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Vladimir_Nesov comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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Existence is relative: there is a fact of the matter (or rather: procedure to find out) about which things exist where relative to me, for example in the same room, or in the same world, but this concept breaks down when you ask about "absolute" existence. Absolute existence is inconsistent, as everything goes. Relative existence of yourself is a trivial question with a trivial answer.
(I just wanted to state it simply, even though this argument is a part of a huge standard narrative. Of course, a global probability distribution can try to represent this relativity in its conditional forms, but it's a rather contrived thing to do.)
Wha?
In the sense that "every mathematical structure exists", the concept of "existence" is trivial, as from it follows every "structure", which is after a fashion a definition of inconsistency (and so seems to be fair game for informal use of the term). Of course, "existence" often refers to much more meaningful "existence in the same world", with reasonably constrained senses of "world".
How do you know that?
An ensemble-type definition of existence seems more like an attempt to generalize the term than it does an empirical statement of fact. What would it even mean for a mathematical structure to not exist?