from what has been said it is evident that the maximum consists in the
minimum and the minimum in the maximum, as in the many is the one, in
the one the many. Yet reason and nature may more readily separate the
minimum from the maximum than the maximum from the minimum. Therefore
the immeasurable universe is nothing but centre everywhere; eternity
nothing but a moment always; immeasurable body an atom; immeasurable
plane a point; immeasurable space the receptacle of a point or
atom."[415]
The chief source of error on the part of the Peripatetics was their
failure to distinguish between the minimum as a part, and the minimum a
_terminus_ or limit. Hence their idea that no combination of physical
minima would give a magnitude, since two or more would touch one
another with their whole surface, _i.e._ would coincide:--otherwise
the minimum would have parts, a part of each touching the other, and
a part not touching. On their theory it would follow that magnitudes
do not consist of parts, or at least not of elementary parts. This is
inconsistent with nature, for existing magnitudes must have been built
up out of nature's elements, and with art, for art can measure only
on the assumption of first parts. It is true that what is posited as
first part in one operation may be the last result in another, for
the _minimum_, as we have seen, is a relative conception, but _some_
first part is always assumed in any operation. And as the operation
of art is not infinite, so neither is there infinite subordination of
parts.[416] When two minima touch one another, they do not do so with
their whole body, _or any part of it_, but one with its terminus or
limit may touch several others; no body touches another with the whole
of itself or a part, but with either the whole or the part of its
_limiting_ surface. The _terminus_ of a thing is therefore no part of
it, and by implication not a minimal part. Hence there are two kinds of
_minima_ concerned--that of the touching body, or part, and the minimum
of that by which the contact is effected, the _terminus_.[417] The
atom, which is the minimal sphere, touches in the absolutely minimal
point, the smallest _terminus_. Other spheres do not touch in a point
simply, but in more than one, or in a plane circle.[418] By adding
limit to limit we never obtain a magnitude; the _terminus_ is no part,
and therefore if in contact it would touch with its whole self, so that
magnitude is not made up of _termini_, whether points, atoms, lines, or
surfaces which are termini; and this was the false ground on which the
Aristotelians denied the possibility of the atom. It remained to ask if
the _termini_ were infinite, since the atoms were not; but it was clear
that their number was determined by that of the atoms. For two limits
do not touch one another:--"They do not cohere or make a _quantum_,
but through them others in contact with one another make a _contiguum_
or _continuum_."[419] It may be added that if the parts of a divisible
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account