
pan has a somewhat special connotation. There, Aris-
totle raises the following question in a rumination of
his: if one views the whole universe, to pan, not as
a cosmic datum but as a physical system however vast,
does it then have a physical topos, and how? (Bochner
[1966], p. 178). This is an intriguing question, and
various aspects of the question have been raised more
than once since.
Thus, Nicholas of Cusa, who had a mathematical
turn of thought, equated the would-be topos of the
universe with a mathematical substratum of it, and he
asked, implicitly but recognizably, whether the uni-
verse, in a suitable substratum, might escape the
dichotomy of having to be finite or infinite. He divined
that there are mathematical universes to which the
dichotomy does not apply (Bochner [1968], p. 325),
and he even knew that the space of the universe may
be endowed with a mathematical homogeneity by
which every point can be viewed as a center of it
(Koyré, Ch. 1). Or, if we envisage not the underlying
space of the universe but the matter in it, then in the
words of a present-day cosmologist: “It is theoretically
possible... for an unbounded distribution of matter
to have its circumference nowhere, and center every-
where” (G. J. Whitrow, p. 43).
After Cusa, Copernicus and Newton entertained
thoughts that were consonant with his. Newton may
have even been perturbed by the question (even if he
would not admit to it) of how to extend the mathe-
matical substratum of our solar system beyond itself,
in case some of the comets should move on hyperbolic
orbits, which are mathematically possible, but mathe-
matically are not contained within the substratum of
the planetary system proper (Bochner [1969], Ch. 14).
A version of Aristotle's problem arises in present-day
cosmology. In the general theory of relativity space
is gravitational space and is thus largely determined
by a distribution of gravitational masses. Now, if this
distribution is known and if the shape of the resulting
space is to be determined, then, for operational pur-
poses, a background space, that is a kind of topos in
the sense of Aristotle, must be chosen a priori; and it
would be desirable to have a procedure for making
this a priori choice in any one given case.
