The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[polymath257]

Go ahead, give me one example of something you can conceive of, and which is logically impossible to exist at the same time.

I can *conceive of* three positive integers x,y, and z and an integer exponent p>2 with x^p +y^p =z^p. But it has been discovered that such is logically impossible.

I can conceive of a finite field with non-commutative multiplication, but it also known that such is logically impossible.

I can conceive of a Fourier series for a continuous function that diverges everywhere, but, again, it is known to be logically impossible.

I can conceive of an odd perfect number, but *nobody* knows if such are logically possible or not.

I can conceive of a non-trivial zero of the Riemann zeta function that isn't on the critical line. Once again, *nobody* knows if such is logically possible or not.

At least part of the  problem is that the notion of 'conceive' is way too vague. How much detail is required to actually have a 'clear conception' of something?