[circlefavshape]

I agree that mathematics is a language, where a language is a system we have for describing the world and communicating with each other.

I don't understand what argument you are making here. "Infinitesimal" is just an idea, as far as I know. Nothing real is infinitesimal.

[unblough]

> "Infinitesimal" is just an idea, as far as I know. Nothing real is infinitesimal.

The unreal (re: abstracted) aspect is what places it outside the confines of “language” for me.

Are black holes real? Do they have singularities? If yes, that can be an example of your “real” infinitesimal.

My opinion is that infinitesimals are more than real they are essential. They are the building blocks of all that is “real”.

Ultimately, what we’re talking about is a philosophical debate that would require one to step “outside” reality to confirm or deny outright so we are just providing our opinions on an unknowable concept.

What is “real” in this context?

Is pi “real”? Is the plank constant? The former was my path to the essentialism of infinitesimals. The latter my path to the essentialism of discrete counting.

[godelski]

> Are black holes real?

Yes

> Do they have singularities?

¯\_(ツ)_/¯

The math leads us there but I don't think anyone is particularly happy about it.

> Is pi “real”?

¯\_(ツ)_/¯

> Is the plank constant?

¯\_(ツ)_/¯

Fuck man, I can't tell you if a quark is real. I'm also not aware of anyone who can. The best we got is our interpretation that the model being indistinguishable from the real thing might as well be the real thing. Metaphysics and metamathematics are mind bending areas that require a deep understanding of the non-meta concepts first.

But given all you've said, I highly suggest looking into the various set theories I mentioned previously. Specifically start with Finite ZF set theory and Peano Arithmetic, where you'll find you can indeed operate on such concepts as pi without infinities.