[FOM] Scotus on Actual Infinity

Dean Buckner Dean.Buckner at btopenworld.com
Tue Nov 4 17:13:06 EST 2003

Further to the debate about whether the medieval philosophers accepted
actual infinity. Scotus writes

"For our purposes, let us change the notion of the potentially infinite in
quantity, if possible, to that of the quantitatively infinite in act [i.e.
in actuality].  For just as it is necessary [in the case of potential
infinity] to that the quantity of the infinite should always grow by
receiving one part after another, so we might imagine that all the parts
that could be taken were taken at once or that they remained in existence
simultaneously.  If this could be done, we would have in actuality an
infinite quantity, beause it would be as great in actuality as it was
potentially.  And all those parts which in infinite succession would be
actualised and would have being one after the other would be conceived as
actualised all at once.  Such an infinite [in actuality] would indeed be a
whole and in truth a perfect whole, since there would be nothing outside it,
and it would be perfect since it lacks nothing.  What is more, nothing in
the way of quantity could be added to it, for then it could be exceeded."
(God and Creatures 5.6)

Dean Buckner,    : If one person can see it as a paradise
London,              : of mathematicians, why should not
ENGLAND        : another see it as a joke?

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