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submitted 2 days ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
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[-] emergencyfood@sh.itjust.works 8 points 2 days ago

you cannot prove a system using the system.

Doesn't that only apply for sufficiently complicated systems? Very simple systems could be provably self-consistent.

[-] Shelena@feddit.nl 14 points 2 days ago

It applies to systems that are complex enough to formulate the Godel sentence, i.e. "I am unprovable". Gödel did this using basic arithmetic. So, any system containing basic arithmetic is either incomplete or inconsistent. I believe it is still an open question in what other systems you could express the Gödel sentence.

[-] bjoern_tantau@swg-empire.de 6 points 2 days ago

I think it's true for any system. And I'd say mathematics or just logic are simple enough. Every system stems from unprovable core assumptions.

[-] CompassRed@discuss.tchncs.de 1 points 1 day ago

Propositional logic as a system is both complete and consistent.

this post was submitted on 01 Oct 2025
407 points (100.0% liked)

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