I agree the argument isn't string but his personality carries weight
I am surprised you don't have issues with infinity PMB have you done much with QM?
I suspect you know the background but for others who aren't I shall give the brief version.
I think the first time I ever realized there are major issues with infinity was very early when studying Schrödinger's equation. The solution has to be linear and finite to get a proper time evolution to work.
Any attempt to make the solutions non linear gives you immediate problems with superposition because if they aren't linear you can't add the superpositions in any meaningful way unless you know the equation of the non linearity and thus you just inserted "consciousness" or "god" into QM take your pick because you can't create time evolution without one of those and so now have a really bad "Wigner's friend".
Even good old wiki gives the background to the problem
(http://en.wikipedia.org/wiki/Nonlinear_Schr%C3%B6dinger_equation)
Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state (except hypothetically, as in some early attempts, in the 1970s, to explain the quantum measurement process).
So having satisfied yourself the solution must be linear you can try infinity observers but there is an immediate problem
Now for the more advanced you can try and solve the equation for infinity. For those not capable the problem is you end up with two possibilities of the waveform at infinity the value goes to zero or at infinity the value goes to some actual value.
For any wavefunction which doesn't go to zero at infinity it is "pathological" you can not make the wavefunction evolution independant of time and you are actually back to the same problem as the non linear case. I will leave this as a statement of what ORAC says open to challenge if anyone wants a go
As a side note this is why any fields that are waveforms go to zero at infinity
So the key thing here is it tells you implicitly that at infinity the result MUST go to zero ... and ZERO means it doesn't exist or at least it's not measurable/observable or however you want to describe it.
So first under Schrödinger and that follows into QM that if there is a real infinity nothing measurable/observable or real exists there. In other words you can treat infinity in the normal mathematical way that it simply means a non existent number that represents a very large and finite number which you don't know.
Under GR/SR and even string theory things are a little easier with infinity but under strict QM infinity is something that can not be real or at the very worst it is something that is not observable.
So I guess for me it comes down to if QM correctly describes the universe it can't be infinite.
