the question "why does anything exist, rather than nothing?" presupposes that there are two possible cases... JJ
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Guys this is tic tac toe. How you begin the ontology determines where you will end. It is symmetric. You can turn this around and begin with the assertion, All That Is, and then demand to know how Nothing could possibly exist. If you postulate Nothing first, then All That Is becomes just as problematical.
Somewhere in Descartes he reasons that nothing, can not exist between two points, except more points. He then reasons that space can not be empty. He uses this rational to argue that the motion of the planets are the consequence of vortices of (tidal-like) forces composed of these points.
Newton on the other hand dodged the whole question of either the fullness or the emptiness of space and how gravity could be `influence' across `nothing' by saying that he didn't know what it was, but he could figure out how it worked, and how it worked was the inverse square law.
The same issue comes up again and again in different disguises.
The theory of light for example. Waves in order to be waves, must have a medium, and there is no medium in space. Einstein dodged this problem on space by making space its own medium (equivalent to a geometry of points). How can nothing be either straight or curved? So Einstein adopted Newton's pose, I don't know the answer to what space is, but I can show mathematically how light paths through space are curved when they come near large masses.
The issue of waves with no medium comes up in quanta. The answer is to turn the constituents into self-bounded strings. But what are the ends connected to? Nada. Again the answer is to dodge the question by showing the math works, and leave it at that.
The big bang crew certainly has the same problem, `before the beginning...' and so forth. It shows up again in Hawking with the so-called `boundry' problem---which is why Hawking offered up God as one answer, and the existance of subjects like us as another answer.
Hegel takes up this problem by identifying the issue (or question) with the processes of thought. He puts forward the dialectic of being and nothing together as the germinal process of thought that is resolved as a synthesis (dialectical consciousness projected in time) as becoming the subject...
It would make a neat exercise to demonstrate that this problem is equivalent to the paradoxes of set theory and the insufficiency of any axiom list, just to close the circle so to speak.
CG