alt Hacker News>That famous quote could use attribution
It could, but doesn't need it.
That models are not direct truth is just logical. If there were such a thing that were indistinguishable from the direct truth, it would be the direct truth, not some other thing called a model.
This is why I've never understood the "revalatory" nature of Godel's incompleteness. Of course any axiomatic system must not contain all truths. Axiomatic systems are models and models can't contain all truth. If an axiomatic system contained all truth it would just be all truth rather than some other thing called an axiomatic system.
The only case in which Godel's argument surprises is the case in which one has a fundamental misunderstanding of what a model can and cannot be, which I suppose must have been more common in his time, but I was really confused when my highschool teacher went to great lengths to explain that a model cannot contain the whole truth because...of course it can't?
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If I present a novel, unique axiomatic system, with no intent that it refers to anything in the world, what is it a model of?
> of course it can’t?
If obvious, can you prove it without reading Gödel’s proof or anyone else’s?
The important (2nd) part of Gödel’s proof is not that a model can’t contain all truth, it’s that a model cannot prove itself true, which is a far stronger statement than the intuition you describe. Of course, belief that your own intuition is independent of history is also highly questionable; you were raised and educated in an environment in which people were already aware of Gödel. It’s like saying the number zero is obvious (which it is now) despite the fact that it took thousands of years before it was used formally as a number. There was a time when it wasn’t obvious to the smartest people alive.
Note that formal axiomatic systems aren’t physical systems; what Gödel was talking about and what George Box was talking about are related but somewhat different concepts. It is obvious in physics that a parabolic ballistic trajectory model doesn’t account for air turbulence. It’s not at all obvious that all of math itself is guaranteed to produce contradictions and cannot prove itself, especially if you’re allowed to change math or use any system you want.