There are other aspects of Infinity which we can get at by studying
series, and which in the conception of series of series give strength
and point to the philosophic conception of an Absolute.
Prof. C. Keyser develops this thought, and shows (in two recent
articles, January and April 1909, in the _Hibbert Journal_) that
certain theological dogmas, such as the doctrine of the Trinity,
and certain attributes of the Divine Being, such as Omniscience and
Omnipresence, are entirely conceivable by the human mind if regarded
without the paralysing limitations of the Finite. He shows that in
our mathematical formulæ which have to do with infinite series we
have the exact replica of what to the lay, non-mathematical mind seem
to be the paradoxes of the Athanasian Creed. He first shows that in
a mathematical analogy points of view about an Infinite Being, even
if partially discordant, may all be true if regard is had to His
Infinity.[26]
Further, he shows that certain assumptions, such as _the whole
is greater than its part_, are inapplicable to Infinite Being.
The conception of a Trinity in Unity in which “none is afore or
after other, none is greater or less than another, but the whole
three persons are co-eternal together and co-equal” is rationally
conceivable by the mathematician who is familiar with the theory of
manifolds.[27]