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”?
In this essay...
Submitted 1 day ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/f7a09b2f-3e66-46a4-8459-b96e38951342.png
Comments
MBM@lemmings.world 10 hours ago
nop@lemmy.world 19 hours ago
Gödel has entered the chat.
Batman@lemmy.world 23 hours ago
One year to prove it, 82 years for that banger of a title
33550336@lemmy.world 12 hours ago
The proof might be somewhat lengthy, but it is quite rigorous.
Midnitte@beehaw.org 23 hours ago
Pffh, Terrence Howard will disprove it in only 4 pages!
/s
SkunkWorkz@lemmy.world 9 hours ago
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.
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.
pebbles@sh.itjust.works 1 day ago
Yk thats something some religious folks gotta understand.
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!
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.
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.
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
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
titanicx@lemmy.zip 14 hours ago
None of that sounded fun…
MeThisGuy@feddit.nl 13 hours ago
and even longer to reach long division?
JackbyDev@programming.dev 14 hours ago
Lambda calculus be like
SaharaMaleikuhm@feddit.org 1 day ago
Yeah, but how many pages did it take?
InternetCitizen2@lemmy.world 1 day ago
As many as needed.
emergencyfood@sh.itjust.works 1 day ago
Doesn’t that only apply for sufficiently complicated systems? Very simple systems could be provably self-consistent.
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.
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.