Tahafut_al-Tahafut-transl-Engl-van-den-Bergh

period, necessarily the proportion between their wholes and between their
parts will be the same. If, however, there is no proportion between two
movements in their totality, because they are both potential, i.e. they have
neither beginning nor end but there exists a proportion between the parts,
because they are both actual, then the proportion between the wholes is
not necessarily the same as the proportion between the parts-although
many think so, basing their proof on this prejudice -for there is no
proportion between two magnitudes or quantities which are both taken to
be infinite. When, therefore, the ancients believed that, for instance, the
totality of the movements of the sun and of Saturn had neither beginning
nor end, there could be no proportion between them, for this would have
implied the finitude of both these totalities, just as this is implied for the
parts of both. This is self-evident. Our adversaries believe that, when a
proportion of more and less exists between parts, this proportion holds
good also for the totalities, but this is only binding when the totalities are
finite. For where there is no end there is neither ‘more’ nor ‘less’. The
admission in such a case of the proportion of more and less brings with it
another absurd consequence, namely that one infinite could be greater
than another. This is only absurd when one supposes two things actually
infinite, for then a proportion does exist between them. When, however,
one imagines things potentially infinite, there exists no proportion at all.
This is the right answer to this question, not what Ghazali says in the
name of the philosophers.
And through this are solved all the difficulties which beset our
adversaries on this question, of which the greatest is that which they
habitually formulate in this way: If the movements in the past are infinite,
then no movement in the actual present can take place, unless an infinite
number of preceding movements is terminated., This is true, and
acknowledged by the philosophers, once granted that the anterior
movement is the condition for the posterior movement’s taking place, i.e.
once granted that the existence of one single movement implies an infinite
number of causes. But no philosopher allows the existence of an infinite
number of causes, as accepted by the materialists, for this would imply the
existence of an effect without cause and a motion without mover. But
when the existence of an eternal prime mover had been proved, whose
act cannot be posterior to his being, it followed that there could as little be
a beginning for his act as for his being; otherwise his act would be
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