SpeedOfSound wrote:I am still uncomfortable with mixing ontological categories.

I haven't done so. When I say that objects exist and facts exist, the difference between these two categories is not due to there being two different meanings of "exist". The proposition <nothing exists> excludes all categories of entities whatsoever from existence. That is, if nothing existed, there wouldn't be any objects/substances, properties, relations, facts/states of affairs, states, processes, or events.

If nothing exists, then the fact "if pineapples existed, they would be yummy" also exists. I mean you don't need to resort to the 'nothing exists' fact.

Panderos wrote:If nothing exists, then the fact "if pineapples existed, they would be yummy" also exists. I mean you don't need to resort to the 'nothing exists' fact.

There are conditional statements or propositions, but it is doubtful whether there are conditional facts (states of affairs).

"My fundamental thought is that the 'logical constants' do not represent."

(L. Wittgenstein, Tractatus Logico-Philosophicus, §4.0312)

That is, according to Wittgenstein, there are no elements of reality which correspond to "not"/"~", "and"/"&", "or"/"v", "if…then"/"->". If he is right, then conditional propositions, including counterfactual ones, don't represent and aren't made true by corresponding conditional facts.

Anyway, "nothing" means "nothing", and so "nothing exists" implies "facts don't exist".
(Only if facts are conceived of as abstract entities, "nothing concrete exists" doesn't imply "facts don't exist".)

So "nothing exists" means "facts don't exist" but we can still have conditional statements in the world of nothing? Billions of conditional statements, trillions, the world of nothing is packed to the brim!

Panderos wrote:So "nothing exists" means "facts don't exist" but we can still have conditional statements in the world of nothing? Billions of conditional statements, trillions, the world of nothing is packed to the brim!

No, if there were nothing, there wouldn't be any statements or propositions either.

Teuton wrote:
I haven't done so. When I say that objects exist and facts exist, the difference between these two categories is not due to there being two different meanings of "exist". The proposition <nothing exists> excludes all categories of entities whatsoever from existence. That is, if nothing existed, there wouldn't be any objects/substances, properties, relations, facts/states of affairs, states, processes, or events.

Doesn't this primarily concern how we think? I can't think that 'nothing exists' since it is logically impossible for 'nothing' to 'exist'

But what makes sense to us is our innate sense of intelligibility.

So it seems to me that the arguement must be formulated thus:

1) If reality is intelligible
2) Then reality must exist

If reality cannot be understood by the human mind, then we can't say attribute anything it - including existence

DrWho wrote:
Doesn't this primarily concern how we think? I can't think that 'nothing exists' since it is logically impossible for 'nothing' to 'exist'

It is doubtless logically impossible for a/the nothing to exist, but in "Nothing exists" "nothing" doesn't function as a count noun combinable with the definite or indefinite article or as a proper noun but as an indefinite pronoun. So, logically speaking, it is simply the negation of "Something exists", i.e. "It is not the case that something exists". The statements "Nothing exists" and "A/The nothing exists" are neither synonymous nor logically equivalent.

Very nice. Sadly though, if we accept the postulate (1) then no laws of logical inference exist, including Modus Ponens (used for 4 and 5) and the law of excluded middle (used for 6, which I think is the key step). So the reductio ad absurdum cannot be performed, and the conclusion cannot be reached.

andrewk wrote:Very nice. Sadly though, if we accept the postulate (1) then no laws of logical inference exist, including Modus Ponens (used for 4 and 5) and the law of excluded middle (used for 6, which I think is the key step). So the reductio ad absurdum cannot be performed, and the conclusion cannot be reached.

Of course, if nothing existed, nobody would or could perform any logical reductios. But we know that premise 1 is in fact false: it is not the case that it is not the case that something exists, i.e. something exists. I exist, logical rules and truths exist, and so why shouldn't I be able to perform a valid reductio regarding nothingness?

Teuton wrote:

Panderos wrote:So "nothing exists" means "facts don't exist" but we can still have conditional statements in the world of nothing? Billions of conditional statements, trillions, the world of nothing is packed to the brim!

No, if there were nothing, there wouldn't be any statements or propositions either.

But you're saying that if nothing exists, the fact 'nothing exists', exists. Therefore we have a paradox and we can't have the nothing state.
Why can't I say that if nothing exists, some random conditional statement exists (which is also true in the nothing world, like your fact), which also gives us a paradox yada yada..?

This question makes me start to wonder whether the whole component of metaphysics devoted to the concept of "possible worlds" lacks validity. Reasoning about what worlds are possible is done using rules of logical inference that we have adopted based on our observations of this world. For example, we repeatedly observe that if A->B is true and A is true then B is true, and after we have observed this enough times for different As and Bs we use the Principle of Induction to infer the Modus Ponens logical rule that ((A->B) & A)->B.

As the justification for Modus Ponens is entirely based on our observations in this world, it seems debatable at best whether we can use it to develop logical arguments about alternative worlds. The same goes for all the other rules of inference. Perhaps all we can say is that, if things were different, then they would be different. And that includes the state of there not being anything. To me, such a state is inconceivable and, since I also know it not to be the case, I dismiss it from further contemplation.

