It's the same with ↪Samuel Lacrampe'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. — SophistiCat

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).

@Sophicat: ~p -> p is not a contradiction! And IMO I can interpret the implication "->" as a kind of "follows from". But even if I do not: If I have ~p and ~p -> p then it is impossible that ~p is true and p is true and isn't that what the creatio ex nihilo - in it's very essence - is all about, a priori to all the physics? It's impossible that ~p and p are true at once, but that is what it would take to create something from nothing...at one moment both would need to exist at once, because otherwise it would be just a case of something from something else..

If I have ~p and ~p -> p then it is impossible that ~p is true and p is true — Pippen

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.

@Srap: We agree. The set of premises ~p and ~p -> p is inconsistent, but I ask you: isn't this set of premises modeling what we think should be going on if something is created from nothing?

~p & ~p -> p leads to a contradiction — Pippen

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.

It'd be an interesting topic whether anything can actually be impossible. Logic and natural laws or part of our universe, so outside it things like statement 2+2=3 being true or a triangular circle might be possible.

OP didn't say ¬p→p, he said ~p->p and could claim that those are not logical connectives. This is basically what he's been doing because he said that p doesn't stand for the claim "something exists" but just "something".

No.

@bluebanana: Let's clearfy things.

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?

¬p→p would mean "if there exists nothing, there exists something", not that something is created out of nothing. If you actually mean ~p -> p and that has a different meaning from ¬p→p, then ~p & ~p -> p is not a contradiction anymore. If you do mean ¬p→p, please write it correctly to avoid unnecessary confusion.

¬p→p would mean "if there exists nothing, there exists something", not that something is created out of nothing. — BlueBanana

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!

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" — Pippen

This is exactly what I said in my previous comment.

and isn't that pretty much what we imagine if we talk about a creation out of nothing? — Pippen

... no? Just absolutely no?

How would your model of a creation out of nothing look like if you don't accept mine?

"If there exists nothing, there exists something" means those are true simultaneously. The correct form is "if there exists nothing, there might (note: not the same as "will without conditions") exist something later".

Logic and natural laws or part of our universe — BlueBanana

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.

"If there exists nothing, there exists something" means those are true simultaneously. — BlueBanana

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.

Logical connectives themselves don't have anything to do with tenses.

• Let A be "I breathe" and B be "I am alive"
• Let C be "my neighbour is alive"
• Then A→B, simultaneous.
• Then B∧C, simultaneous.
• Let D be a premise "people die for a reason" and E be "there was nothing to cause my death yesterday."
• Then E→B, not simultaneous.
• Then E∧C, not simultaneous.

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.

saying "2+2=3" is not any more sensical than saying gibberish like "the smell of purple has". — Samuel Lacrampe

It's also not any more nonsensical.

Practical test: if it is unimaginable, then it is illogical, then it is impossible. — 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.

~p -> p is not equivalent to ~p & p, that's my point.

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.

If we observe something to be unimaginable, then that proves it is unimaginable within our universe, and it is impossible within our universe. — BlueBanana

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.

That's not really a valid argument to counter my argument, just another example of what you claim to be 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.

That scenario has no contradiction if there's no law of contradiction. The law is there and is not. Everything contradicts and doesn't contradict itself. Also, just because there isn't the law of contradiction doesn't mean every contradiction is true. So the law of contradiction not existing does not imply that it exists.

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.

I don't have any argument for what I'm suggesting being actually true, I'm just saying it's a possibility and there imo aren't any arguments for it being impossible that logic is only a part of our universe.

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.

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). — Pippen

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").

(Y)

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)?