>>16641404
>But nevertheless, why should existence be reduced to algirithm procedures?
Arguably, we would have never started doing mathematics if it didn't spit out useful results.
"Algorithmic procedures" makes it seem like it's something new, but computation has been at the heart of mathematics since forever, and the ancients were wary of wandering too much into non-computation (e.g. irrationals).

>Shouldn't the very obvious geometric intuition that there should be a zero in the interval counteract that perspective.
But of course there is a sense in which there shouldn't not be a zero, constructively speaking. But you can't show one -- it's not about rejection one or the other notion of existence, the question is why should these two notions be conflated *and then* recovered by studying algorithmics in classical logic, when constructive logic does it automatically? Isn't proper mathematical practice all about about drawing the correct distinctions so that the pieces fall into place by themselves?
Now, the circumlocution that constructive logic forces on you, the double negation, is as unelegant as you want, but it's still a significant fact (a mathematical truth, an abstract fact) with practical consequences.
That's not to say that constructive logic is the ultimate logic and classical logic has nothing, constructive logic has its faults, and it's not as powerful at backwards reasoning (disjunctive syllogism, possible existence) as classical logic, which analysis employs a lot of. Fortunately, rather than forcing us to step back to classical logic, we can step forward to linear logic, although I don't know anyone developing analysis in LL, since it's niche even among CS people.

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