> the paradoxical part isn't that there's two from one What do you think the paradoxical part is then? > We can do this with only the real number line Actual

> the paradoxical part isn't that there's two from one What do you think the paradoxical part is then? > We can do this with only the real number line Actually you don't even need the reals. You can do the same trick with just the rationals. Half of aleph-zero is still aleph-zero. > Church numerals--they encode numbers, just the numbers with no associated nouns. That's debatable. I would say that a Church numeral's noun is an action (actions are nouns), specifically, function application. [UPDATE] > My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." I guess I didn't make it sufficiently clear that I'm not claiming this is an accepted consensus, this is a hypothesis that I am advancing and prepared to defend. Maybe I should be more explicit about that. > They are largely axiomatic systems of logic. I don't deny that. But not all axiomatic systems of logic are mathematically interesting. Chess, for example, can be axiomatized, but it's not particularly interesting from a mathematical point of view. You're not going to win a Fields medal for finding interesting chess puzzles. > That they correspond to such a degree with our experience of the 'real' world is the shocker. Yes, exactly. That is one of the facts that supports my position.