Comment on In this essay...

bjoern_tantau@swg-empire.de ⁨1⁩ ⁨day⁩ ago

• 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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    • GandalftheBlack@feddit.org ⁨1⁩ ⁨day⁩ ago

      The best thing is when the holy book *doesn’t * claim to contain the single, eternal truth, because it contains hundreds of contradicting truths of varying eternality due to being written by countless authors over more than a thousand years

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      • Stonewyvvern@lemmy.world ⁨1⁩ ⁨day⁩ ago

        Dumbfuckery at its finest…

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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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• HexesofVexes@lemmy.world ⁨18⁩ ⁨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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• 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 ⁨1⁩ ⁨day⁩ 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 ⁨1⁩ ⁨day⁩ 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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    • bleistift2@sopuli.xyz ⁨1⁩ ⁨day⁩ ago

      I find this axiomatization of the naturals quite neat:

      1. Zero is a natural number. 0∈ℕ
      2. For every natural number there exists a succeeding natural number. ∀_n_∈ℕ: s(n)∈ℕ (s denotes the successor function)

      Now the neat part: If 0 is a constant, then s(0) is also a constant. So we can invent a name for that constant and call it “1.” Now s(s(0)) is a constant, too. Call it “2” and proceed to invent the natural numbers.

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      • anton@lemmy.blahaj.zone ⁨1⁩ ⁨day⁩ ago

        That axiomisation is incomplete as it doesn’t preclude stuff like loops, a predecessor to zero or a second number line.

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      • unwarlikeExtortion@lemmy.ml ⁨22⁩ ⁨hours⁩ ago

        What’s missing here os the definition that we’re working in base 10. While it won’t be a proof, Fibbonaci has his nice little Liber Abbaci where he explains arabic numerals. A system of axioms for base 10, a definition of addition and your succession function would suffice. Probably what the originals were going for, but I can’t imagine how that would take 86 pages. Reading it’s been on my todo list, but I doubt I’ll manage 86 pages of modern math designed to be harder to read than egyptian hieroglyphs.

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    • fushuan@lemmy.blahaj.zone ⁨1⁩ ⁨day⁩ ago

      Yeah, that’s what meant with “2 is just the shortened representation of 1+1”.

      Same with 1+1+1=3, really. We need to decide the value of 1,2,3,4… Before we can do anything. In hindsight if you think about it, for someone that doesn’t know the value of the symbols we use to represent numbers, any combination that mixes numbers requires the axiom of 1+1+1+1+… = X

      I’d be surprised if someone proved that something equals 5 without any kind of axiom that already makes 5 equal to another thing.

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    • Matriks404@lemmy.world ⁨23⁩ ⁨hours⁩ ago

      It’s only difficult to prove if you somehow aren’t able to observe objects in real world.

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      • captainlezbian@lemmy.world ⁨22⁩ ⁨hours⁩ ago

        That’s just empirical data, not a mathematical axiom. I know it’s true, you know it’s true but this is math as philosophy not math as a tool

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  • titanicx@lemmy.zip ⁨1⁩ ⁨day⁩ ago

    None of that sounded fun…

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  • MeThisGuy@feddit.nl ⁨23⁩ ⁨hours⁩ ago

    It took a long while to reach division

    and even longer to reach long division?

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  • JackbyDev@programming.dev ⁨1⁩ ⁨day⁩ 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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    • SaharaMaleikuhm@feddit.org ⁨1⁩ ⁨day⁩ ago

      But if it’s less than 83 do we really know if it’s better than whatever the initial 1+1 guy wrote?

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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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    • CompassRed@discuss.tchncs.de ⁨4⁩ ⁨hours⁩ ago

      Propositional logic as a system is both complete and consistent.

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