1. It is not the case that something exists. [assumption #1]

2. If it is not the case that something exists, then the negative fact that it is not the case that something exists doesn't exist. [assumption #2]

3. If the negative fact that it is not the case that something exists doesn't exist, then it is not the case that it is not the case that something exists. [assumption #3, instance of: the fact that p exists <–> it is the case that p]

4. The negative fact that it is not the case that something exists doesn't exist. [from 1+2 by modus ponens]

5. It is not the case that it is not the case that something exists. [from 3+4 by modus ponens]

6. Something exists. [from 5, instance of: ~~p <–> p]

7. Something exists and it is not the case that something exists. [from 1+6 by &-introduction]

8. Therefore, necessarily, something exists. [from 1+7 by reductio ad absurdum]

Q.E.D.

Teuton wrote:
3. If the negative fact that it is not the case that something exists doesn't exist, then it is not the case that it is not the case that something exists. [assumption #3, instance of: the fact that p exists <–> it is the case that p]

1. the fact that p exists <–> it is the case that p
<–>
2. the fact that ~p exists <–> it is the case that ~p
<–>
3. ~(the fact that ~p exists) <–> ~(it is the case that ~p)
<–>
4. the fact that ~p doesn't exist <-> ~~p
<–>
5. the fact that ~p doesn't exist <–> p
->
6. the fact that ~p doesn't exist –> p

[p <–> it is the case that p]

Run that by Godel.

Oh wait, it is not the case that Godel exists. If it is not the case that Godel exists, then the negative fact that it is not the case that Godel exists doesn't exist.
per your logic.
8. Therefore, necessarily, Godel exists.

So go ask him.

Steve wrote:Oh wait, it is not the case that Godel exists. If it is not the case that Godel exists, then the negative fact that it is not the case that Godel exists doesn't exist.
per your logic.

No, you're wrong, because that doesn't follow from "my" logic.
If Gödel doesn't exist, then the negative fact that Gödel doesn't exist may well exist.
For the negation of the existence of Gödel doesn't entail the negation of the existence of negative facts.

the fact that p exists <–> it is the case that p
instance:
the fact that Gödel exists exists <–> it is the case that Gödel exists

This implies

the fact that Gödel exists exists –> it is the case that Gödel exists

This implies

it is the not case that Gödel exists –> it is not case that the fact that Gödel exists exists

This is synonymous with

Gödel doesn't exist –> the fact that Gödel exists doesn't exist

I fail to see how you can get from the premise above to

Gödel doesn't exist –> the fact that Gödel doesn't exist doesn't exist

Man.

I already knew something existed before I even thought about it.

What do you do for a living Teuton? Is this it? I mean I often appreciate your input but sometimes...

Onyx8 wrote:
I already knew something existed before I even thought about it.

The question is not whether there is in fact something. We all know for certain that this is case.
The question is whether there could be or could have been nothing rather than something.

The basic point is that if nothing existed, then there wouldn't exist any cases/facts or truths.
And "nothingness" as the absence of all facts and truths is not consistently conceivable or expressible.

For instance, the proposition <Nothing exists> is logically necessarily false, since if it were true, it would exist, because nonexistent propositions cannot have any truth-value. But if the proposition <Nothing exists> exists, then it is not the case that nothing exists, and then the proposition is false, and necessarily so.

For instance, the fact that nothing exists is logically necessarily nonexistent, since if it existed, it wouldn't be the case that nothing exists but be the case that something exists.

"Note too that the question of the existence of facts is a horse of a very different color from that of the existence of things. There being no things is undoubtedly a possible situation, there being no facts is not (since if the situation were realized, this would itself constitute a fact)."

(Rescher, Nicholas. The Riddle of Existence: An Essay in Idealistic Metaphysics. Lanham, MD: University Press of America, 1984. p. 17)

It's already inconsistent to call there being nothing a "situation", since if there is a situation, there isn't nothing.
It is plainly illogical to say that the sentence "Nothing exists" refers to a (possible) situation, state of affairs, fact, case, or truth, since as long as there are any situations, states of affairs, facts, or truths, there does exist something.
The sentence "Nothing exists" cannot be true or refer to anything.

Teuton wrote:

Steve wrote:Oh wait, it is not the case that Godel exists. If it is not the case that Godel exists, then the negative fact that it is not the case that Godel exists doesn't exist.
per your logic.

