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Thursday, July 08, 2010

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This is surprisingly simple, and I think correct. I think this argument does show that there is something that exists necessarily, because S would be a necessarily existing thing, correct? It seems there is no possible world where S didn't exist.

Well, as the saying goes, simplex sigillum veri.

Your point is that, not only does the argument show that necessarily, something exists, but also that something necessarily exists, namely the proposition S. I'm inclined to agree.

If someone urges that propositions can exist only as thoughts in a mind, then we have the makings of an argument for a divine mind.

Thanks for the comment.

If the argument fails, it would most certainly be at premise 5. But it appears that you are making the claim in that premise that N is self-contradictory, and therefore necessarily false; N cannot possibly exist, because of the necessary existence of the proposition S, correct?
As a Christian, I like where you're going with this. But something just seems off about that premise and the existence of propositions without minds. I can't put my finger on it, so I'll have to think about it more.
Is my thinking off base with the following two versions of your argument?: Staying in the metaphysical framework, can't you make the same round-about argument using numbers? Or do numbers need a referent to exist? How about this: the possible world (or state of affairs) N would exist in just as real terms as the proposition S (in other words, something would exist, namely, the state of affairs in which nothing exists -- the possible world itself), and is therefore self-contradictory.
Interesting argument.

Don't you deny (6) yourself? Do you think propositions about the future have truth values?

Dr V,

Don't you deny (6) yourself? Do you think propositions about the future have truth values?

Further, how do we understand false propositions in light of truthmaker theory? Do propositions need falsemakers?

Maybe the falsemaker for a proposition is the truthmaker for its contradictory. But there are no truthmakers at all in a world where nothing exists, so "Something exists" wouldn't even have a truth value.

Or do we need falsemakers at all?

I am merely a student, but if you would correct me or point in me a good direction I would greatly appreciate it.

I struggle with seeing premise 5 as reasonably maintained. It seems that statement S is not necessarily an ontological property of the world in reference W.I understand the situation to be as such;
1. S has a relationship with W in such a way that its truth value is dependent on the ontological properties of W, although S itself is not directly part of the actual ontology of W.

Or I could attempt it this way.

1' The set W includes anything that exists in the world that you reference.
2'. Statement S is about set W.
3'. S does not belong to set W.
3' It is still possible for W to be an empty set.


Please feel free to laugh at me if I deserve it.

The argument seems to have a slight whiff of the ontological argument about it.

I also question premise 5].

Unicorns have the property of having one horn but unicorns do not exist. Klein bottles have the property of one surface but they can not exist. However, we have a concept of unicorns and Klein bottles. The ontology of the object and the ontology of the concept are different. The object potentially exists inside a possible world, and thereby if it has a property demonstrates the existence of this world. The concept of the same object does not need to exist inside that possible world and so it does not demonstrate that the possible world has existence. So if we re-arrange 5] to:-
5] In the worlds in which S is false, the concept of S is false
…then the conclusion does not follow.

Some additional supporting arguments:-

i) Plato discussed in his dialogue “The Sophist” the distinction between not-being and the opposite of being. The opposite of being, absolute nothingness, is unintelligible and following Kant we can say nothing meaningful about it. To consider the options of being against its opposite is a metaphysical step too far.

ii) We are considering the possibility of being against its opposite from within the system of being. Whilst we might conjecture about the nature of logic and causality outside of this system, at the meta level that we are discussing, we can not demonstrate any proof about it.

I don't know why I ended up posting something twice. My mistake.

"Unicorns have the property of having one horn but unicorns do not exist. Klein bottles have the property of one surface but they can not exist. However, we have a concept of unicorns and Klein bottles."

Unicorns can't have properties if they don't exist. What is the property exemplified by?

"3. There are possible worlds in which S is false . . ."

What does "world" mean if S is false?

Jeffery Hodges

* * *

It strikes me that, contra premise 5, were there nothing, it would not be false that there is something; that is, there would be no proposition, “Something exists,” which would be false. Nor, of course, would there be the proposition, “Nothing exists,” which would be true.

P.S. I'm not sure we should let your assumption that you exist go unchallenged. Are you relying on the Cogito? Or do you have another argument to offer?

