51

From my "watched a YouTube video" understanding of Gödel's Incompleteness Theorem, a consistent mathematical system cannot prove its own consistency, and any seemingly consistent system could always have a fatal contradiction that invalidates the whole system, and the only way to know would be to find the contradiction.

So if at some point our current system of math gets proven inconsistent, what happens next? Can we tweak just the inconsistent part and have everything else still be valid or would we be forced to rebuild all of math from basic logic?

you are viewing a single comment's thread
view the rest of the comments
[-] CanadaPlus@lemmy.sdf.org 2 points 1 week ago

I mean, me neither. But if all sets are finite AoC just trivially holds, right? You can do it "manually".

If you back off to just ZF, parts of functional analysis will break. L^infinity^ space isn't separable, and so isn't necessarily Baire anymore, for example.

If we go all the way to finitism or ultrafinitism it doesn't really exist as a concept in the first place. But, whatever numerical engineering calculation will still work, and you can probably do something that looks like functional analysis to determine a mode of vibration, even if you're actually just using a series of high-dimensional but finite spaces. Probably, anyway. Don't ask me to prove it.

[-] mathemachristian@lemmy.ml 1 points 1 week ago

You still need to select the class is what I think. If you don't have infinitely many numbers than how many do you have line of thinking.

this post was submitted on 03 Feb 2026
51 points (96.4% liked)

Asklemmy

52971 readers
138 users here now

A loosely moderated place to ask open-ended questions

Search asklemmy 🔍

If your post meets the following criteria, it's welcome here!

  1. Open-ended question
  2. Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
  3. Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
  4. Not ad nauseam inducing: please make sure it is a question that would be new to most members
  5. An actual topic of discussion

Looking for support?

Looking for a community?

~Icon~ ~by~ ~@Double_A@discuss.tchncs.de~

founded 6 years ago
MODERATORS