RE: Reverse Russell's Paradox
February 20, 2012 at 8:23 pm
(This post was last modified: February 20, 2012 at 9:42 pm by Categories+Sheaves.)
(February 20, 2012 at 12:48 am)AthiestAtheist Wrote:(February 19, 2012 at 2:34 pm)LastPoet Wrote: On the other hand you proposed the reversal and didn't said anything worth about it, so what is it that you are saying? Do you even know what a paradox is?
I think you have it backwards there.
To be fair, there isn't much to say about the original post. Even ZFC insists that for every set S, the powerset P(S), namely the set of all subsets of S (including S itself) exists. A statement that begins with 'Can the set that cannot be contained...' holds as much water as a statement that begins with 'Can the square with five sides....'
It doesn't matter what absurd things we might conclude once we assume there exists a square with five sides: by using proof-by-contradiction (or if you're a fan of xkcd, thanks to the principle of explosion) we're able to prove everything. Until we have a reason to accept the existence of a 'set that cannot be contained,' we don't have a paradox. The real work is in showing that there is a set that cannot be contained, or that we can produce one via some agreed-upon axioms.
Can the color Sweden be eaten by Catholicism?