No, you're wrong, because that doesn't follow from "my" logic.
If Gödel doesn't exist, then the negative fact that Gödel doesn't exist may well exist.
For the negation of the existence of Gödel doesn't entail the negation of the existence of negative facts.

the fact that p exists <–> it is the case that p
instance:
the fact that Gödel exists exists <–> it is the case that Gödel exists

This implies

the fact that Gödel exists exists –> it is the case that Gödel exists

This implies

it is the not case that Gödel exists –> it is not case that the fact that Gödel exists exists

This is synonymous with

Gödel doesn't exist –> the fact that Gödel exists doesn't exist

I fail to see how you can get from the premise above to

Gödel doesn't exist –> the fact that Gödel doesn't exist doesn't exist

That was my best shot. I guess I can't help you.

"I suspect that our attempts at conceiving of total non-existence are irredeemably partial. We are always left with something, if only a setting from which we envisage everything having departed, a void which we confront and find empty, but something which it makes sense to speak of as having once been home to bodies, radiation, or whatever.
‘There might have been nothing’ need not, of course, be the same as ‘Nothing might have existed’, an evident falsehood contradicted by the many things which could—indeed do—exist. Likewise, imagining (conceiving, supposing) nothing is not what we are being called upon to do. That is not imagining anything, which is simply failing to imagine, not imagining at all. None the less, talk of imagining there was nothing—which is what is called for—does run the risk of being treated as if a matter of imagining nothing, and that is refraining from imagining anything. Either that, or, I suggest, it is to imagine things lacking where there might have been something: we suppose we can imagine the stars ceasing to exist one by one—like so many lights going out—but we still look to where they were. It makes sense to suppose a reversal of the development described—objects now start reappearing before us in the space which had been vacated. We have not discarded the setting; something we might search in vain, but something—a previously occupied region—none the less. Envisaging an empty terrain, sky, chasm, or even space does not give us what we want. To imagine, conceive, or postulate space is not to imagine, etc., nothing; as I say, that is not to imagine or postulate anything."

(Rundle, Bede. Why there is Something rather than Nothing. Oxford: Oxford University Press, 2004. p. 111)

Teuton wrote:[from 1+7 by reductio ad absurdum]

If it's not the case that anything exists, then it's not the case that logical principles exist.

Teuton wrote:2. If it is not the case that something exists, then the negative fact that it is not the case that something exists doesn't exist. [assumption #2]

So, a proof can only be attempted from an assumed position external to the world. Accordingly, premise 2 is false.

ughaibu wrote:If it's not the case that anything exists, then it's not the case that logical principles exist.

Yes, so what? Something does in fact exist, and logical reasoning about the possibility of there being nothing is feasible.

ughaibu wrote:

Teuton wrote:2. If it is not the case that something exists, then the negative fact that it is not the case that something exists doesn't exist. [assumption #2]

So, a proof can only be attempted from an assumed position external to the world. Accordingly, premise 2 is false.

What do you mean by "assumed position external to the world"?

Teuton wrote:What do you mean by "assumed position external to the world"?

A definition of the empty set is that it is the set of all x such that it's not the case that x=x, given the principles of classical logic there is no such x. Accordingly, from outside the empty set, we can say that it is not the case that anything exists within that universe of interest.
If one is going to say anything interesting about the possibility that it might have been not been the case that anything exists, globally, one similarly needs a point of view external to the universe of interest, even if that universe is the world. Otherwise the proof is trivial.

Teuton wrote:
Yes, so what? Something does in fact exist, and logical reasoning about the possibility of there being nothing is feasible.

For example, the proposition <if nothing existed, this proposition wouldn't be true> is true, and there is nothing self-contradictory about saying so, because the proposition does in fact exist and is in fact true.

Teuton wrote:

Onyx8 wrote:
I already knew something existed before I even thought about it.

The question is not whether there is in fact something. We all know for certain that this is case.
The question is whether there could be or could have been nothing rather than something.

Ah, thanks.

ughaibu wrote:A definition of the empty set is that it is the set of all x such that it's not the case that x=x,

you sure about that ~(x=x) part?

SpeedOfSound wrote:

ughaibu wrote:A definition of the empty set is that it is the set of all x such that it's not the case that x=x,

you sure about that ~(x=x) part?

http://au.metamath.org/mpegif/dfnul2.html

Nice and strange.