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?
Hofstadter’s “Godel Escher Bach: an Eternal Golden Braid” was on this, & mind.
Either self-consistency XOR completeness.
You can’t have both.
IF self-consistent, THEN incomplete.
IF complete ( completely-matching-universe ) THEN self-inconsistent.
.: self-consistent theory ONLY can describe a limited subset of universe.
Period.
( Hofstadter later identified, in his revised version of the book, in its preface, that his work was also on the nature of mind.
He claimed that nobody got it.
He obviously had no Buddhist friends.
When his illustrative-vignettes with the Tortoise & the Hare showed that you can present evidence to a formal-system ( represented by the Tortoise ), & it’ll say “oh, yes, of course that’s valid”, the next thing it’ll do, is demonstrate that it ignores all such evidence.
That is characteristic of ideologies, prejudices, “religions”, & formal-systems.
It’s the same “we only accept what is self-consistent with our belief, NOT what contradicts it” as formal-systems embody.
As a grotesque remapping, imagine being tasked with proving that mothering is meaningful, but you’re only permitted to use arithmetic, for proving it?
Well, you can’t, then, can you?
Mothering’s meaning ISN’T knowABLE within arithmetic: it’s in a different-kind of reality!
But people who insist that ONLY their-schema be allowed to measure “what is valid” … are all doing exactly the same scam that Hofstadter called-out in his absolutely-brilliant book, decades ago.
Anyways, Susskind has identified that “Time as a Fractal Flow” fits reality well, but he apparently hasn’t clued-in that if Time is fractal, … then isn’t Space also fractal?
The implications of Space being fractal … kinda nuke much of our whole physics-paradigm: continuum is completely-bogus, then.
Anyways, it all comes down to inapplicability:
Each model ISN’T applicable outside its applicability.
… isn’t Dunning-Kruger, or something, rooted in that?
People mistaking chess-competence for universal-competence?
Arithmetic isn’t universally-applicable.
Even something as specific as probability-calculus, with its “the difference between a tribe of 150 reduced to 149 is “IDENTICAL” with a tribe being reduced from 1 down to 0, because the ONLY difference is subtraction-of-1”…
that’s categorically wrong:
Reducing a tribe from 150 down to 149 is an ARITHMETIC difference of 1, but reducing it from 1 to 0, means the tribe’s continuity has been broken: it’s extinct now.
Using the wrong model makes one incapable of understanding true-meaning.
Based on what I earned from that book by Hofstadter, I’d say the thing is that we’re prone to applying models waaay outside of their applicability, & therefore we’re being bogus, while believing that we aren’t.
& THAT is problem.
Models are limited in their applicability.
& we are … perhaps wired … to ignore that.
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