Perhaps, but what's to say the Earth isn't an abstract? Since the Earth does not exist physically, why can't it be abstract?

After all, if a philosphy can have an impact on the physical world while being abstract, surely the Earth can too.

So what kind of person are you? I submit that you fit into one of four categories:

1) People who want to cross bridges.

2) People who want to build bridges, and realize that they'll need to do some math to get it done.

3) People who want to do math for its own sake, because it's pretty or fun.

4) People who are very concerned with the realization that the connection between the bridges and the math is not perfect, that there are some serious philosophical errors with trying to treat the universe as an abstract mathematical ideal, and that, in the end, philosophy and mathematics might just be rooted in assumptions that are, as far as anybody can tell, just plain insane.

So, notice how there are connections (and overlap) between groups 1, 2, and 3, but that 4 is kind of on its own. Nobody in the other groups really cares about what group 4 has to say. Stuff that group 4 does is only relevant to other people in group 4. No matter what group 4 does, bridges will not suddenly collapse or cease to exist. People will go about their lives, crossing bridges, building bridges, and solving mathematical puzzles (about bridges), without giving a hoot about the problems of the philosophical roots of mathematics.

Currently I'm in group 4.

-Erasmus