by Sauwelios » Tue Nov 15, 2011 9:51 pm
In fact, the more I think about it, the more Russell's paradox appears to be much ado about nothing. The smallest set that contains the set [1] is either the set [1] (if sets are defined by their members) or the set [[1]] (if they are not). So either sets by definition contain themselves, or they by definition do not. If sets are defined by their members, the notion that the set of all squares does not contain itself because it's not itself a square is bullshit: the only reason it's not a square is that it's multiple squares---supposing that there's more than one square. If the set of all squares cannot contain multiple squares, because multiple squares are not a square (i.e., one square), then the set of all squares can only exist if there's no more than one square!
"Eternal return is philosophy's _natural_ edifying teaching; it does not comfort itself or others with the next world ostensibly more perfect than our own; it says of the only world there is, or rather it 'shouts insatiably' (aph. 56) to the world as it is: Be what you are, be eternally what you are." (Laurence Lampert, _Leo Strauss and Nietzsche_, page 57.)
"Plato and Nietzsche share [...] the essential paganism of all philosophy, eros for the earth, and that is the deepest sharing, for each discovered that in being eros for what is, philosophy is eros for _eros_, for being as fecund becoming that allows itself to be glimpsed in what it is: eros or will to power." (Lampert, _How Philosophy Became Socratic_, page 417.)