Proof of nihil ex nihilo?
How do you prove that nothing can come from nothing? I always wondered why so many people take this statement like a logical truth.
My try is simple: Let p stand for anything. Then "~p" = nothing. "~p -> p" would mean: something follows from nothing. But ~p & (~p -> p) is a contradiction, so it's impossible that something can follow from nothing (and even more that something can be caused from nothing), so that only nothing can follow from nothing. Thoughts?
My try is simple: Let p stand for anything. Then "~p" = nothing. "~p -> p" would mean: something follows from nothing. But ~p & (~p -> p) is a contradiction, so it's impossible that something can follow from nothing (and even more that something can be caused from nothing), so that only nothing can follow from nothing. Thoughts?
Comments (64)
"Nothing can come from nothing" is accepted because (a) people think of events as being causally related to an extent where they can't imagine acausal events, (b) people, and especially engineering, mathematics etc.-oriented folks, are attracted to the idea of a deterministic, "clockwork" world, and (c) something from nothing is seen as a conservation of energy violation, and a lot of people have an essentially dogmatic, almost religious attitude towards fundamental physical principles/laws.
Forget proof for a moment, how do you even understand "nothing can come from nothing?"
I think that your attempted proof only serves to illustrate your own confusion. Start with conceptual analysis.
I think logic and proofs are not going to bring anyone any closer to understanding the nature of human experiences. Sometimes I wonder how it every got elevated to that status that it had within academic philosophy. Philosophers, such as Bergson, I don't believe, ever resorted to logic. He simply studied and observed.
Again:
1. Let p stand for all objects (in the form of sentences so that propositional logic is applicable).
2. Then ~p is pretty much what we would call nothingness.
3. ~p -> p is pretty much what we would call something concluded/followed from nothing.
4. ~p & ~p -> p leads to a contradiction, so it's false that something (p) can come from nothing (~p).
That is no clearer than the original sentence: you just rephrased it and replaced "come from" with "follow from."
Quoting Pippen
We don't know whether causality has anything to so with ex nihilo any more than inference does, because we don't know what ex nihilo means in the first place.
That said, if you think that causality is a special case of logical inference, then you are already on a wrong path.
My try is simple: Let p stand for anything. Then "~p" = nothing. "~p -> p" would mean: something follows from nothing. But ~p & (~p -> p) is a contradiction, so it's impossible that something can follow from nothing (and even more that something can be caused from nothing), so that only nothing can follow from nothing. Thoughts?
--Pippen
I have a very simple philosophical 'rule of thumb' for when anyone either talks about something coming from nothing and/or an effect coming into existence without a cause; and that is to say that whenever something either theoretically (or happening in a real world case for whatever reason) comes from nothing or is an effect without cause it is best to say that it is very, very probable that the cause is just something we are unaware of or that we really can't know enough of the process to say anything about it.
A prime example of this is "God" and "magic". What allowed "God" come into existence? Did he come from nothingness, always exist, or something else and when he creates stuff does it too come from nothingness? Is his power much like the technology we use today or is it closer to what we use to think of and call "magic" which supposedly could create thing from nothingness. Is "magic" in some ways like how people know and understand technology and if it is why isn't it in and of itself just another form of technology or science? If not than how do people even understand it?
And whether or not magic is like technology, if someone can understand enough to use it how can they determine if the things that magic creates actually comes from nothingness or from someplace we are completely unaware of?
I think the rule of thumb I just gave does a pretty decent way of answering/encapsulating this issue in a way that it answers most problems I have encounter in a satisfactory way. I can't say there isn't exceptions to this rule, but I don't think that they are that many to worry about. :D
The argument, which is statistical, should be as follows:
All observations show that nothing comes from nothing
Therefore,
Nothing comes from nothing
This conclusion, nothing comes from nothing, now can be used as a premise, in fact I think this is the primary use of the proposition.
1. ~p
2. ~p -> p
3. p | mp
4. ~p |premise
5. p & ~p, so 1. or 2. must be false.
I think we agree on that proof, do we? So it's just about if 1. & 2. models what we call creatio ex nihilo. That is my question! Why are 1. & 2. not modelling it properly? SophistiCat said causuality is not a special case of inference, but then she/he would need to give me one example of casuality that we cannot express as an inference...I don't think she/he can. Anything else?
That would be every example of causality per most interpretations of conditionals.
As far as I know, p are statement variables in logic. To have an argument you must have statement constants - using uppercase letters - and only then is there an argument we can judge.
