Re: Mathematical existentiality and triviality.

RadicalLibertarian@xxxxxxxxxxx wrote:
Another weird example.


You have a number eight, and I also have a number eight. You have
yours, and I have mine. Call yours 8_(1), and call mine 8_(2).

Of course, 8=8, and indeed 8_(1) = 8_(2) = 8.

We can dispense with any of these additional 8's as long as we keep at
least one of them. Their existence is arbitrary because they are all
trivial. The number 8 is unique. Of course, so is every other number.

(whoops - I meant backwards E, not upside down A)

so -

For every number in R, there are at least uncountably infinitely many
such trivial numbers, because they can be constructed. And you can just
as easily call this false, because the numbers in question are all
trivial in the first place.

So, existence of such trivials can be considered as being arbitrary.
Trivials exist, and also do not. It's a paradox.

So, you can consider trivial domains, ranges, functions, dimensions,
whatever. None of it really exists. That is - it does exist, and also
does not. It's trivial. Existence is arbitrary.

I think that people tend to not consider such things, because math &
science culture seeks to eradicate paradox instead of simply
appreciating it for what it is.

.

Relevant Pages