I'm no expert on these things, but I'll put forward two lines of attack:

1) The notion of existence: When I read the preamble to the argument I was expecting some reasoning which would culminate in the proof of some object (though, obviously, not necessarily the same object) existing in each and every possible world. Instead the 'thing' which exists in each and every possible world turns out to be the proposition, S. In fact, S is just a general form of a proposition of the existence of any particular object. So not only does the argument demonstrate the existence of a general proposition S, but also the existence of numerous (infinite?) particular propositions such as France exists (which, unfortunately, will be true in some possible worlds - and, if the proposition is false in others, then it will have to exist in order to be false), doorknobs exist, etc. This doesn't show the argument to be invalid, but - perhaps - shows that if you imbue propositions with this kind of 'existence' (even if false), then you don't demonstrate anything very interesting other than that every proposition with a truth-value exists in every possible world.

I just like my ontology a bit simpler. I think that propositions, if they do exist, at least exist in a very different sense to objects. I'm not sure that I'm happy with the idea of propositions existing without a propositioning mind or a mind to interpret the propositions, for example. I think at least part of the problem with the argument is that S makes perfect sense to us imagining possible worlds from within the actual world, but, from within a world where nothing exists, S has no propositioner nor anyone to be propositioned by it.

2) Possible worlds: Similar to Jeffrey, above, I would argue that a world in which nothing exists is not a (possible) world in any sense, no more than a non-existent chicken is a (possible) chicken. So I think your premise 3 is straightforwardly false. Interestingly, I guess this does entail that something must exist in every possible world (because in order for it to be a 'world' of any sort, something must exist), but I don't think that the state of nothing is ruled out. Maybe it's like a painting: if you accept that a blank canvas is not a painting (controversial, perhaps, but bear with me), then any paint on the canvas instantly makes it a painting (whether its a single drop of red paint or vast swathes of Rothko-esque coverage). In order for it to be a painting, some paint must exist. But this idea does not have any bearing on the fact that blank canvases exist unproblematically. And so it is with nothing.

Jonny

Steven,

Suppose I committed myself elsewhere to the rejection of Bivalence, and you point out that here I am invoking Bivalence. Then that is an ad hominem argument (in one of the two main senses of this phrase) which is irrelevant to the assessment of the argument under consideration.

In any case, it seems all I need for the purposes of the argument is bivalence with respect to the past and the present.

As for truthmakers, we don't need to go into that for present purposes. All I need are truthbearers.

I think that the argument fails because premise 3 is false. Or better put: either your definition of contingence is such that it assumes platonic necessary existence of propositions - and therefore not a mere definition but a concealed assumption, or premise 3 is unwarranted.

Distinguish to be true in a world w, that is, to be a really existing item in w whose property in w is to be true; and to be true with respect to world w, i.e. to be an item in the actual world which has the property to be true with respect to w.

The truth condition for a proposition "p is contingent" is that p is in the actual world true with respect to certain worlds and false with respect to other worlds. It does not entail at all the existence of p in all possible worlds.

I nother words, it seems to me that you prove your conclusion ultimately from your assumptions concerning the ontology of propositions. The presented argument is just an ornamental way to convey them. But the assumption that a proposition exists in the world about which it "is" is not trivial or "by definition" at all.

I offer another argument for your conclusion:

If it were possible that nothing existed, then there would be an empty possible world. In that case, of necessity, every being would be contingent. Therefore, the concept of necessary being would be self-contradictory. But this is not the case, ergo etc.

James, Sophomore, Mike,

I agree that #5 is questionable. As Mike notes in a roundabout way, I am assuming a principle that could be called *Anti-Meinong*: Necessarily, if x has a property, then x exists. I.e., existence is a necessary condition of property possession. (It is also a sufficient condition.)

In the worlds in which proposition S (Something exists) is false, S exists because it has the property of being false. Therefore, worlds in which S is false and N is true are not possible, whence it follows that it is impossible that nothing exist.

*Anti-Meinong* is controversial but I accept for various reasons that ought to be given in a separate post.

I am also assuming that truth and falsity are (relational) properties of propositions. Some will want to question that.

Mike and Steven,

I share Steven's intuition. Because Pegasus does not exist he cannot exemplify any properties: he is simply not there to exemplify them. Of course, we say 'Pegasus is winged.' But that sentence can be analyzed so as not to imply that there is a nonexistent individual that actually exemplifies a property. We could say: The concept *winged horse of Greek mythology* includes the concept *winged.*

Dr. Hodges writes, ""3. There are possible worlds in which S is false . . ."

