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Before I get to the argument here's a primer on modal language copied from Wikipedia:
All possible worlds have something in common, namely, that they exist. Just like all triangles in all possible worlds have something in common, namely, that they have three corners. So if in every possible world the world exists and triangles have three corners, then the world, our world, exists necessarily and trinagles necessarily have three corners. With this argument we can establish that the world (which includes all that exists, universe or multiverse, etc.), exists necessarily, i.e., it couldn't have not existed (worlds exist in all possible worlds).
I think this also shows that the question typically formulated as "why is there something rather than nothing?" has been formulated the wrong way round, it should be "why isn't there nothing rather than something"? The default is something, as established above since the world exists necessarily, and we should now wonder why there isn't nothing, if it is even coherent to talk about absolute nothingness.
- True propositions are those that are true in the actual world (for example: "Richard Nixon became president in 1969").
- False propositions are those that are false in the actual world (for example: "Ronald Reagan became president in 1969"). (Reagan did not run for president until 1976, and thus couldn't possibly have been elected.)
- Possible propositions are those that are true in at least one possible world (for example: "Hubert Humphrey became president in 1969"). (Humphrey did run for president in 1968, and thus could have been elected.) This includes propositions which are necessarily true, in the sense below.
- Impossible propositions (or necessarily false propositions) are those that are true in no possible world (for example: "Melissa and Toby are taller than each other at the same time").
- Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried").[1]
- Contingent propositions are those that are true in some possible worlds and false in others (for example: "Richard Nixon became president in 1969" is contingently false and "Hubert Humphrey became president in 1969" is contingently true).
All possible worlds have something in common, namely, that they exist. Just like all triangles in all possible worlds have something in common, namely, that they have three corners. So if in every possible world the world exists and triangles have three corners, then the world, our world, exists necessarily and trinagles necessarily have three corners. With this argument we can establish that the world (which includes all that exists, universe or multiverse, etc.), exists necessarily, i.e., it couldn't have not existed (worlds exist in all possible worlds).
I think this also shows that the question typically formulated as "why is there something rather than nothing?" has been formulated the wrong way round, it should be "why isn't there nothing rather than something"? The default is something, as established above since the world exists necessarily, and we should now wonder why there isn't nothing, if it is even coherent to talk about absolute nothingness.