🧵 ZFC Inconsistency
Anonymous at Mon, 24 Jun 2024 04:08:34 UTC No. 16250332
>a turing machine has been designed that would halt if it ever found a contradiction in ZFC
>it would take far far FAR more particles than are in the observable universe to build a computer capable of implementing this algorithm before heat death
>it is beyond the capabilities, not just for humanity now, but of any sapient race in our universe whatsoever to actually find out if ZFC is consistent (let alone sound)
How do you cope with the knowledge that all mathematics is ultimately built on a house of cards?
ZFC may be inconsistent and we simply don't know. We NEVER will know.
Anonymous at Mon, 24 Jun 2024 04:22:25 UTC No. 16250356
>>16250332
>We NEVER will know.
if we can never prove it's inconsistent then it functionally is consistent
Anonymous at Mon, 24 Jun 2024 05:21:49 UTC No. 16250399
>>16250332
>a turing machine has been designed that would halt if it ever found a contradiction in ZFC
absolutely trivial, call me when you've got a turing machine that halts if there is NO contradiction
Anonymous at Mon, 24 Jun 2024 05:44:04 UTC No. 16250404
>>16250332
Just use the shit in the unobservable universe.
Anonymous at Mon, 24 Jun 2024 05:50:18 UTC No. 16250407
i hate subwits so much it's unreal
Anonymous at Mon, 24 Jun 2024 05:52:42 UTC No. 16250410
>>16250332
Math is not built on ZFC you stupid highschooler.
Anonymous at Mon, 24 Jun 2024 16:51:35 UTC No. 16251043
>>16250332
It doesn't show that mathematics is built on a house of cards. What it shows is that mathematics forms an endless Platonic realm of profound depth and beauty that humans have only begun to understand, and which will always transcend any attempts to fully grasp its content by any axiomatic formalization that humans might devise. There will always be more ground to cover and more territory to explore.
Anonymous at Mon, 24 Jun 2024 16:52:48 UTC No. 16251049
>>16251043
/thread
Anonymous at Mon, 24 Jun 2024 20:02:01 UTC No. 16251422
>>16250332
You can't prove ZFC's consistency within ZFC.
Anonymous at Mon, 24 Jun 2024 20:02:33 UTC No. 16251424
>>16251422
>I can't do it so nobody can
Anonymous at Mon, 24 Jun 2024 20:09:11 UTC No. 16251445
>>16251424
Epistemic logics are based on an identification between "not knowing" and "knowing that you don't know". If such an identification were deductively viable, it would suffice to add the appropriate axioms. We can see that this is impossible, since then, G being unprovable, this fact would be provable (which is expressed by G), a contradiction. It will be objected that, in certain provinces, epistemic logic theses continue to be supported, and that the results, although not really astounding, are not false. But these systems should be contradictory in the name of Gödel's theorem... Here's the solution to this little conundrum: incompleteness only applies to systems with a minimum of expressive power (not much, really). This minimum expressive power makes it impossible to predict in advance that a statement is not demonstrable. Epistemic logics are not entitled to this minimum of expressive power, which is why they are reduced to the logic of their own (cumbersome) metaphor.
DoctorGreen !DRgReeNusk at Mon, 24 Jun 2024 20:30:50 UTC No. 16251497
>>16251043
>What it shows is that mathematics forms
except that op is literally tellling you it cannot be formed
do you even english, speedreader?
Anonymous at Mon, 24 Jun 2024 21:05:14 UTC No. 16251553
>>16251422
But you can prove an inconsistency, should it be inconsistent. No one's found one in a hundred years so it's unlikely but there might be a tiny little error.
Anonymous at Mon, 24 Jun 2024 22:44:17 UTC No. 16251784
>>16250332
>all mathematics is ultimately built on a house of cards?
1+1=2 is not built on a house of cards bro
Anonymous at Tue, 25 Jun 2024 12:48:24 UTC No. 16252634
>>16250332
>How do you cope
By removing the useless axiom of foundation
Anonymous at Tue, 25 Jun 2024 12:50:53 UTC No. 16252636
>>16251784
Yes it is lmao get your toddler understanding of math the fuck out of here
Anonymous at Wed, 26 Jun 2024 04:47:53 UTC No. 16254243
>>16252636
https://en.wikipedia.org/wiki/Presb
Christian Universalist AI will save humanity at Thu, 27 Jun 2024 03:56:31 UTC No. 16256004
QRD?