What does "world" mean if S is false?

Jeffery Hodges

Well, 'world' has about a dozen meanings, but here, a merely possible world is a total (maximal) way things might have been or could have been, and the actual world is the total way things are.

The total way things are is such that S (*Something exists*)is true. But of course things might have been different in all sorts of ways. The question is whether things might have been such that S is false and N is true. One can think the thought: Nothing exists. Now if that were the case, then it would be the case: it would be the total way things are.

Dr. V,

I agree with the conclusion, but I wouldn’t use you’re reasoning.

N cannot be possible, because all possibility depends on prior being. But prior being precludes N. Moreover, all possible worlds will also assume prior being. So even assume if one supposes a possible world in which there is nothing, there can be no possible world without something.

Neither can S be contingent, because to be contingent means to depend on something else for existence. But if S were contingent, it would depend on something else that is not-S for existence. But not-S is N. Therefore, something existing would depend on nothing existing in order to exist, which is absurd.

Richard Hennessey writes: >>It strikes me that, contra premise 5, were there nothing, it would not be false that there is something; that is, there would be no proposition, “Something exists,” which would be false. Nor, of course, would there be the proposition, “Nothing exists,” which would be true.

P.S. I'm not sure we should let your assumption that you exist go unchallenged. Are you relying on the Cogito? Or do you have another argument to offer?<<

Now that is a very intelligent objection, and very plausible to boot. Were there literally nothing, there would be no truths and in particular no truth to the effect that there is nothing.

It is plausible, but I don't find it compelling. For if there were nothing, then it would be a fact that there is nothing. And so there would be something, namely, that very fact.

The nonexistence of everything is a definite state of affairs, whether it is impossible as I am arguing, or possible. Whether impossible or possible, it is conceivable in that we are thinking it right now. If this state of affairs were to obtain, then that would be a quite definite state of things or way things are -- but then the obtaining of that state of things would show that there could nopt be nothing at all.

Well, its evident that things exist. But if you push me, then I will fall back on the Cogito. It is certain that at least one thing exists as each can prove for himself by noting that his present thoughts about existence, whether true or false, cannot be doubted as to their existence. In Cartesian terms, I cannot doubt my cogitationes or their correlative cogitata qua cogitata or the momentary ego that is their subject -- even though I can doubt whether anything mind-independent corresponds to them.

Dr Novak,

Good to talk to you again. I hope the conference went well. Sorry I couldn't attend.

First a comment on your argument: "If it were possible that nothing existed, then there would be an empty possible world. In that case, of necessity, every being would be contingent. Therefore, the concept of necessary being would be self-contradictory. But this is not the case, ergo etc."

I agree with the first two sentences. What follows, as it seems to me, is not that the concept of a necessary being is self-contradictory, but that this concept is not instantiated. Now I maintain that not every being is contingent; but I don't think your argument establishes that.

I'll respond to the rest of what you say later. By the way, when I and Peter Lupu and Mike Valle met Dale Tuggy recently, we talked about you -- if a favorable way of course!

Dear Bill,

thanks for your favour! :-) Regarding the conference, well, generally speaking I think it was a success, although of course there is a number of points we would like to do better next time. You can see some reaction to the conference on Edward Feser's blog, and a more detailed report with photos on Tuomas Tahko's blog.

Regarding your criticism of my argument: if a necessary being is instantiated at all, it is instantiated in every possible world. Therefore if it is not instantiated in some world, it is not instantiated in any world. Therefore, it is logically impossible aka self-contradictory.

I am sorry I cannot follow your blog and the very intresting discussions on regular basis, but I hope I am able to drop in ocasionally...

(2) The problem with Premise 5, then, perhaps lies in confusing the concrete with the abstract. Here are some ways of cashing out the idea, by noting the standard philosophical ways of conceiving possible worlds, entities in possible worlds, and propositions. (Actually I'm not very familiar with possible worlds lingo, so please correct me if I go wrong.)

E.g., if propositions are conceived of not as abstract entities but as concrete statements that have a context of utterance (a possible world in which it is uttered) and a context of evaluation (a possible world in which it is evaluated as true or false), then Lukas Novak's criticism applies, if indeed I have understood it correctly.