You seem to be using sentential logic in a very odd way. Can you clarify? Thanks
Note that the statement is about our reality. So, it has to be proven through observation. My proof:
1) All observed things in this world are not things that come from nothing
Therefore,
2) ALL things in the universe are not things that come from nothing
2) is identical to nothing comes from nothing
The argument is inductive; statistical to be specific.
Why don't you use propositions like we normally do? Perhaps, with your enthusiasm, we can get somewhere.
Also, you haven't commented on my argument.
I'll offer you a normal deductive argument below. It follows from my inductive argument here.
1) If something comes from nothing then we should see things appearing from nothing
2) We don't see things appearing from nothing
Therefore,
3) It's false that something comes from nothing.
3) is just another phraseology for nothing comes from nothing.
That's what he wants to show, no? that (1) and (2) cannot both be true.
Not that this trivial exercise reveals anything interesting, of course. If p stands for "something exists" and then ~p stands for "nothing exists," all that he shows is that, if nothing exists, then it is not also the case that something exists. Duh.
Hello. I never learned to read logic symbols like this, and just caught up by reading wikipedia for 5 minutes. But what happens if we reverse the variables, as such?
1. Let n stand for nothingness.
2. Then ~n is not nothingness, that is, something.
3. ~n?n means we can get nothing from something.
4. ~n & ~n?n leads to a contradiction, so it's false that 'nothing can come from something'.
But... it seems possible to get nothing from something, by common sense.
I'll play devil's advocate. Just because we don't see something from nothing, it does not mean that we can't see something from nothing.
Having said that, since we have indeed never seen it, then it becomes the prima facie, and the other side has the onus of proof to demonstrate that something from nothing is indeed possible.
Perhaps I should've restricted my domain of discourse to macroscopic physical objects.
The end of our statement is interesting "...we can't see something from nothing.
Can you clarify. Thanks
We need to differentiate between 3 modes of reality:
(1) Impossible, (2) possible and not actual, (3) possible and actual.
(1) 2+2=3 is impossible. It is unimaginable. It cannot exist in any universe.
(2) A unicorn is possible and not actual. It is imaginable. It can exist in another universe, or in ours later.
(3) A horse is possible and actual. We have observed it. It exists in our universe.
Mr. Pippen's argument is aiming to make 'something from nothing' impossible, thereby making 'nihil ex nihilo' a necessary principle. Your argument here would at best make 'something from nothing' possible and not actual, but not impossible.
If p stands for "something exists", ~p stand for "nothing exists" and ~p -> p for "something follows from nothing" then I can prove that ~p and ~p -> p is a contradiction and therefore 1) can't be true and 2) can't be true necessarily. But since this very logical conjunction is the model for what we call "creatio ex nihilo" we can conclude its impossibility as well and that means its negation is true and its negation goes: nihil creatio ex nihilo, nothing can be created from nothing.
The proof is bulletsafe, the only thing one could criticize is that ~p and ~p -> p is not a model of what we call "creatio ex nihilo" by giving arguments, but I think my model is the very radical model of a creatio ex nihilo. All other models are not as radical. But maybe I oversee something....
You have to learn the basics.
The logic you're using is tenseless. "¬p?p" says tenselessly "If nothing exists, then something exists." It is true if something exists; false if nothing exists.
What you want is to say is more like this:
1. at time t[sub]0[/sub] there is nothing
2. at time t[sub]1[/sub] there is something
3. t[sub]1[/sub] > t[sub]0[/sub]
I don't know how to represent "comes from," but it seems like this is close enough.
While "p" can stand for any proposition, you are not free to choose the meaning of logical predicates - that is, if you are appealing to logic for your argument. If you accepted the rules of the game, then you cannot assign the meaning to ~p -> p by fiat. That expression states that the denial of the proposition "p" logically entails the proposition "p" - only that and nothing else. (Although entailment can be understood somewhat differently even in logic - semantically, syntactically - that ambiguity won't help you.) The implication of disproving ~p -> p is utterly trivial and has nothing to do with proving ex nihilo, as I already argued.
We can use mathematical and logical terminology metaphorically for creative expression (1 is the loneliest number), but the truth of these sayings does not derive from the use of logical and mathematical terms, it has to stand on its own.
It's the same with 's attempt to prove ex nihilo with arithmetic: he interprets 1 apple + 1 apple =/= 3 apples as saying that an extra apple cannot appear outta nothin'. But, if arithmetic is his tool of choice, then all this says is that if you got an apple and another apple, then together you have two apples (and not three). If then, by some miracle, another apple appears outta nothin', then with the two apples that you already had, you will have three apples all told. That's all that arithmetic gives him. Any other interpretation that he assigns to the symbols will have to be justified independently from the literal meaning of the borrowed terminology.
