He used math to show that all statements, in any language, can be expressed as math statements. He then proved that it’s impossible to create any consistent set of math statements that completely describes everything.
That doesn’t make it fundamentally flawed. I also can’t completely describe all muscle movement involved and yet I can walk.
Gödel’s incompleteness theorem has to be the most overhyped thing since a certain cat. For logicians, it mainly means that “is it probable” is a valid question for prepositions that are otherwise vastly esoteric in nature.
That’s not a flaw. It’s one of the greatest mathematical revelations of the 20th century.
It’s only a “flaw” for people who want to believe in some imaginary positivism. This is a popular grift under capitalism. See also the entire field of economics.
Nah, euclidean geometry was not complete. Tarski didn’t come up with a complete version until the 20th century. I’m not sure how famous Tarski geometry is, but it doesn’t seem very famous in USA outside of math depts.
this doesn’t mean that “it’s impossible to create any consistent set of math statements that completely describes everything,”
It says far less than that: “It’s impossible for a mathematical system containing the natural numbers to be both complete and consistent.”
In itself it has very little to do with physical reality. I think it’s more about how we think about math and then its applications.
reality itself could be a complete system, understandable from both the outside and inside if only viewed at the right angle…
It has to do with creating measuring devices out of what we can empirically derive, and building successive generations off of those. It’s fine for our local system but by the time you get intergalactic (or quantum) with it, flaws start to propagate themselves bigly.
I can’t reveal more at this time or Big Math will get suspicious.
Interesting! Could you elaborate on this? I’m intrigued to know the intrinsic flaws.
Kurt Gödel wrote a whole paper on it.
He used math to show that all statements, in any language, can be expressed as math statements. He then proved that it’s impossible to create any consistent set of math statements that completely describes everything.
That doesn’t make it fundamentally flawed. I also can’t completely describe all muscle movement involved and yet I can walk.
Gödel’s incompleteness theorem has to be the most overhyped thing since a certain cat. For logicians, it mainly means that “is it probable” is a valid question for prepositions that are otherwise vastly esoteric in nature.
That’s not a flaw. It’s one of the greatest mathematical revelations of the 20th century.
It’s only a “flaw” for people who want to believe in some imaginary positivism. This is a popular grift under capitalism. See also the entire field of economics.
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Nah, euclidean geometry was not complete. Tarski didn’t come up with a complete version until the 20th century. I’m not sure how famous Tarski geometry is, but it doesn’t seem very famous in USA outside of math depts.
It says far less than that: “It’s impossible for a mathematical system containing the natural numbers to be both complete and consistent.”
In itself it has very little to do with physical reality. I think it’s more about how we think about math and then its applications.
This has been largely debunked.
I dunno what his dream was, but Hilbert’s program is very much dead.
It has to do with creating measuring devices out of what we can empirically derive, and building successive generations off of those. It’s fine for our local system but by the time you get intergalactic (or quantum) with it, flaws start to propagate themselves bigly.
I can’t reveal more at this time or Big Math will get suspicious.
Big Math comes knocking: “you mean Big Physics?”
quoi? Oh désolé, je ne sais pas. Vous devez avoir le mauvais numéro.
*sounds of fleeing*