[gerdesj]

"If one takes natural language as a means to definite sets, you quickly get a plethora of paradoxes"

Which is why I think if you resort to natural language to refute the consequences of a more rigorous treatment of the concept of number then there will be trouble. The whole paper attempts to refute things like Cantor through a weird recourse to French.

However I think it is possible to reduce real numbers as being a sort of subset of French purely through the same construct that Mr Cantor describes because that's the way descriptions work. If you define a real in some way in some form of symbolic language - I recall from GED that SSS might embody "three" and so does "trois". So I don't see why French can't encompass reals SSS can be considered exactly equivalent to trois.

I suspect I need to know and understand the formal, rigorous definition of "real" before I really give it some.