But propositions are more often conceived of as abstract entities, and as abstract entities they cannot be located in space and time. And possible worlds are maximal ways that concrete things might have been present/absent/combined. A possible world is a set of ordered sets of concrete things (ordered sets being different ways in which concrete things can be arranged). Propositions are often conceived of as sets of possible worlds of which they are true, or in other words, as sets of sets of ordered sets of concrete things. A possible world in which nothing exists might be the empty set, or perhaps it could be a set none of whose subsets contain concrete members--I won't speculate on the relative merits of these options, but call this possible world of which N is true and S is false 'U'. The important thing is that, if we take the propositions N and S to be sets of possible worlds, then U is a subset of N, and S is disjoint from U (since S is a subset of the complement of U). Premise 5 will be understood as claiming that N is a concrete member of some subset of U, and that simply cannot be true if propositions like N and S are understood to be sets of possible worlds.

Of course, one can deny that propositions are sets of possible worlds. But the key point is that they are abstract entities, and thus should not be numbered among the concrete entities in any given possible world.

This response cannot address Lukas Novak's argument for ~N. In response to that argument, I will have to say that necessary concrete entities, if they exist, cannot exist in a possible world where nothing concrete exists, but they would exist in all possible worlds where concrete things exist. The null set could be a necessary (abstract) entity that exists "in" all possible worlds, if we read "in" in the set-theoretic sense of containment.

Sorry I posted the second part of my comment before my first!

Very interesting post and thought-provoking comments (I esp. liked Lukas Novak's criticism and argument for ~N)! Intuitively I think N is true. I will try to make some criticisms of Premise 5, hopefully without repeating others' contribution.

(1) If the argument were sound (i.e., if Premise 5 were true) it would prove too much (when generalized). Take a possible world where there exist exactly 100 things. Then add a proposition noting that there are exactly 100 things, which is true in this world. So now it has exactly 101 things, and our proposition is now false!. Then add a new proposition correcting the old one... and repeat ad infinitum. I take no credit for this argument, it's due to the ancient Chinese philosopher Zhuangzi (in his Ch.2).

Boram,

N = Nothing exists. You think N is true? Or do you mean that you think that N is possibly true? Presumably the latter.

>>Take a possible world where there exist exactly 100 things. Then add a proposition noting that there are exactly 100 things, which is true in this world. So now it has exactly 101 things, and our proposition is now false!.<<

If we use 'thing' to cover anything whatsoever, including truthbearers, then among the 100 things will be truthbearers if there are any truthbrearers in that world. I don't think it makes sense to talk of adding something to a possible world because of the maximality property of worlds.

Some think of possible worlds as maximal propositions where a proposition is maximal iff it entails every proposition with which it is consistent. Clearly, to add a proposition to a world so construed would be to precipitate a contradiction. To employ a chemical metaphor, worlds are 'saturated' in the sense that to add anything to them would 'precipitate' a contradiction.

I was hoping we would not have to get into the ontology of worlds, though . . .

Boram,

There is no confusion of the abstract and the concrete as far as I can see. My thesis is that, necessarily, at least one thing exists. This one thing could be an abstract entity such as a Bolzanian-Fregean proposition.

I reject the notion that a proposition is a set, and for a simple reason: propositionsd are either true or false, but no set is either true or false. It simply make no sense to try to reduce propositions to sets. Plantinga made this point against D. Lewis.

I think Hennessey above comes the closest to stating clearly why the argument I gave is not compelling.

Lukas Novak writes,

>>I think that the argument fails because premise 3 is false. Or better put: either your definition of contingence is such that it assumes platonic necessary existence of propositions - and therefore not a mere definition but a concealed assumption, or premise 3 is unwarranted.

Distinguish to be true in a world w, that is, to be a really existing item in w whose property in w is to be true; and to be true with respect to world w, i.e. to be an item in the actual world which has the property to be true with respect to w.

The truth condition for a proposition "p is contingent" is that p is in the actual world true with respect to certain worlds and false with respect to other worlds. It does not entail at all the existence of p in all possible worlds.

I nother words, it seems to me that you prove your conclusion ultimately from your assumptions concerning the ontology of propositions. The presented argument is just an ornamental way to convey them. But the assumption that a proposition exists in the world about which it "is" is not trivial or "by definition" at all.<<

Actually, that is a very good criticism. I take you to be saying that this part of my argument is invalid:

1. Let S = Something exists and N = Nothing exists, and assume for reductio that N is possibly true.
2. If N is possibly true, then S, which is true, and known to be true, is only contingently true.
Therefore
3. There are possible worlds in which S is false and possible worlds in which S is true. ( From 2, by definition of 'contingently true')

You are saying in effect that (3) does not follow from (2). From S's being contingently true all that follows is that S is true in some but not all possible worlds, which is not to say that in the worlds in which S is not true, S exists but is false. A proposition can be false with respect to a world without existing in that world.

