Psy-Kosh: let's Taboo "exist" then... What does it exactly mean? For me, it's something like "I have some experiences, whose cause is best modeled by imagining some discrete object in the outer world". The existence or non-existence of something affects what I will feel next.
Some further expansions: "why": how can I predict one experience from another? "world": all the experiences we have? (Modeled as a discrete object... But I can't really imagine what can be modeled by the fact that there is no world.)
So the question "why does our world exist" becomes something like "what is the experience from which we can predict we will have any experiences at all... Sounds a little bit more controversial than the original.
By the way, have we tried this transformation in the opposite direction? Turning the question "what is the sound of blue" to one which seems to make sense...
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Psy-Kosh: Maybe I really tried to approach the meaning of the question from the direction of subjective experience. But I think that the concept of "existence" includes that there is some observer who can decide if that thing we're talking about does really exist or doesn't, given his/her stable existence.
Maybe that's why the question can't be easily answered (and maybe has no answer at all) because the concept of "world" includes us as well. So if we want to predict something about the existence of the world (that is what the word "why" means, I think), we haven't observe anything: it's a logical truth that any world in which this question is asked really does exist.
But if we statisfy the two assumptions in the question (the existence of the world is observable by us, and is repeatable, so we can make predictions about it), it starts to make sense, but it becomes less mysterious somehow. Some possible answers: because the previous one did already collapse in an anti-big-bang, I've just seen that..., or we usually have to wait for it to recreate itself, therefore nothing exists right now... Or it exists because I was bored and created a new one, or maybe because I was bored and started Half-Life (which also fits our new world-concept in some way)... etc.
And... physical equations are definitely _something_ which differ from nothing. Some rules for a... world... But I think if something is becoming so blurry like the concept of "world" just now, we better ask what subsystem in our mind is applied for the wrong problem, and what are those problems which it is intended to solve.