On Generation and corruption
'element', yet another contrariety will belong not only to Q but
also to F (Fire). And, similarly, every addition of a new 'element'
will carry with it the attachment of a new contrariety to the
preceding elements'. Consequently, if the 'elements' are infinitely
many, there will also belong to the single 'element' an infinite
number of contrarieties. But if that be so, it will be impossible to
define any 'element': impossible also for any to come-to-be. For if
one is to result from another, it will have to pass through such a
vast number of contrarieties-and indeed even more than any determinate
number. Consequently (i) into some 'elements' transformation will
never be effected-viz. if the intermediates are infinite in number, as
they must be if the 'elements' are infinitely many: further (ii) there
will not even be a transformation of Air into Fire, if the
contrarieties are infinitely many: moreover (iii) all the 'elements'
become one. For all the contrarieties of the 'elements' above F must
belong to those below F, and vice versa: hence they will all be one.
As for those who agree with Empedocles that the 'elements' of body
are more than one, so that they are not transformed into one
another-one may well wonder in what sense it is open to them to
maintain that the 'elements' are comparable. Yet Empedocles says
'For these are all not only equal...'
If it is meant that they are comparable in their amount, all the
'comparables' must possess an identical something whereby they are
measured. If, e.g. one pint of Water yields ten of Air, both are
measured by the same unit; and therefore both were from the first an
identical something. On the other hand, suppose (ii) they are not
'comparable in their amount' in the sense that so-much of the one
yields so much of the other, but comparable in 'power of action (a
pint of Water, e.g. having a power of cooling equal to that of ten