Return to Infinity

There is a use of [the concept] "infinity" which is valid, as Aristotle observed, and that is the mathematical use. It is valid only when used to indicate a potentiality, never an actuality. Take the number series as an example. You can say it is infinite in the sense that, no matter how many numbers you count, there is always another number. You can always keep on counting; there's no end. In that sense it is infinite—as a potential. But notice that, actually, however many numbers you count, wherever you stop, you only reached that point, you only got so far. . . . That's Aristotle's point that the actual is always finite. Infinity exists only in the form of the ability of certain series to be extended indefinitely; but however much they are extended, in actual fact, wherever you stop it is finite.

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