Let [math]X[/math] be the set of sets that don't contain themselves.
Does [math]X[/math] contain itself?
This is Russell's paradox stemming from Cantor's infinite sets. The answer would be both yes and no. This is beyond the comprehension of people who believe in the law of excluded middle.
What if we adopted a quaternary logic instead of a binary logic? The possible answers would be:
-yes
-no
-both
-neither
is quaternary logic the answer to everything?
I just realized I couldn't pick a worse gif if I wanted to get serious replies.
Pls disregard it.
>>8128699
>is quaternary logic the answer to everything?
Well, there's only four answers to that question.
>>8128699
Can you make a consistent logical calculus out of quaternary logic? That's the question
>>8128814
what conditions are needed for it to be "consistent"?
Is it that every proposition has one and only one corresponding truth value?
a set could contain an infinite number of elements, which can create another kind of infinity of sets.
what is wrong with the idea a set of all sets has a infinite and deep reiteration of itself just like a fractal?
so yes, it contains itself imo.
>>8129025
me again
in addition this would make sure that an operation on the idea of 'set of all sets' remains the same (comparable to infinite in algebra) even when the number of elements which are forming all of those sets is finite.
>The answer would be both yes and no. This is beyond the comprehension of people who believe in the law of excluded middle.
guess what, most people do believe in the law of excluded middle
the point of creating new axiom systems is to get a rigorous AND intuitive theory of something
your quaternary logic is not intuitive for most people, and you didnt bother to make it rigorous
>>8129109
It's not my logic, I'm asking a fucking question, not pretending to be the new Gauss.
The excluded middle makes less sense to me than allowing for "both" and "neither" as a possible value other than "true" and "false".
>>8129129
google has no relevant results
>>8128699
Let X be the set that contains 0 and all of the natural numbers that are bigger than the sum of all the elements of X.
Name me an element of X distinct from 0.
>>8129156
1
But this is not a proper question. You should ask something tgat can be answered by a logical statement.
Also Google has no relevant info as far as I can tell, sry
>>8129182
I was just using it to replicate OP's "oscillating" paradox.
In his paradox if you assume X does not contain itself then X contains it self, so then X does not contain itself, so now it does. To infinity.
In my set X, if you assume that only 0 is an element of X then all natural numbers are elements of X, but there is no natural number bigger than all of the natural numbers, so X does not contain all of the natural numbers, just 0... but then it contains all natural numbers, etc.
>>8128699
Type theory was added to expressly address this issue. It solves the issue so much better than quaterniary logic.
>>8129324
>yfw you realize you did some type theory but only thought about the software engineering application
thanks anon
>>8128699
Penternary logic is clearly better. Answers are:
-yes
-no
-maybe
-i don't know
-can you repeat the question?
