Chapter 1
Guénon argues that what moderns call “the infinite” is not actually the Infinite; the Infinite is the unlimited, and anything limited is finite. He claims we should differentiate between “the indefinite” and “the Infinite”. Space, time, and the integers are “indefinite” since we can imagine them extending indefinitely in different “directions”. The examples just mentioned, however, are limited, and therefore not the Infinite.
Guénon’s concept of “the indefinite” seems to me to be the same as the “potential infinite”.
Chapter 2
Guénon argues against the concept of an absolute or completed infinity by saying it implies that “a part can equal the whole”, e.g., the number of even numbers must equal the number of natural numbers. This is the same argument Leibniz used against an actual infinity. The argument is basically nonsense.