The moral of the story, ironically, is that in an argument, too, you cannot get something from nothing: if you want to prove a metaphysical principle, you will have to do the hard work of arguing metaphysics, instead of looking for sophistic shortcuts. But first and foremost, you will have to understand what that principle means, and neither you nor Lacrampe have taken that trouble.
~p -> p is already a contradiction. Srap was right (and I wasn't paying attention): this second iteration of your argument made little sense. Your first attempt was already logically bulletproof, as you say - it just didn't prove anything interesting, and neither did your second attempt.
'By some miracle'? As in 'caused by a miracle'? But a miracle is not nothing. What this says is that, while miraculous events escape the laws of physics by definition, they too don't escape the nihil ex nihilo principle. And neither do you in practice, apparently. ;)
(Y)
I understand your point, that at the time that there were 2 apples, then there were 2 apples, and at the time that there were 3 apples, then there were 3 apples. And to that I agree. But my argument says more than this:
In theory, 2?3, that is, 3 cannot result from 2 and nothing else. But in the apple thought experiment, if 'nihil ex nihilo' is false, it follows that in practice, 3 apples could result from 2 apples and nothing else. The consequence is that there is a discrepancy between theory and practice, or between logic and reality. And this is absurd.
While I agree with Mr. LeMaitre that religion and science should be separate, it is not fair to keep the 'creation ex nihilo' hypothesis while removing the 'supernatural cause' hypothesis; because the 'creation ex nihilo' hypothesis implies that the 'supernatural cause' hypothesis is false. Both should be removed on the ground that they are both unscientific (above the realm of science).
I keep trying to help you but you're not putting the work in, so this is my last time.
It's always already the case that ¬p and p cannot both be true. Seriously, man.
It has nothing at all to do with whatever premises you have.
If you assume ¬p as a premise, you cannot possibly derive p unless your premises are inconsistent.
And guess what? ¬p and ¬p?p as a set of premises IS INCONSISTENT.
As a matter of fact, ¬p?¬(¬p?p) is a tautology.
1)
No, it doesn't. What you're correct about is that you can indeed put something other than statements in these logic formulas, unlike everyone else here seems to claim, but you have to note that then ¬p&p isn't a contradiction anymore. Define p as, say, a potato. Then ¬p means anything but a potato. Potatoes exist, so does that mean nothing but potatoes exist?
2)
The problem with the English language is the meaning of nothing, as it's kind of a homonym. "Nothing exists" can mean that there is no thing that exists, or that a thing that is called nothing exists. ¬p in your claim means the latter, closer to nothingness than to nothing in its meaning, which is why ¬p&p is not a contradiction.
3)
If you mean nothing as in the former sense, then ¬p?¬p?p is not what you're claiming anymore, as once ¬p?p has happened, ¬p is no longer true. ¬p is the case before, ¬p?p is the case after. Even if they contradicted each other, it wouldn't matter because they don't exist simultaneously.
4)
You can't assume that if something is created from nothing, then ¬p?p. The correct statement would be ¬p?p?¬(¬p?p), or A?(¬p?p)?B?¬(¬p?p) where A and B are some conditions, maybe even the events themselves.
5)
Feel free to correct me, but so far it seems like you don't have any real argument. You're just using logical connectives without understanding their actual meaning. If the formula was correct and contradicted intuition, it'd rather imply that logical connectives are fundamentally wrong. This is your contradiction translated to English: if nothing always results in something, then nothing can't exist, because it'd already then be something. This is basically the fourth point again but in English: your argument is false because it assumes that if something can follow from nothing, then something can and will always follow from nothing.
1. Let p = "There exists at least one thing", so ~p = "There exists no thing at all".
2. Let creatio ex nihilo = ~p & ~p -> p.
3. By logic it follows that 2. is false (and therefore impossible).
Yes, usually we'd need Predicate Logic here, but why, it's so simple, we can use Propositional Logic instead, no different results. So where is your problem?
I disagree, because I interpret the implication arrow (->) as "then", a consequence in a formal, non-physical way. So ~p -> p means "if there exists nothing, then there exists something" and isn't that pretty much what we imagine if we talk about a creation out of nothing? Remember: A creation out of nothing has to be non-physical since otherwise there were already elementary physics present which would be something already and therefore no creation out of nothing!
This is exactly what I said in my previous comment.
Quoting Pippen
... no? Just absolutely no?
If by natural law, you mean laws of physics, then I agree about that; but it is not possible for logic. "Being illogical" does not mean "standing outside of our universe's laws logic", but rather "making no sense". It is an error made by the subject of discussion, and does not say anything about the object of discussion. As such, saying "2+2=3" is not any more sensical than saying gibberish like "the smell of purple has". Practical test: if it is unimaginable, then it is illogical, then it is impossible.
