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Our abstraction possesses a double ability when beholding a multitude. We can perceive a
multitude as a collection of distinct objects by bringing them together one by one in a mental act
of collecting, but we can also grasp large multiplicities of sensory objects as a whole ‘in one
glance.’ 130 A teacher can walk into a classroom of students he has never met and without coming
to know any of them individually make the class a subject of his judgements. This ability of
grasping a multitude as a One at a single glance explains how we can form concepts of very large
collections, possibly infinite ones, because it does not rely on counting all of elements of the
multitude. Hence, in geometry, while one is aware of the infinite multiplicity of points of a line,
one grasps the existence of an infinite straight line from the knowledge of two distinct points.
The abstraction from the two given points to the infinite line is instantaneous; it does not proceed
through drawing (or imagining) more and more points. If one tries to imagine a line by
successive addition of points, one will never comprehend the line which is infinite in length.
Cantor, also, demonstrates a great conviction in man’s ability to know: “all things,
whether finite or infinite are definite and, with exception of God, can be determined by the
intellect.” 131 For Cantor, a being is determined by the intellect if it can become an object of
mathematical knowledge. Both finite and transfinite quantities are objects of mathematics;
however, the absolute infinite; i.e., God, falls beyond the scope of mathematics. God is the only
being that cannot be known, not even approximately. According to Cantor, God can only be
acknowledged. 132 It is important to emphasize that the transfinite numbers do not provide a kind
of asymptotic reasoning for making God accessible to human reason. In fact, God’s infinity
130
Ibid, 246.
Newstead, "Cantor on Infinity,” 546.
132
Ibid, 544.
131
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