Proof that something can never come from nothing
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.
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.
Comments (58)
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."
https://en.wikipedia.org/wiki/Russell%27s_paradox
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.
I also wonder if my proof could just start to define Nothingness as just the empty set. Why bother?
You fail to understand the argument. Surely no set contains anything that doesn't exist. What could that even mean?
Quoting Pippen
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.
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).
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.
Quoting Pippen
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.
Quoting Pippen
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.
Quoting Pippen
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.
Quoting Pippen
Lost me there, what are p1 and p2 etc?
Quoting Pippen
Beyond what? Are you insulting your own argument? You lost me here too.
Quoting Pippen
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.
[I should say I agree only for purposes of conversation. Else what of {Captain Kirk, Captain Ahab, the Flying Spaghetti monster}. Is that a set of three elements? Or is it the empty set? Conversation for another time!!]
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.
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.
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.
Other than things exist occupying specific times and places?
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.
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.
The absolute vacuum ....
[quote=Edward Tryon]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.[/quote]
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.
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.
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.
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.
'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?
Not even God?
Quoting unenlightened
Pretty much. So is popping into.
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.
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?
Absence of anything.
Quoting Christoffer
I'm not aware of anything in reality that matches that.
Point certainly taken. I didn't really want to suppress @Pippin's perhaps interesting ideas. It's just that when someone invokes set theory and Russell's paradox, to me that brings in a whole host of baggage. Suppose you do have the empty set {}. Then by the laws of set theory you have its powerset {{}}, and the powerset of that, {{},{{}}}, and the powerset of that, and so forth. You can take a power set for each positive integer; then you can take the union (via another axiom) to get an infinite collection of iterated powersets, and then you can take the powerset of that, and keep on going.
So it's generally a bad idea to call something a "set" if you only mean a collection or perhaps a class. Collections and classes don't have the mathematical baggage that sets do.
But I don't think my criticism was wrong. The OP said the set of "anything (that exists)." That's the literal quote. Then he took its complement, which is an operation on sets, to get the empty set. I'm perfectly within my rights to treat sets as sets.
Perhaps @Pippin can rephrase his ideas without invoking the machinery of set theory.
Doesn't absence make the heart grow fonder? In which case, absence is a thing.
I'm not only using wordplay. Absence is a thing. Suppose you come upon a universe that is empty. You say, "Oranges are absent. Pears are absent. Pomegranates are absent ..." That's a lot of absence, and it takes a mind or an observer to notice it. In a universe containing nothing, there is nothing ... not even absence. This is the same conceptual error the OP is making. Nothing is nothing. There can't be anything. No concepts, not even absence. If you notice there are no oranges, who is doing the noticing?
What does the word absent mean? Something that is supposed to be there, isn't. A student who is supposed to be in class, isn't there that day. She's absent. But a person who isn't enrolled in that class in the first place, is not regarded as being absent from class. You agree? If the class has 30 people enrolled and 29 show up, one is absent. Not seven billion.
But you could perceive the concept that a room is still a room if what is inside it is the absence of anything. From this, the property of nothing as something is what makes the room a room.
Exactly. There is no such thing as an entirely empty universe with nothing in it.
Quoting fishfry
Agreed. Also all the people that don't exist, or are dead, or will be born.
Presumably, in order to do this, there are sets.
Sets all the way down.
That notation is not supported by the axioms of set theory. It's meaningless unless there are a FINITE number of bracket pairs. You may indeed have {}, {{}}, {{{}}}, ... one term for each positive integer; but to go beyond that you have to take their union. You can not take a limit of this notation.
:up: :ok:
Where is nothing in the real world? It's just an idea and can't be physically represented. Space is the best candidate for a physical nothing but it is, if my science is correct, an electromagnetic field. Space isn't nothing.
Thanks
Bill
Let's define nothingness as the conjunctions of negations of any possibly or actually existing things: ~p1 & ~p2 & ~p3 & .... From that definition is follows trivially that no object can exist out of nothingness.
2. I still think the set S (representing the Being) of all existing things is neither the set of everything nor does it lead to it. It's different, because it only assumes things that are already existing and therefore non-contradictory, while the set of everything doesn't. Because S exists, ~S exists (~S = empty set = nothingness) and from there it follows trivially as well that if we assume ~S we cannot assume anything out of this empty set.
Yes, this model cannot grasp total nothingness (the same with 1.), but that's how far we can imagine nothingness anyway, there's no consistent way to imagine some more total nothingness because we always need something to define nothingness. Total nothingness is actually meaningless like triangle with four angles, it just looks like it means something due to its letters, but contentwise it's the same as "%$%/&%$/$/$" - meaningless.
So, dispensing with the unnecessary formalism, what you have stated is that if nothing can possibly exist, then there isn't a possibility of anything existing.
Color me impressed.
Just a thought - carry on...
Aside from the problem of reifying abstractions and positing some questionable definitions there, you don't actually present any sort of argument as to why something can't "come from nothing." You seem to just be assuming that part as obvious, but that's supposed to be what the thread is about. Definitions would only be preliminary work. Once you set out definitions, you need to get on with the argument.
1. Let's postulate only ? (Nothingness).
2. Let's assume some t, but that's contradicting 1., so it's impossible.
3. Conclusion: If only ? then nothing can exists no matter in which way or modus, nihil ex nihilo.
p.s. It's obvious for me that only ? can represent nothingness, one could prove that with raa since any other set would have elements and certainly unable to grasp our intuition of nothing.
p.p.s. Also be aware that Nothingness is relative here since ? is not really nothing, but that's our only chance to reason about it; we cannot grasp or refer to absolute nothing since that reference alone would make it something.
p.p.p.s. This proof uses set theory as a model. We could proof the same with just predicate logic by using "There exists nothing" as our assumption, we could even use propositional logic to use "~p1 & ~p2 & ..." to model it roughly.
No one would be saying that there's something and nothing (to the same extent, in the same respect, etc.) at the same time. (2) only contradicts (1) if we assume it's at the same time, to the same extent, etc.
Does nature conform to our ability to comprehend it?
Put differently:
What is logic a reflection of?
We cannot comprehend how something can come from nothing. My claim is that this points to a human limit rather than to some truth about the world.
Again, time matters because that's what people are saying re "something coming from nothing." It's a temporal idea.
You can't successfully argue against a notion if you don't even understand it, or if the argument isn't addressing it but rather a straw man.
Ok, let's assume only ? + time. Still it's (logically) impossible for a thing to exist from these premises.
1. We postulate the empty set as an universe (= representation of nothingness).
2. We assume some t in the universe which contradicts 1.
3. So it follows that no t can be in the universe.
If you want to add time it's pretty much the same:
1. We postulate the empty set + time as an universe. (= representation of nothingness within time)
2. We assume some t in the universe which contradicts 1.
3. So it follows that no t can be in the universe.
But if we denote by P- something then ~P - nothing.
Then we have the conditional ~P->P which is false if nothing doesn't entail something.
But if nothing existed we could have claimed 'nothing' as something (but that's meta-language mambo jumbo); I think you cannot create something from nothing since it would be like believing that the rabbit wasn't there in the magician's hat to begin with, it just came out of thin air.
I mean all of evolution in biology will be regarded as hogwash if something can come up from nothing, hell all of human evolution started just a few seconds ago ... :-D