[gowld]

A way to make peace with the Reals is to understand them as "potential numbers". Every where you look, there is Real number. Everyone logical agrees about that.

But what about where you don't look? Either you take the orthodox axiomatic view that Real numbers are there too, or you take the constuctivist or finitist (or perhaps quantum mechanical?) view that nothing is there until you look, because the act of looking is the same as the act of creation.

[drdeca]

I wouldn’t call it quantum mechanical. The “looking” in math is not like the measurement of an observable/operator in quantum mechanics. When you consider a thing in math, there’s no alternative thing that you could have considered instead which would correspond to a different operator that doesn’t commute with the first one.