I genuinely appreciate your respectful tone TD, so don't take this the wrong way, but I actually don't think LF is even correct in that respect. As long as scientific 'proof' is based on observable evidence and repeatable experiments, then ultimately it remains a question of probability.
In science, you perform an experiment numerous times, and every time get the same result. Therefore we conclude that in all probability, given the same conditions we will always get the same result, and we draw conclusions based on that. However, there is always a possibility, however remote, that were we to perform the experiment again under the same circumstances, we would not get the same result, and this would undermine our original conclusion.
For that reason, I do not believe you can prove anything about the 'real world' beyond all doubt, even if you avoid more philosophical questions.