I don’t why the Cartesian skeptic would want to invent calculus. I’m only saying it would be possible.
My point is that we humans are not ideal Cartesian skeptics. We live in a universe which, at the very least, appears to be largely independent of our minds (though of course our minds are parts of it). And in this universe, a vast majority of mathematical concepts have practical applications. Some were invented with applications in mind, while others were found to have such applications after their discovery. How could this be, if math is entirely non-empirical ? That is, how do you explain the fact that math is so useful to science and engineering ?
My point is that we humans are not ideal Cartesian skeptics. We live in a universe which, at the very least, appears to be largely independent of our minds (though of course our minds are parts of it). And in this universe, a vast majority of mathematical concepts have practical applications. Some were invented with applications in mind, while others were found to have such applications after their discovery. How could this be, if math is entirely non-empirical ? That is, how do you explain the fact that math is so useful to science and engineering ?