Notp does not equal nothing. Negation is not the same as nothing, negation is a valuation.

Also, "Nothing can come from nothing" isn't anything like a conditional in logic. Conditionals aren't about causality.

"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.

How do you prove that nothing can come from nothing? — Pippen

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.

To truly have nothing, one must extinguish consciousness sensing. Actually I was once unconscious for a few minutes and there truly was nothing. And then there was something. My mind shut itself down and then reawakened. In this manner the mind created something out of nothing. Pretty extraordinary. In the same way, I guess, we experience nothing and then something when we are asleep and not dreaming and then wake up, unless we are dreaming all the time.

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.

@Sophisticat: I understand "nothing can come from nothing" as: it is false that something can follow from nothing. I see causality as a special case of inference, so if I can show that such an inference is wrong then it holds even more for causality.

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).

I understand "nothing can come from nothing" as: it is false that something can follow from nothing. — Pippen

That is no clearer than the original sentence: you just rephrased it and replaced "come from" with "follow from."

I see causality as a special case of inference, so if I can show that such an inference is wrong then it holds even more for causality. — 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.

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?
--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

Nothing can come from nothing is about the physical world; an observation made of the external world.

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.

Hm...let's switch gears:

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?

"¬p→p" has an obvious countermodel when p is false, which happily you assumed in (1).

@srap: I don't understand what you mean. The creatio ex nihilo is modeled by me as "~p & (~p -> p)" and that is logically impossible which means nothing can be created out of nothing. So there is no countermodel, all models are just false, like in any contradiction.

but then she/he would need to give me one example of casuality that we cannot express as an inference. — Pippen

That would be every example of causality per most interpretations of conditionals.

I don't understand how p can be equated to something or how ~p can be nothing.

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.

@madfool: My claim is that we can prove from logic that nothing must come from nothing. Yes, I use propositional logic in an odd way for my variables refer to objects insteads of propositions. But why not take that short-cut? A variable p would stand for any object, ~p would stand for no object and ~p -> p would be the claim that something can follow from nothing, but we can prove that ~p and ~p -> p leads to a contradiction, so it must be false that something can come from nothing. I think this proof is pretty much safe, the only question is if my model with ~p & ~p -> p is somehow misleading, but I like it and see no obvious no-no's (which doesn't mean much though).

You cannot begin to cogently discuss a proposition when you cannot even explain what it means. All that symbol manipulation is child's play. You are not even touching the subject.

To the extent that I know, logic doesn't allow the flexibility your argument seems dependent on.

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.

If you find logic interesting, you should really take some time and study it.

"¬p→p" has an obvious countermodel when p is false, which happily you assumed in (1). — Srap Tasmaner

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.

Just because we don't see something from nothing, it does not mean that we can't see something from nothing — Samuel Lacrampe

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.

(Y)

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. — SophistiCat

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....

follows from — Pippen

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 t₀ there is nothing
2. at time t₁ there is something
3. t₁ > t₀
I don't know how to represent "comes from," but it seems like this is close enough.

By way of footnote, the cosmological theory popularly referred to as 'big bang theory' comes awfully close to a literal 'creation ex nihilo'. When it was first proposed in the 1930's, it was resisted by many scientists on just those grounds; and when the Pope learned of it, he seized on it, saying that it 'affirmed Catholic doctrine'. This last embarrassed the discoverer of the principle, George LeMaitre, a Catholic, who wanted to keep the science and religious aspects separate; to this end, he had the Pope's science adviser lobby against the Pope mentioning it.

If p stands for "something exists", ~p stand for "nothing exists" and ~p -> p for "something follows from nothing" — Pippen

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.

I can prove that ~p and ~p -> p is a contradiction — Pippen

~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.

If then, by some miracle, another apple appears outta nothin' ... — SophistiCat

'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. ;)

By way of footnote, the cosmological theory popularly referred to as 'big bang theory' comes awfully close to a literal 'creation ex nihilo'. — Wayfarer

(Y)