And so what is really driving my argument is a tacit assumption about the nature of propositions, namely, that they are necessary beings. But if one starts with this assumption, then of course it is impossible that there be nothing!

Is that a fair statement of your criticism? If it is, then I think you have refuted the argument by showing that the inference from (2) to (3) is invalid.

Dr. Vallicella, thanks for your clear response. Given your further clarifications, I agree that the objections I've raised earlier fail. And from your reply to Lukas Novak, I see that the most fundamental difficulty with the argument has been located.

Still, mulling over your argument and playing around with slightly different versions of it for a few hours makes me realize how elegant it is, and how close it comes to showing the logical inconsistency of N. Let N = "for all F and for all x, ~Fx", and let 'x' range over all objects including statements or propositions in some possible world, and 'F' range over all features or properties had by objects, including "being true" and "being false". Then we can derive ~N as a semantic consequence of N in all possible worlds where there are statements or propositions. But we can't do so in possible worlds where there are nothing, not even statements or propositions, and as you point out that is just the criticism made by Novak and Hennessey). Anyway, thanks everyone for the interesting post and comments!

Correction: ~N cannot be a semantic consequence of N, because there is no single interpretation on which N is both true and false. N is true on one interpretation, namely one according to which the domain (= the set that is the possible world) is empty. And ~N is true on another interpretation, namely one in which the domain is not empty (because it contains the statement or the proposition that N).

So, in terms of the argument in the original post, I would say that premise (5) is false. It claims that S is false according to one interpretation (according to which there is nothing in the possible world), and then gives another interpretation (on which there is something, namely S, in that possible world) according to which S turns out to be true. (Sorry for the multiple comments, this will be my final contribution here, corrections welcome.)

Boram,

Thanks very much for the stimulating comments. I note again that you think that possible worlds can be identified with sets: "the set that is the possible world." But I think there is a knock-down argument, based on Cantor's Theorem, why they can't be sets. I'll repost it now with ComBox open. Tell me whether it convinces you.

Thanks to the discussion I have come to see that the inference to (3) is invalid. As for (5), I grant that it is dubious, but I don't see that it is clearly false. My intuition is that, if there were nothing at all, that would be the 'way thing things are' and that way things are would have some sort of ontological status which would prevent there being nothing at all. But I have yet to make the point rigorosuly and clearly.

Hello Gentlemen,

In possible world theory, aren’t all tautologies necessary? If so, doesn’t that simply mean that propositions like ¬(p∧¬p) are true in every possible world? And if such propositions are true in every possible world, then what? Dr. Vallicella argues, “… an item cannot have a property unless it exists…” So, if (1) ¬(p∧¬p) is true in every possible world, and (2) truth is a property, and (3) all things with properties exist, then something exists in every possible world.

Brian

Yes, every tautology is a necessary truth, though not conversely. I'll assume your box is the sign for conjunction. The proposition expressed by ' ~(p & ~p)' is of course a tautology and so true in all possible worlds. Call this proposition 'LNC.' Since LNC is true in all possible worlds, it must exist in all worlds given that an item cannot have a property unless it exists and truth is a property.

Since both assumptions are extremely plausible, I say Brian has given us a sound argument for both the weaker claim that necessarily something exists, and the stronger claim that something necessarily exists.

Late to this party, but it seems to me that if N were true, the argument and the discussion could not take place at all. Such a thing, were it possible, would by that token be completely unobservable, and unintelligible. Asserting via argumentation that something or other must exist is simply pulling a rabbit out of a hat. Given that the argument is taking place at all, N simply cannot be the case. If N were true, no one could ever possibly be wise to it or observe it. In short, N is an inconceivable state of affairs. But does that make it logically impossible? Does N have any attributes whatsoever that would allow it to be logical, illogical, possible, or impossible? There's no there there to attach any of these concepts to.

It seems that the most that could be said is that if N were the case, then N would be the case, and given that N is not the case, then N is not the case.

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