## Proof that something can never come from nothing

• 67
I always wondered why there are no logical/analytical proofs for nihil ex nihilo or creatio ex nihilo, so I came up with my own and wonder if it holds water. My result: nihil ex nihilo wins because creatio ex nihilo is impossible.

The proof is simple and doesn't even need modal logic or elaborations on what it means that something "comes from" nothing (causality? implication? ...?):

1. We define (N)othing as the complement of the set of anything (that exists), so N = ∅.
2. We assume N and only N. (= ex nihilo)
3. We assume (hypothetically) some (existing) object. (creatio ex nihilo)
4. Contradiction since the object cannot exist because of 2. which makes 3. false.

Note: We can only reason about a kind of Nothingness we can define properly. We cannot reason with an absolute Nothingness since in that moment it wouldn't be absolute nothing and we would contradict each other.
• 594
1. We define (N)othing as the complement of the set of anything (that exists), so N = ∅.

Well your proof is busted there as Russell's paradox shows that there is no set of all sets. So there is no "set of anything," by which I understand you to mean the set of everything. There is no set of everything. If there was we could form its subset defined by the set of everything that's not a member of itself. That subset both is and isn't a member of itself. Contradiction, hence there is no set of all sets, hence no set of "everything" and no set of "anything that exists."

DOA on line 1.

As a second objection, note that the empty set is not nothing. The empty set is a particular set. If you have a universe that contains the empty set, then that universe is not empty. It contains the empty set. The empty set is a thing. It's a particular set. It's not nothing.

Besides (objection 3) if something can't come from nothing, where did all this stuff come from? If it didn't come from nothing, then it was always here. That seems equally untenable. Unless you're William Lane Craig and you think this proves that God did it. Because anything that "begins to exist" must have a cause; hence God must have always existed. Yeah I know it sounds like bs, but a lot of people take Craig seriously.
• 67
Russell's paradox is no problem since I don't talk about the set of everything, but the set of everything that exists. That's a huge difference. Obviously Russell's paradoxical set doesn't exist since it's contradictory.

I also wonder if my proof could just start to define Nothingness as just the empty set. Why bother?
• 594
Russell's paradox is no problem since I don't talk about the set of everything, but the set of everything that exists. That's a huge difference.

You fail to understand the argument. Surely no set contains anything that doesn't exist. What could that even mean?

I also wonder if my proof could just start to define Nothingness as just the empty set. Why bother?

It would be a tighter argument since I couldn't so easily throw Russell's paradox at it. Just start with the empty set. But where did that come from? As I already noted, if there's a universe that is empty except that it contains the empty set, well then the universe has something in it. The empty set has no members, but it is itself a thing. It's like a grocery bag before you put in your groceries. It's an empty bag, but it's still a bag.

It's an interesting question in mathematics. We write down the rules of set theory, but how do we know that any sets exist? There's only one axiom that says a set exists, and that is the axiom of infinity. The axiom of infinity says that there exists a set that contains the empty set; AND whenever it contains a set X, it also contains X U {X}. That's essentially the principle of mathematical induction, and it gives us all the counting numbers.

But where did the empty set come from? One story I've heard is that the underlying laws of logic include the law of identity, which says not only that a thing is equal to itself; but that also there is at least one thing. That's one theory.

Another theory is that set theory secretly includes an axiom that posits the existence of the empty set.

It's not an important question, but it is a little bit of a puzzler. Most people think the axiom of infinity gives us a set, and that given one set we can form the empty set. But the axiom of infinity references the empty set so that's not entirely satisfactory. Basically nobody cares about this much. We can always say, "Ok there's at least one set" to end that conversation.

Your argument has a problem. If you require the empty set, where did it come from? You may well have an empty universe. But if you do, it can't contain the empty set. Because then the universe is not empty!

But your argument is definitely better without starting by assuming a set of everything, which provably doesn't exist.

Here's a question for you. How does a car move? It sits all night with velocity zero. Then at some instant of time, it has nonzero velocity. This is a commonplace occurrence that we see every day. But it's very mysterious. Note that this is not Zeno's paradox, at least not directly. It's just the question of how velocity can be zero at one instant and nonzero at a later instant. Perhaps universes come into existence the same way. God steps on the accelerator.
• 67

1) By definition my set contains only things that exist (non-contradictory). That excludes Russell's set. No Russell's set, no problem. In other words this set is defined like: containing everything that does not lead to a contradiction somehow. It should be clear that such a set is clean of problems by definition alone, don't u think?

2) I think nothing has to be the empty set very naturally since otherwise only sets with members could be available that obviously couldn't serve as nothingness.

3. You are right that the empty set is itself a thing and just basically postulated. But as I wrote in my note: that's how we have to interpret nothingness, there's no better way. We simply cannot postualte a further-going nothingness since it would lead to contradictions/falseness. What we mean when refering to "nothing" is the empty set (or e.g. in logic the conjunction ~p1 & ~p2 & ...), that's "our" nothing, beyond that is just a brainf*ck that doesn't mean anything, just like when we talk about the universal set that SEEMS alright but isn't (as Russell showed).
• 594
1) By definition my set contains only things that exist (non-contradictory). That excludes Russell's set. No Russell's set, no problem. In other words this set is defined like: containing everything that does not lead to a contradiction somehow. It should be clear that such a set is clean of problems by definition alone, don't u think?

