> So, although I had to start out by thinking > that CH would decide something, what I have > learned is that pluralism on these matters > is far more valuable.
Heisenberg's matrix mechanics and Schrodinger wave mechanics were a 'pluralistic interpretation' in the development of quantum mechanics. Nonetheless, they ultimately proved to be identical . Pluralism has its value, but pluralism for pluralism's sake is unacceptable in mathematics . We should always seek out to understand where and why pluralism arises, and thus construct a 'unified theory' , a higher vantage point from which all the 'pluralistic interpretations' would appear as facets, if they cannot be reconciled in themselves. If we don't understand how to look at a cube, one may see a square, another , a hexagon . Practitioners of intuitionist and classical logic can understand one another and 'translate between languages' even if they do not speak a common language . So it is with standard and non-standard analysis . My fear is that we'll never manage to find a clear unambiguous interpretation for the concept of set, let alone several.