The basis for continuous hierarchy is that things change in time. Anything in physical reality is different every time you measure it--every concrete set is different. The question is, do things we think of (abstract sets) change in time when we measure them. Our understanding of a situation may change. We may get more insight into ourselves or a situation. We have a set in our minds that is the set of all squares. There are an infinite number of squares in the square set--assuming our mental universe is unbounded in size. There is no such thing as a concrete set of squares...they are all imperfect examples of something in the abstract set of squares.
Continuous hierarchy is not about abstract sets, it's about concrete sets. I cannot argue about stuff that is infinite in nature. It would take me too long.
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