@fulhamish: To start with, I realize know that when I say "exist", it is shorthand for "know to exist", which is the most anyone can claim. Thus, 1,000 years ago a European would not know the Mississipi river existed, and indeed, a map of what Europe believed to be the entire world would not have included the Mississippi.
Now we know more, and can measure both how long it is and for how long it has been flowing. There's a certain subjectiveness to existence
The size of the universe (at least the observable parts) has been estimated, as has the event horizon of a black hole. and it would be pretty extraordinary to claim that four doesn't exist, but infinity does. Multiple universes, separated either temporally or spatially, are just as extraordinary a claim as God. Unless there is a corollary you can measure in this universe, you have no basis for saying they exist.
Perhaps it would be better to say that only things which can in principle be measured exist, but that's not fundamentally stronger than saying things that can be measured. Our perception of the possible can also change.
@Draugnar: You're right, I jumped from Maimonides to my own beliefs. I've taken the time to look back at your comment, and you are one hundred percent right. The soul does not exist, to exactly the same extent that God does not exist.
The reason I quoted Maimonides is that he very firmly believed in God, and made belief in God and various attributes of God at least 3 of his 13 Principles of Judaism. And yet, here is his proof of the nonexistence of God. But again (and this is still according to Maimonides; I say again because it's been said before) there must have been a primordial cause, and he says that this primordial cause was God, who is pure intellect. Please don't make me try and explain all of Maimonidean philosophy, it's frightfully complicated and I've barely studied it.