Belief in the Tasalsul of causes, is belief that a single contingent is caused by an infinite sequence of contingents, each member of the chain being the effect of the previous one, ad infinitum. This article will offer a proof called “Burhan Al-Tatbiq”, which demonstrates the impossibility of this belief. So we say:

    • If an actualized amount accepts decreases, then this amount cannot be infinite.
    • The set of all contingents is an actualized amount that accepts decreases. 
    • Therefore, the set of all contingents cannot be infinite.

Premise 1: If an actualized amount accepts decreases, then this amount cannot be infinite.

If an amount decreases, then the amount before the decreasing is necessarily more than the amount after the decreasing[1]. This is true by virtue of what ‘decreasing’ is. 

The above however, cannot be the case if the amount is infinitely long. Since an infinity cannot be greater than or less than another infinity[2]. After all, for an amount to be less another, requires the lesser amount to have a limit that was exceeded by the greater one. And having a limit precluded infinitude.

Premise 2: The set of all contingents is an actualized amount that accepts decreases.

The set of all contingents is comprised of contingents. And each contingent accepts non-existence[3]. Thus, any one of those contingents accepts cessation by virtue of what it is. 

So given the possibility of the above, it is possible for the set of all contingents to become smaller than what it is. And this is all what we mean by decreasing.

Therefore, the set of all contingents cannot be infinite.

Thus, the set of all contingents is comprised of a finite number of contingents.


 

[1] To say otherwise, is to say that the amount did not decrease when it decreased. Entailing that ‘decreasing’ is not ‘decreasing’. Which is a violation of identity.

[2] For a response to possible objections based on Cantor’s transfinite set theory, see here.

[3] Since a contingent is an existent that accepts non-existence by definition.

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