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C ONCLUSION .
The question of the temporal beginning of the world challenged both Aquinas and
Bonaventure to clarify their understanding of creation and infinity. Both Aquinas and
Bonaventure accept the five Aristotelian properties of infinity: infinity cannot be ordered,
increased, traversed, or grasped by a finite intellect, and a multitude of beings cannot be actually
infinite. Bonaventure simply applies the above properties of infinity to show the nonsensical
character of the infinite past time. Aquinas questions the manner in which these properties of
infinity apply to infinite past time but does not doubt the validity of these properties (except for
the possibility of existence of an infinite multitude of spiritual beings.)
Cantor’s responses to the five objections to the eternity of the world arising from the
notion of infinity are strikingly different from those of Aquinas and Bonaventure. Cantor claims
that the Aristotelian description of infinity is false. Infinity can be ordered, increased, and
grasped by a finite intellect. An actual infinity can be traversed in an instant, and actually infinite
multitudes can exist both in the mind as well as in the reality. While these differences can be
attributed to Cantor’s almost unreserved openness to the existence of an actual infinity and his
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