On Generation and corruption
'being' is necessary: and if it is eternal, its 'being' is
necessary. And if, therefore, the 'coming-to-be' of a thing is
necessary, its 'coming-to-be' is eternal; and if eternal, necessary.
It follows that the coming-to-be of anything, if it is absolutely
necessary, must be cyclical-i.e. must return upon itself. For coming
to-be must either be limited or not limited: and if not limited, it
must be either rectilinear or cyclical. But the first of these last
two alternatives is impossible if coming-to-be is to be eternal,
because there could not be any 'originative source' whatever in an
infinite rectilinear sequence, whether its members be taken
'downwards' (as future events) or 'upwards' (as past events). Yet
coming-to-be must have an 'originative source' (if it is to be
necessary and therefore eternal), nor can it be eternal if it is
limited. Consequently it must be cyclical. Hence the nexus must be
reciprocal. By this I mean that the necessary occurrence of 'this'
involves the necessary occurrence of its antecedent: and conversely
that, given the antecedent, it is also necessary for the consequent to
come-to-be. And this reciprocal nexus will hold continuously
throughout the sequence: for it makes no difference whether the
reciprocal nexus, of which we are speaking, is mediated by two, or
by many, members.
It is in circular movement, therefore, and in cyclical
coming-to-be that the 'absolutely necessary' is to be found. In
other words, if the coming-to-be of any things is cyclical, it is
'necessary' that each of them is coming-to-be and has come-to-be:
and if the coming-to-be of any things is 'necessary', their
coming-to-be is cyclical.
The result we have reached is logically concordant with the eternity
of circular motion, i.e. the eternity of the revolution of the heavens
(a fact which approved itself on other and independent evidence),'
since precisely those movements which belong to, and depend upon, this
eternal revolution 'come-to-be' of necessity, and of necessity 'will