they were both even and odd, this would be impossible, because an even number can be divided into two equal parts, whereas an odd number cannot. The same number cannot both admit and not admit such division. If they were neither even nor odd, this would entail an intermediate state between negation and affirmation, which is impossible. These impossibilities arise only from positing a number without limit; therefore, positing such a number is impossible.”

He said:

“This claim of impossibility is as unsound as the first, for two reasons:

First: We may concede that what is infinite cannot be even or odd. But the claim that what is infinite cannot be short of the one that would make it even if it were odd, or odd if it were even, is a bare assertion—a mere judgment of implausibility unsupported by evidence.

Second: The same objection would apply to numerical orders, to the objects of Allah’s knowledge, and to the things within His power. These are infinite in possibility, yet the foregoing argument could be applied to them.”

[Ibn Taymiyyah’s commentary]

I say:

Someone might respond: The first objection is weak, for the notion that what has no