Correct! Indeed that is a crucial point that is used in an important proof I gave you. — TonesInDeepFreeze
'There exists a z such that for all y, y is a member of z' contradicts this instance of the axiom schema of separation: For all z, there is a x such that for all y, y is a member of x iff (y is a member of z and yis not a member of y). — TonesInDeepFreeze
That is not "once again". Previously you said that "a set cannot be both a member of itself and a member of other than itself". That is different from "a set cannot be both a member of itself and not a member of itself". — TonesInDeepFreeze
An item in a subset cannot be both a member of the subset and the set. If it is a member of the subset, it is a member of the subset. If it is a member of the set, it is a member of the set. — Philosopher19
Something cannot be both a member of itself and a member of other than itself at the same time. For example, take z to be any set that is not the set of all sets, and take v to be any set. The z of all zs is a member of itself as a z (as in in the z of all zs it is a member of itself). But it is not a member of itself in the v of all vs, precisely because in the v of all vs it is a member of the v of all vs as opposed to a member of itself. If we view the z of all zs as a z, it is a member of itself. If we view the z of all zs as a v, it is a member of the set of all sets. You can't view it as both a member of the z of all zs and a member of the v of all vs at the same time. That will lead to contradictions. In other words, we can't treat two different references as one (as in are we focused on the context of vs or the context of zs?) — Philosopher19
Then you're a dumbass for arguing with me when I was correct that Infinities do indeed have different sizes if that's your stance too. Either way, you're an "egregious" dipshit. "Oh, this guy is arguing the same thing as I am, and he's being comical, I should "correct," him about infinities not having sizes even though that's MY STANCE! Oh, wait, it's my stance, noone else can have it!" Eitherway, the fact is, you're a dumbass when it comes to communication. — Vaskane
An item in a subset cannot be both a member of the subset and the set. — Philosopher19
If it's a member of other than itself, this means that it's not a member of itself. — Philosopher19
I take you to be saying that a set cannot be a member of another set and also a member of itself. — TonesInDeepFreeze
Do you mean: If S is a subset of some set T and x is member of S, then x cannot be a member of T ? — TonesInDeepFreeze
That's incorrect. By the definition of 'subset', if S is a subset of T, and x is a member of S, then x is a member T. — TonesInDeepFreeze
Take z to be any set that is not the set of all sets, and take v to be any set. The z of all zs is a member of itself as a z (as in in the z of all zs it is a member of itself). But it is not a member of itself in the v of all vs, precisely because in the v of all vs it is a member of the v of all vs as opposed to a member of itself. If we view the z of all zs as a z, it is a member of itself. If we view the z of all zs as a v, it is a member of the set of all sets. You can't view it as both a member of the z of all zs and a member of the v of all vs at the same time. That will lead to contradictions. In other words, we can't treat two different references as one (as in are we focused on the context of vs or the context of zs?) — Philosopher19
distinguish between "member of self" and "not member of self" — Philosopher19
I am not sure if this is so much a problem with mathematics though as it is with how it gets applied to the sciences and philosophy. It seems to me that infinite divisibility might be worth investigating even if it doesn't accurately reflect "how things are." — Count Timothy von Icarus
I believe the solution to Russell's paradox is in here:
http://godisallthatmatters.com/2021/05/22/the-solution-to-russells-paradox-and-the-absurdity-of-more-than-one-infinity/ — Philosopher19
I mean that all makes sense, although my understanding was that the question of whether or not space-time is infinitely divisible was an open one. — Count Timothy von Icarus
I'm really sceptical of the idea that there is any one true math to decide these issues of infinity. — Mark Nyquist
it can be possible that one model can be inconsistent with another and not be false. — Mark Nyquist
A smaller infinity can reach any finite number that a larger infinity can by freezing the larger infinity and letting the smaller one catch up. — Mark Nyquist
It's just philosophy here not pure math. — Mark Nyquist
I'm in over my head — Mark Nyquist
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting. — Mark Nyquist
I've had college algebra, trig and calculus.
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting. — Mark Nyquist
I believe the solution to Russell's paradox is in here:
http://godisallthatmatters.com/2021/05/22/the-solution-to-russells-paradox-and-the-absurdity-of-more-than-one-infinity/ — Philosopher19
Honestly, I am having trouble dissecting the arguments used here.
Thoughts, jgill ? — Lionino
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting. — Mark Nyquist
I've heard that in the USA a huge amount of natural gas just goes missing. Where does it go? — Metaphysician Undercover
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