I agreed that your argument is stronger without trying to define the empty set as the complement of the set of everything, since the latter provably doesn't exist. In any event, you are still misunderstanding Russell's argument. There is no claim that the set of all sets contains sets that don't exist. We start with YOUR claim that there is a set of all sets that DO exist, and we immediately derive a contradiction. But again, you don't need this in your argument. Just posit the empty set if you must. But now you just produced something from nothing.

2) I think nothing has to be the empty set very naturally since otherwise only sets with members could be available that obviously couldn't serve as nothingness.

There's an analogy. Suppose we deny infinite sets. We all have an intuition that there are infinitely many counting numbers 1, 2, 3, 4, ... (with or without zero, I don't care). That does not give us an infinite set; only infinitely many individuals.

The axiom of infinity says that there is a SET containing all the natural numbers. That's a huge leap beyond merely saying that there are infinitely many natural numbers.

Likewise, I can perfectly well imagine an empty universe. But now you have a SET that is empty; and that is a thing that you claim exists. You are going beyond the idea of emptiness to the idea that there is a CONTAINER for the emptiness that also happens to be a SET. So you have made an extra ontological assumption; not only that nothing exists; but that nothing is CONTAINED in a SET. That's a lot more ontological baggage than a merely empty universe.

3. You are right that the empty set is itself a thing and just basically postulated. But as I wrote in my note: that's how we have to interpret nothingness, there's no better way.

Just say the universe is empty. Because if you put the emptiness in a SET, that's a huge additional assumption. It is an act of creation out of nothing! You start with nothing and now you have a set! You just defeated your own argument, didn't you? You created the empty set out of nothing.

We simply cannot postualte a further-going nothingness since it would lead to contradictions/falseness. What we mean when refering to "nothing" is the empty set

But NO. The empty set is not nothing. It's a particular set. We've been over this. You start with nothing; and a moment later you have a SET containing nothing. That's a huge leap of creation. Out of nothing.

(or e.g. in logic the conjunction ~p1 & ~p2 & ...), that's "our" nothing,

Lost me there, what are p1 and p2 etc?

beyond that is just a brainf*ck that doesn't mean anything,

Beyond what? Are you insulting your own argument? You lost me here too.

just like when we talk about the universal set that SEEMS alright but isn't (as Russell showed).

This last paragraph got a little tangled I think. Let's go back to the key point. You have an empty universe. Now you have a SET containing that emptiness. Where did the set come from? Isn't that a creation out of nothing?

To make this more concrete, isn't the empty set just an idea? And if it's an idea, who is the mind having that idea? If you are a Platonist who believes that the empty set exists independently of minds, that's perfectly fine with me ... but if the empty set exists, it's not nothing. It's the empty set. I guess I can't say that anymore, I've said it several times already. The empty set is a particular thing.

The empty set CONTAINS nothing; but the empty set itself IS something. It's the empty set. To prove that, we can form the set containing the empty set, {∅}. That's a set containing exactly one element, namely ∅. That shows that ∅ is something. It's something that can be a member of a set! By your own definition it exists. Since things that don't exist can't be members of sets. I agree with you about that.

• 9.2k
2. We assume N and only N. (= ex nihilo)
3. We assume (hypothetically) some (existing) object. (creatio ex nihilo)

The problem with this is that you're contradicting yourself. It doesn't say anything about ontology. If you're assuming N and only N, you can't assume something else too.
• 318
The mathematical field of Homology (and by extension Cosmology) runs into a similar problem, namely the problem of how to define a hole in a surface purely in terms of the substance of the surface. It gets around this problem by formulating a constructive definition of holes in terms of the cycles that characterise the surface. That way a hole can be described without resorting to a transcendental ontology containing a 'nothing substance'.

Nevertheless we see that Donuts contain 'nothing' in the middle. Which is equivalent to remarking that a sphere cannot be made into Donut unless we tear the middle.
• 2.5k
Lucretius made the argument that something can't come from nothing or else anything could pop into existence at any time. We don't observe that, therefore it's impossible. If it were possible, we would observe it, because there's nothing stopping something from popping into existence.

But really it's just a semantic argument because nothing isn't a thing. It denotes lack of existence in language, because it's useful for us to have that concept. It doesn't make any sense to say that something could come from nothing, when nothing is merely a concept.

Here is one place where I agree with the Witty enthusiasts about abusing language to create a seemingly deep philosophical puzzle.
• 1.6k
not sure the concept of an absence of something occupying some specific space, in some specific time is any less meaningful than the concept of something occupying some specific space at some specific time.
• 2.5k
not sure the concept of an absence of something occupying some specific space, in some specific time is any less meaningful than the concept of something occupying some specific space at some specific time.

