“Perhaps different mathematicians do actually have inherently different perceptions as to the truth of statements that relate to non-constructively infinite sets. It is certainly true that they often profess to having such different perceptions. But I think that such differences are basically similar to the differences in expectations that different mathematicians might have with regard to the truth of ordinary mathematical propositions. These expectations are merely provisional opinions. So long as a convincing demonstration or refutation hs not been found, the mathematicians may disagree amongst themselves as to what they expect, or guess is true, but the possession of such a demonstration by one of the mathematicians would (in principle) enable the others also to become convinced. With regard to foundational issues, such demonstrations are indeed lacking. It might be the case that convincing demonstrations will never be found. Perhaps they cannot be found because such demonstrations do not exist, and it is simply the case that there are different equally valid viewpoints with regard to these foundational issues.”