This is a pragmatic justification rather than a proof. I decide not to contemplate it further, not because I know for sure there is no truth about the matter, but because I am convinced that if there is any such truth, it is unknowable.

Panderos wrote:
But you're saying that if nothing exists, the fact 'nothing exists', exists. Therefore we have a paradox and we can't have the nothing state.

If nothing existed and negative facts were entities, then the fact that nothing exists would exist. And then it would follow logically that it is necessary that something exists.

Panderos wrote:
Why can't I say that if nothing exists, some random conditional statement exists (which is also true in the nothing world, like your fact), which also gives us a paradox yada yada..?

What you can say is that if nothing existed and it were true that nothing exists, then the true proposition/statement <Nothing exists> would exist; and then there would be another contradiction.

Question of whether metaphysical
worlds exist or not is academic. Since
the very simple reason is that the means
to investigate such phenomena is evidently
beyond us. As we can only investigate what is
physical. Anything beyond that is impossible plain
and simple. That is why such discussions really belong
in the realm of philosophy and not science. That does not
automatically negate their existence of course. So the natural
position therefore to take on this is an agnostic one. Though most
atheists - myself included - probably do not believe in them at all period

andrewk wrote:This question makes me start to wonder whether the whole component of metaphysics devoted to the concept of "possible worlds" lacks validity. Reasoning about what worlds are possible is done using rules of logical inference that we have adopted based on our observations of this world. For example, we repeatedly observe that if A->B is true and A is true then B is true, and after we have observed this enough times for different As and Bs we use the Principle of Induction to infer the Modus Ponens logical rule that ((A->B) & A)->B.

It's actually all based on alphabeti spaghetti. At lunch, Frege came across A A ⊃ B. He ate the As and the U, and was left with just the B. From this insight, most of logic was born.

Generally, since Modus Ponens is valid, you can make up any wacky antecedent to justify it, from the moon being green cheese, to alphabetti spaghetti, or perhaps something even more outlandish such as it being learned from experience.

P -> Modus Ponens is valid

You can shove anything in for P.

Teuton wrote:You don't know what I understand and what I don't understand, so shut up!

When it comes to formal logic, understanding and technical competence go hand in hand, just like with algebra. If someone tries to solve the quadratic equation x^2 = 0 by laboriously carrying out every step in the "completing the square method", I'll tell them they don't (yet) understand elementary algebra. Similarly, when you write the sort of formalisation in your OP, and then fail to register its immediate simplification, I'll tell you that you don't understand elementary formal logic.

That's the cool thing about formal logic and maths. You get to demonstrate understanding by doing technical stuff. You can't get away with idle commentary on an SEP article.

Teuton wrote: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.

lol.


In possible world w nothing contingent exists.

Thus, in possible world w, something exists but nothing contingent exists.

Necessarily, if something exists, it is either a necessary existent or a contingent existent (you cant have an impossible existent in a possible world).

Thus, in possible world w, something exists which is either a contingent or necessary existent.


Thence, in possible world w, a necessary existent exists.
Thence, a necessary existent exists.

yay! logic ruuuules.

I was away from the forum when this one came up, which is a shame because I would have enjoyed it. Still, better late than never.

This argument is a variant on the thoroughly debunked old relativism-is-self-refuting chestnut, except instead of saying that the fact that there is no objective truth would itself be an objective truth it's now claimed that the fact that nothing exists would itself be an existing thing. Similarly one could argue that there must be something of significance, since if it was shown that nothing was significant this would be a significant result. And we must be talking about something, because how else could we say we weren't? For more details see My Big Blue Book of Word Games About Self-Reference (Cambridge Kindergarten Press). This was a pretty cheesy joke when Odysseus persuaded the cyclops that his name was Nobody and the millenia since then haven't freshened it up much.

As a fresh twist, however, facts are now existing things! The fact that p exists if and only if it is the case that p! So true statements exist and false statements don't exist.



Now if you think there were some centred italics there you're hallucinating because there was nothing there that existed.

We see now that it's nonsense to say to someone "the statement you made was false" because false statements don't exist and you can't perform a non-existent action.Of course you could define your way around this problem by making some distinction between true statements and facts or by defining the italics as not a statement, merely something that bears a superficial resemblance to one.

A cynic might say that redefining words to mean what your argument needs the to mean is a bit crap, but as Teuton himself tells us: "What logically and philosophically uneducated people say and think is irrelevant. Your appeal to the people has no argumentational force whatsoever."

Then again, in that same thread Teuton assured us that something exists if and only if the number of things which are identical to it is not zero. It seems to me that what I typed above is identical to the false statement that I am Hugh Heffner, so false statements do exist and Teuton helpfully provides the refutation of his own argument.

Or is it all, in fact, a load of bollocks?

Seriously, anyone who likes philosophy and considers the time they've spent on it not to have been wholly wasted needs to vigourously point and laugh at this kind of pretentious pseudo-logical fake-rigourous wankfest which ensures that most sane people continue to find the whole subject ridiculous.