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Suppose an opponent said: “Burhan al-Tatbiq is categorical proof for the impossibility of an actual infinite. Yet, you believe that God actually knows all facts. And the number of facts is infinite, since you claim that the number of future events is infinite, and that God beginninglessly knows about each and every one of those events. How do you resolve this contradiction?”
Ibn Al-Tilimsani responds to this in his commentary of Ma’alim Usul Al-Deen. The Shaykh writes:
| If one grants that Burhan Al-Tatbiq is a sound proof, and that it is impossible for an infinite amount to increase or decrease, then this would not apply to the facts that the Creator Most High knows.
For this proof [Burhan Al-Tatbiq], is what the logicians call a proof by contradiction. And this means that we take the belief of the opponent as a premise in an argument, and we add true premises to this argument [while maintaining the argument’s validity], until a false conclusion is entailed from the argument. Then we say: this false conclusion, is either due to the invalidity of the argument, or because at least one of the premises is false. And the argument is valid, since its form is valid. Thus, the problem is in one of the premises. And the premises we added are all true, except the belief of the opponent. Thus, the problem is in the belief of the opponent. [Entailing that the opponent’s belief be false.] And since the opponent’s belief is false, then its negation is necessarily true. And this negation is our belief[1]. And when we cut some of the past events, and supposed their non-existence, then what we supposed is possible. Since those events were non-existent before they emerged. [Entailing that non-existence be possible for them.] As for supposing that the Creator Most High, lacked knowledge of some facts, then this is impossible according to us. And the opponent has not presented proof for its possibility. And we do not grant it for Him. Rather, He Most High, necessarily knows all facts, and it is impossible for necessities to be negated[2][3]. |
– Ibn Al-Tilmisani, Sharh Ma’alim Usul Al-Deen (pg.286)
[1] In other words, we take the opponent’s belief as a premise: “The sequence of all past events is an infinitely long sequence”.
And we add to it true premises like: “An infinitely long sequence cannot increase or decrease”.
And what is concluded is: “The sequence of all past events cannot increase or decrease”.
But this conclusion is known to be false. Since the sequence of past events increases as time progresses. Thus, either the problem is in the validity of the argument, or the problem is in one of the premises. The argument is valid, and the second premise is true by agreement (between us and the opponent; the opponent being the Philosophers). Thus, the conclusion is false due to the falsity of the first premise. And this first premise is the opponent’s belief. So the opponent’s belief is false.
[2] Unlike the sequence of all past events, which increases as time progresses, what Allah ﷻ knows does not increase or decrease. And so Burhan Al-Tatbiq does not apply to it.
For the proof depends on the possibility of removing some of the members in the supposed infinite set that is being investigated. And this removing is possible for a group of contingents, because each one of those contingents accepts non-existence by virtue of what it is. It is also possible in the case of past events, because those past events were non-existent before they emerged. But this removal is impossible in the case of the facts that Allah ﷻ knows. Since it is impossible for His Knowledge to not relate to something. Rather, He ﷻ knows all facts beginninglessly and necessarily, by virtue of being attributed with a single Knowledge.
[3] And all other proofs that demonstrate the impossibility of Tasalsul, do not apply to God’s Knowledge. Since they seek to prove that the sequence of past events is finite, by appealing to the fact that this sequence comes to an end with the present moment. Whereas His Knowledge does not come to an end.
Keys to the Unseen 