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In this essay...

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Submitted ⁨⁨1⁩ ⁨day⁩ ago⁩ by ⁨fossilesque@mander.xyz⁩ to ⁨science_memes@mander.xyz⁩

https://mander.xyz/pictrs/image/f7a09b2f-3e66-46a4-8459-b96e38951342.png

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  • bjoern_tantau@swg-empire.de ⁨1⁩ ⁨day⁩ ago

    And shortly after that some other guy proved that he was wrong. More specifically he proved that you cannot prove that 1+1=2. More more specifically he proved that you cannot prove a system using the system.

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    • HexesofVexes@lemmy.world ⁨8⁩ ⁨hours⁩ ago

      Ehh…

      So, it’s more a case that the system cannot prove it’s own consistency (an system cannot prove it won’t lead to a contradiction). So the proof is valid within the system, but the validity of the system is what was considered suspect (i.e. we cannot prove it won’t produce a contradiction from that system alone).

      These days we use relative consistency proofs - that is we assume system A is consistent and model system B in it thus giving “If A is consistent, then so too must B”.

      As much as I hate to admit it, classical set theory has been fairly robust - though intuitionistic logic makes better philosophical sense.

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    • pebbles@sh.itjust.works ⁨1⁩ ⁨day⁩ ago

      Yk thats something some religious folks gotta understand.

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      • Diplomjodler3@lemmy.world ⁨1⁩ ⁨day⁩ ago

        What are you talking about, filthy infidel? My holy book contains the single, eternal truth! It says so right here in my holy book!

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      • TaterTot@piefed.social ⁨1⁩ ⁨day⁩ ago

        Sure, but I can hear em now. “If you can’t prove a system using the system, then this universe (i.e. this “system") can not create (i.e. “prove") itself! It implies the existance of a greater system outside this system! And that system is MY GOD!”

        Torturing language a bit of a speciality for the charlatan.

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    • Klear@quokk.au ⁨1⁩ ⁨day⁩ ago

      I like how it’s valid to use “more specifically” as you’re specifying what exactly he did, but in both cases those are more general claims rather than more specific ones.

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    • fushuan@lemmy.blahaj.zone ⁨23⁩ ⁨hours⁩ ago

      In logic class we kinda did prove most of the integer operations, but it was more like (extremely shortened and not properly written)

      If 1+1=2 and 1+1+1=3 then prove that 1+2=3

      2 was just a shortened representation of 1+1 so technically you were proving that 1+1 plus 1 equals 1+1+1.

      Really fun stuff. It took a long while to reach division

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      • Taldan@lemmy.world ⁨23⁩ ⁨hours⁩ ago

        Presumably you were starting with a fundamental axiom such as 1 + 1 = 2, which is the difficult one to prove because it’s so fundamental

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      • titanicx@lemmy.zip ⁨14⁩ ⁨hours⁩ ago

        None of that sounded fun…

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      • MeThisGuy@feddit.nl ⁨13⁩ ⁨hours⁩ ago

        It took a long while to reach division

        and even longer to reach long division?

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      • JackbyDev@programming.dev ⁨14⁩ ⁨hours⁩ ago

        Lambda calculus be like

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    • SaharaMaleikuhm@feddit.org ⁨1⁩ ⁨day⁩ ago

      Yeah, but how many pages did it take?

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      • InternetCitizen2@lemmy.world ⁨1⁩ ⁨day⁩ ago

        As many as needed.

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    • emergencyfood@sh.itjust.works ⁨1⁩ ⁨day⁩ 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.

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      • Shelena@feddit.nl ⁨1⁩ ⁨day⁩ 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.

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      • bjoern_tantau@swg-empire.de ⁨1⁩ ⁨day⁩ 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.

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  • MBM@lemmings.world ⁨10⁩ ⁨hours⁩ ago

    Is this where I go “actually it took 83 pages to set up an extremely rigorous system and then a couple of lines to show you could use it to prove 1+1=2”?

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  • nop@lemmy.world ⁨19⁩ ⁨hours⁩ ago

    Gödel has entered the chat.

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  • Batman@lemmy.world ⁨23⁩ ⁨hours⁩ ago

    One year to prove it, 82 years for that banger of a title

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  • 33550336@lemmy.world ⁨12⁩ ⁨hours⁩ ago

    The proof might be somewhat lengthy, but it is quite rigorous.

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  • Midnitte@beehaw.org ⁨23⁩ ⁨hours⁩ ago

    Pffh, Terrence Howard will disprove it in only 4 pages!

    /s

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    • SkunkWorkz@lemmy.world ⁨9⁩ ⁨hours⁩ ago

      Image

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