 Finally, Avicenna argues that even if separate mathematical objects exist, they cannot be the principles (or causes) of natural things. It seems intuitively plausible that if a separate mathematical object is the principle of any material existent, it must in the first place be the principle of its own sensible counterpart. Note that, according to Avicenna, the claim that a separate mathematical object, say a triangle, exists cannot be justified unless we have come to know it through knowing a sensible counterpart of it that exists in the material world. Now if that separate triangle is the cause of any material thing, it must in the first place be the principle of its own sensible counterpart, or so Avicenna believes. But if the sensible triangle is caused by the separate triangle, then we can legitimately ask why the former needs the latter. It is either the essence or (some of) the accidents of the sensible triangle that make it dependent on its separate counterpart. However, if it is due to the essence of the sensible triangle, then the separate triangle itself needs a principle. This is because the separate and the sensible triangles share the same essence. Thus, if it is the essence of the sensible triangle which makes it need the separate triangle, then the separate triangle (having the same essence as its sensible counterpart) must itself be caused by another separate triangle. Repeating the same line of argument, we can conclude that there must exist an infinite chain of causally connected triangles. Since such infinite regresses are unacceptable, what makes a sensible mathematical object need its separate counterpart is not their shared essence. But it is also impossible that (some of) the accidents of a sensible mathematical object make it dependent on its separate counterpart. The accidents of the sensible object do not exist unless that object itself exists. But it is also assumed that the sensible object itself does not exist unless the separate object exists. This means that the separate object has some sort of explanatory priority over the accidents of the sensible object. Therefore, the accidents of a sensible mathematical object cannot explain, in a non-circular way, why this object needs its separate counterpart (Avicenna [MPh]: chap. VII.3, sec 4). Thus, it seems that there is no convincing justification for why a separate mathematical object must be the cause of its sensible counterpart, let alone the cause (or principle) of any other natural thing. Avicenna takes this argument as refuting  (PM).