Azamat,
When we use the words 'possible' and 'actual', we must distinguish
pure mathematics and applied mathematics:
1. Pure mathematics is pure possibility. It can never make any
claims about what is or is not actual.
2. But *applied* mathematics must determine which of the infinitely
many theories are the best approximations to some actuality
[JFS] Challenge: I claim that it's impossible to find or
describe anything that is somewhere in between possible/actual
or mathematical/physical -- according to the way I defined it.
[AA] It was shown by Aristotle that the method of dichotomy is
not good in making an exhaustive division into two and ONLY two
classes.
But that statement is about applied mathematics, where we have to
choose among all the possibilities. That is the gray area where
there is no certainty. We can never do an exhaustive analysis.
AA
Reality is so rich and diverse that hardly any formal science
or logical scheme could meet its infinite complexity.
Yes. But I would prefer to emphasize the choice:
JFS
Reality is so rich and diverse and the possibilities are infinite.
We can never be certain which formal science or logical scheme is best.
John
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