The argument is, if you believe anything, you must have come to your belief through some process. If the process had an undiscoverable flaw in it, it would be invalid. Moreover, it is not possible to tell whether any process has a flaw which is undiscoverable. So there is no absolute way to tell whether any reasoning is valid or invalid. This may seem a little strange, but think of it as making mistakes. No matter how many times you check your work and how sure you may seem, there is no way to know for certain that you didn't make a mistake somewhere. Quantum uncertainty is a possible mechanism for undiscoverable flaws. Every particle has some nonzero chance of being found almost anywhere. So it is possible, albeit unlikely, that the action of any system could be drastically different from the way you expect it to go. Any reasoning carried out must be done by some system, such as your brain or a computer. There is a tiny chance that your brain or the computer will act drastically different from how you would expect it to--for example, in such a way as to arrive at the same wrong answer, completely randomly, every single time. This possibility may seem negligible, but consider that your judgment that it is negligible is simply the result of a process in your brain, and subject to the same quantum effects as anything else. So there is a chance that your judgment that it is negligible is completely wrong, and it actually is quite common for a system to arrive at the same wrong answer through random quantum effects every time. So long as the probability-judging processes are susceptible to any error--no matter how improbable such error seems--there is no way to know how likely or unlikely error in all your thoughts is.