Other than things exist occupying specific times and places?
• 1.6k
or they don't - both options exist and have meaning.
• 3.2k
Very interesting question although your proof seems inadequate. You're simply stating the original assertions (nihilo ex nihilo AND creatio ex nihilo) and declaring it as a contradiction. Yes, the two are contradictory. We already know that. What we don't know is which of the two is true. You're saying something like:

1.A (nihilo ex nihilo)
2.~A (creatio ex nihilo)
3. A ....assume for Reductio ad absurdum (RAA)
4. A & ~A....conj 2, 3
5. ~ A.........3 to 4 RAA

But we could easily have proved A as below:

1. A (nihilo ex nihilo)
2. ~A (creatio ex nihilo)
3. ~A.....assume for RAA
4. A & ~A conj 1,3
5. ~~A...RAA 3, 4
6 A...5 DN

See? From a contradiction anything follows.
• 3.6k
So where does it all come from?
• 3.2k
Well your proof is busted there as Russell's paradox shows that there is no set of all sets. So there is no "set of anything," by which I understand you to mean the set of everything. There is no set of everything. If there was we could form its subset defined by the set of everything that's not a member of itself. That subset both is and isn't a member of itself. Contradiction, hence there is no set of all sets, hence no set of "everything" and no set of "anything that exists."

The @Pippen didn't say ''S = the set of all sets''. He said the ''E = set of everything''. I'm paraphrasing a little bit. Do you mean E = S? Why? Afterall the OP is talking about physical stuff (matter and energy) and not about mathematical objects.
• 3.2k
Perhaps nothing is just a concept, an abstraction. The stuff (matter and energy) aren't just mental objects; they exist in the real world. Even the vacuum of empty space isn't nothing (electromagnetic fields). So to ask or consider the relationship between a pure abstraction (nothing) and the physical (something) is to make a category error.
• 1.6k
again not sure "nothing" is pure abstraction. There are such things as time and space. In a specific space at a specific time there exist either something or nothing. Either option has meaning.
• 2.5k
Meaning to us, but that doesn't mean the absence of something exists as far as nature is concerned.
• 2.5k
So where does it all come from?

The absolute vacuum ....

I visualized the universe erupting out of nothing as a quantum fluctuation and I realized that it was possible that it explained the critical density of the universe. — Edward Tryon

I can't tell you how much that language bothers me. Perhaps the actual math/physics makes sense, but what he's saying sounds like nonsense to me.
• 1.6k
again not sure, if a mouse does or does not occupy some specific space at a specific time may have great meaning to a hawk. Maybe I am looking at this incorrectly, if you point is “nothing” has no physical presence, I agree- but I don’t think that is any kind of important concept
• 2.5k
Maybe I am looking at this incorrectly, if you point is “nothing” has no physical presence, I agree- but I don’t think that is any kind of important concept

If we're trying to show why something cannot come from nothing, then a good starting place would be to decide whether nothing has any ontological existence. If it doesn't, then there isn't a problem in my book. It's just a play on language.
• 543
You have to add nothing to the building blocks; walls, floors, and ceilings of a house in order for space to create rooms.
• 1.6k
understand. Then I am back to my point that nothing has an ontological meaning, existence is harder. Guess the question would be does the space between objects exist.
• 2.5k
Guess the question would be does the space between objects exist.

Well, the atomists thought the void had to exist for a variety of reasons. But modern physics makes space out to be something and not just a void. It's a good question.
• 2.5k
You have to add nothing to the building blocks; walls, floors, and ceilings of a house in order for space to create rooms.

That sounds like a really weird way to phrase building a house. But okay, you're creating space for rooms. It's only nothing in the context of it not being building material. There's still air, hopefully.
• 3.6k
I can't tell you how much that language bothers me.

'The absolute' is a special philosophical realm of 'you're not allowed to question'. See also 'absolute bullshit'.

I hold to my own absolute truth: no cunning arrangement of words can oblige things to be thus and not so.

Shall we we say that 'coming from' already presumes space and time?
• 2.5k
I hold to my own absolute truth: no cunning arrangement of words can oblige things to be thus and not so.

Not even God?

Shall we we say that 'coming from' already presumes space and time?

Pretty much. So is popping into.
• 543
That sounds like a really weird way to phrase building a house. But okay, you're creating space for rooms. It's only nothing in the context of it not being building material. There's still air, hopefully.

Is it not still a room even if space in between is a vacuum, not even with quantum particles? Does a room need air to be a room?
• 2.5k
Is it not still a room even if space in between is a vacuum, not even with quantum particles? Does a room need air to be a room?

No. Just pointing out that the space isn't nothing. It's just not building material.
• 543

If you define that space as having properties, but if there are no properties to that space, isn't it then nothing? How do you define nothing?
• 2.5k
How do you define nothing?

Absence of anything.

If you define that space as having properties, but if there are no properties to that space, isn't it then nothing?

I'm not aware of anything in reality that matches that.
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