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Geometry (mander.xyz)

submitted 4 months ago by [email protected] to c/[email protected]

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[–] [email protected] 79 points 4 months ago (18 children)

the point isn't to prove that the triangle is a triangle it's to prove that the system of mathematics you made up actually works

[–] [email protected] 18 points 4 months ago (10 children)

Until you prove that you can't prove that the system you made up works.

[–] [email protected] 3 points 4 months ago (6 children)

Nobody is practically concerned with the "incompleteness" aspect of Gödel's theorems. The unprovable statements are so pathological/contrived that it doesn't appear to suggest any practical statement might be unprovable. Consistency is obviously more important. Sufficiently weak systems may also not be limited by the incompleteness theorems, i.e. they can be proved both complete and consistent.

[–] [email protected] 2 points 4 months ago (1 children)

I think the statement "this system is consistent" is a practical statement that is unprovable in a sufficiently powerful consistent system.

Can you help me understand the tone of your text? To me it sounds kinda hostile as if what you said is some kind of gotcha.

[–] [email protected] 1 points 4 months ago

Just explaining that the limitations of Gödel's theorems are mostly formal in nature. If they are applicable, the more likely case of incompleteness (as opposed to inconsistency) is not really a problem.

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