Originally Posted by
Xei
I think this is the crucial point: something existing for infinitely long does not mean it encounters the point '∞'; it's a local concept.
We don't have any problem with the idea that something will go on to keep experiencing moments infinitely, because by definition, all this means is that at any point you encounter it, it has only had a finite life span, and has not had to experience an infinitude of moments to reach you. It never actually becomes an infinitely old being.
The other case is totally different; at any point you meet it, you can name a point in the distant past, and the being will be older than that. In other words, at any point you meet it, it has had to experience an infinitude of moments to reach you; it actually has 'reached' ∞, which we take to be impossible.
So in effect, this paradox is just a corollary of a simpler, more general problem: can something be infinitely old?