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Please look if my following argument is correct, otherwise point to my mistakes!

I distinguish two cases:

  1. We have nothing but logic, i.e. we have an empty set of premises. And here the answer seems clear: yes, we can always introduce tautologies like p v ~p. So in such a scenario we can "create" something out of nothing. So in such a scenario God could have created the world out of nothing, because the world can certainly be seen as a tautology of the form: things that are or things that are not.

  2. We have nothing, not even logic. But then logical impossibility seems impossible itself because you need logic to be able to get contradictions. That means a creatio ex nihilo in that sense is not logically impossible, but only unlogically. So even here a theologian could point out that God doesn't act contradictory when he creates the world (which is important because by christian dogma God cannot do logically impossible things, but he wouldn't need to do as we have just seen).

So overall a creatio ex nihilo seems not logically impossible which means that its opposite 'nihil ex nihilo' (nothing comes from nothing) is NOT a tautological truth.

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    On your first point: We can write down tautologies in a formal system because they're entailed by the rules we assume govern the formal system. For example, "P v ~P" is a tautology in propositional logic (PL) because it is assumed in the meta-theory of PL that no proposition is both true and false and every proposition is either. Tautologies are no more creatio ex nihilo than arguments that beg the question, e.g. (1) P; (2) Hence, P (which is, incidentally, valid). Jun 18 '20 at 4:32
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    The world (if any) is not a tautology. Jun 18 '20 at 6:04
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    Creation ex nihilo of what ? Physical world ? You have assumed some "we" that is using logic, and the existence of a God. Jun 18 '20 at 6:06
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    This sounds like a roundabout way to get to the obvious. Yes, creation from nothing has no contradiction in terms. I am not sure that this reasoning makes it any more obvious, and the second part seems entirely redundant since "logically impossible" already presupposes logic. If you really want to make it more persuasive you'd have to formalize what creation is in some system (e.g. in temporal logic) and state it as a formal argument with premises and inferences.
    – Conifold
    Jun 18 '20 at 6:07
  • @Mauro: The world consists of all the existing things and all non-existing things, kind of P union ~P which represents the universe and which is defined thru p v ~p, i.e. P union ~P := x in P or x in ~P.
    – Pippen
    Jun 18 '20 at 13:39
1

Let me see if I have your overall argument correct:

  1. Prior to the existence of the Universe, logic constrained how the universe could be structured or it did not
  2. If logic constrained how the universe could be structured, then God could create within those constraints
  3. If God could create within those constraints, then God could create ex nihilo
  4. Hence, if logic constrained how the universe could be structured, then God could create ex nihilo
  5. If logic did not constrain how the universe could be structured, then God could do anything at all
  6. If God could do anything at all, then God could create ex nihilo
  7. Hence, if logic did not constrain how the universe could be structured, then God could create ex nihilo
  8. Hence, God could create ex nihilo
  9. If God could create ex nihilo, then it is possible for nothing to come from nothing
  10. Hence, it is possible for nothing to come from nothing

If I've captured what you meant to argue, I can address your request to point out errors. Consider line 9. I'm not sure why it is supposed to follow from God being able to create ex nihilo that nothing could come from nothing. I think there's equivocation over 'nothing':

  • (A) Nothing existed before the Universe (but God)
  • (B) Nothing existed before the Universe (at all)

If I say "nothing existed before the Universe", I might mean either. But they've different meanings. The latter is - logically speaking - more general than the former, and so treating (A) as equivalent to (B) is fallacious. Unfortunately, I believe there's a slip in line 9 from (A) to (B) in just this way. Specifically:

  • (C) If God can create the universe without anything else existing, then it is possible that if there is no universe and also no God, then something could emerge and exist

This seems straightforwardly false; that's one reason to think your argument is incorrect.

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"Creatio ex nihilo" occurs all the time. The results are called fiction. These non-real objects do have value, and a major portion of the economy is driven by them.

If you want to know whether it's "possible" for real physical objects to come from "nothing", that would depend on the physical laws of the universe. (You basically set up a false dichotomy in which physical laws are ignored.)

In principle, it's an open question, but the vast majority of evidence is that it simply does not occur. So it's pretty safe to assume that it will continue to not occur until such time that it does.

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At the hypothetical beginning of time before God had his first thought absolutely nothing besides God exists. Not even as much as the idea of "nothingness" exists.

The absolute minimum unit of knowledge from information theory is a single binary digit. Nothingness can be thought of as represented by a single zero-bit.

On this basis the absolute minimum change in the body of knowledge would be toggling this zero-bit and creating primordial concept of Boolean negation.

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