No. It's an implication, not a conjunction.
So your model would look like this: ~p & ~p -> p(t>0). Correct? Well, this would be inconsistent too, because you introduce a time frame for the whole formula (~p need to be at t=0 to make sense) and so you say in ~p that nothing exists, but at the same time you say that time exists which leads to a contradiction as well. So in my and your model creatio ex nihilo would be logically impossible, just that the contradictions would lay on different spots.
Something out of nothing would be ¬p?q, where p="something exists" and q="something will exist".
And, again, please use correct symbols, or find a source that states ~ means negation.
It's also not any more nonsensical.
Quoting Samuel Lacrampe
If we observe something to be unimaginable, then that proves it is unimaginable within our universe, and it is impossible within our universe.
Now if creatio ex nihilo is modeled as: ~p & ~p -> q then it's logically possible.
Is there any book, article or link that describes how to formulate a creation out of nothing in a formal way? I mean I wonder that I can't find anything that proves or disproves the old proverb that nothing can come from nothing in a logical way.
Yes, and also impossible in all universes. Example: It is impossible for Caesar not to cross the rubicon in our universe, because we cannot change the past. But I can image Caesar not crossing the rubicon. It is therefore possible in another universe. However, I cannot imagine Caesar crossing and not crossing the rubicon at the same time. That last statement is therefore impossible in all universes.
I guess you are right. What was your argument though? I thought you too were just giving an opinion.
I'll try an argument for fun: one fundamental law of our logic is the law of non-contradiction. Now if another universe does not have our logic, then it does not have the law of non-contradiction. But if it does not have it, then it also has it (since contradictions are allowed if the law is not present). But once it has the law, then it cannot not have it (since contradictions are not allowed if the law is present). Therefore, all universes have the law of non-contradiction, which is a fundamental law of our logic.
I think you are right about the second half. Man arguing about logic itself is hard.
Still, what was your argument for thinking that other universes may have a different logic? To say that something is possible implies that it is logically possible. But as such, to say that another logic is possible is to say that another logic is logically possible, which is nonsensical.
Fair enough. I looked up the concept of 'possible worlds' here. In it, it does define 'impossible propositions' as propositions being true in no possible world. And impossible propositions are ones that have contradictions. Thus logical contradictions are true in no possible worlds.
Strange, I can't seem to find an error in the argument. There's something wrong though.
P = something exists
~P = nothing exists
That's fine.
~P > P.......here something is wrong. This doesn't capture the full meaning of ''creatio ex nihilo'', which is, ''something comes from nothing''. The relationship between ~P and P isn't the logical implication (->) you're using. Let me explain:
~P > P means: IF nothing exists THEN something exists. Surely, this is NOT what you mean.
Creatio ex nihilo means: Something comes from nothing.
In predicate logic it would be:
If, Nx: x arose from nothing
(Ex)(Nx) = there exists something that arose from nothing.
Better would be a two-place predicate, since "nothing" is an English quantifier, so the principle would be:
¬?x¬?y(x came from y)
which is the same as
?x?y(x came from y),
which is "Everything came from something" (and not to be confused with "There is something everything came from").
Doesn't (Ax)(Ey)(x came from y) mean ''everything came from something''?
Creatio ex nihilo (CEN) would be true IF there exists a thing that came from nothing. To me, CEN seems to be expressing the existence of at least ONE thing that came from nothing. That's why I used the particular quantifier Ex.
Wouldn't it be better translated as:
(Ex)(Ay)~(x came from y)?
Sorry for the confusion -- I was formulating the negative, "Nothing comes from nothing."
Yours is the negative of mine, so it's all good.
[B]Nihil ex nihilo = nothing comes from nothing.[/b]
Nothing comes from nothing = everything comes from something = (Ax)(Ey)(x comes from y) = not the case that there exists an x such that it is false that there exists a y such that x comes from y
= ~(Ex)~(Ey)(x comes from y).
(1) ~(Ex)~(Ey)(x comes from y)
[B]Creatio ex nihilo = something comes from nothing.[/b]
Something comes from nothing = there exists an x such that for all y, it's false that x comes from y = (Ex)(Ay)~(x comes from y).
(2) (Ex)(Ay)~(x comes from y)
Oh now I see it. Thanks. Had to write that down to understand it.
(1) is the negation of (2). Am I right?
Nailed it.
You just have to get used to how quantifiers and negatives go together. "All" is the same as "There isn't one that isn't" and "There is" is the same as "Not all aren't".
¬?¬ can be traded for ?
¬?¬ can be traded for ?