Friday, March 21, 2008

Not necessarily possible

William Bynoe’s most excellent talk provided a argument against two axioms which I find a priori absurd in any case. One is that anything that is possible is necessarily possible. The other is that anything actual is possible. Will gave these principles in terms of accessibility relations between possible worlds. So we can call them:

1. Equivalence: For any worlds A and B, if A is accessible from B, then B is accessible from A.

2. Reflexivity: Every world is accessible from itself.

This fevered adding of axioms renders accessibility redundant and meaningless, since all possible worlds become equally accessible from all others. Will’s argument comes from two premises:
1. (Roughly, there was no hand out): Truths about what is possible are grounded in the actual world.
2. It is possible that there could be nothing at all.

The argument then is, call the actual world WA: it seems possible grounded in the actual world that there could have been nothing. Let us call this possibility WN. WN is accessible from WA. But WA is not accessible from WN, since if WN was the actual world, then there would be nothing in WN that would ground the truth of the possibility of facts in WA. Further more, it might also be claimed that WN is not accessible from itself. So WN provides a counterexample to equivalence and reflexivity.

A lot of the discussion focussed on the nature of N. People found reflexivity and equivalence to be so “intuitively plausible” that the argument just showed that N was impossible. But this kind of thing I found weak for this reason: the intuitive nature of the two dodgy axioms rests on a few examples. But all this shows is that reflexivity holds in some central cases, as does equivalence. To jump from this to the claim that it necessarily holds in all cases requires more than considering a few tailor made examples. It involves a proof, or at very least a confrontation with ordinary usage which in fact throws up many counterexamples. I’ve never seen anything like a proof, and when ever I have offered counterexamples I usually meet with hostile verbal evasion of this kind “You are confusing metaphysical modality with epistemic modality”.

Will began with the intuitive case for the two axioms by giving an example of something possible but not actual. He was actually standing, but he could have been sitting. Reflexivity and equivalence clearly hold in this case. Had he been sitting then it would have been possible that he was standing, and given that he was standing, it is clearly possible that he was standing. So far all we have got is a generalisation based on a single case. 1 is prime, 3 is prime, 5 is prime, 7 is prime, therefore all odd numbers without exception are prime.

Later, for contrast something impossible was considered. Tim is Portugal was the example. This is supposed to be clearly impossible. Why? Because it is nonsense, because it is impossible to imagine. But I thought we were talking about metaphysical possibility, not conceivability or semantics. A state can be defined in terms of its citizens and its territory and perhaps it constitution and economy. It is possible for a state to lose all its territory and all its citizens but one and that one could be Tim. The remaining citizen would then embody the whole of the state. If the state was democratic, and Tim was the last citizen, then the constitution of Portugal would be identical with Tim’s will, its territory identical with Tim’s property and body. Tim would be Portugal in this case. “I am the state of Portugal.” He could say with uncharacteristic grandeur. Is this scenario possible? What relevance does it have to the accessibility relationship?

Perhaps this is not possible because “Tim” and “Portugal” are rigid designators, and this scenario just changes Portugal too much for us to have a hold on what the possibility is supposed to consist in. With this in mind lets go back to the central example. It is possible that William Bynoe (rigidly designated) is sitting down at time t, when actually he was standing at that time. This is clearly not epistemic, since we know he was actually standing. So the accessibility relationship holds symmetrically between WA ( the actual world) and W1 (where William Bynoe was sitting not standing at time t). Now let us consider a second possibility: It is possible that William Bynoe (rigidly designated) does not exist. This is clearly not epistemic since in order to rigidly designate William Bynoe he must exist. The reference fixing must be grounded in the actual world. So the accessibility relationship holds between:
WA (the actual World) and W2 (a world in which William Bynoe does not exist). But is it symmetric? Well no, because in W2, William Bynoe doesn’t exist, so the possibility that William Bynoe is standing is not grounded in W2 and therefore can’t be a possibility. Complicated? Baroque? A misunderstanding of some kind? I don’t think so. Here are two propositions that, realist as you like about possibility, are straightforwardly true:

If William Bynoe did not exist then it would be impossible that he is now standing.

It is possible that William Bynoe did not exist.

There for it is possible that it is impossible that he is now standing.

This is a counterexample to the equivalence relation. It is also a counterexample to the axiom that whatever is actual is necessarily possible, since if William Bynoe is in fact now standing, then it is still possible that it is impossible that he is now standing.

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7 Comments:

Blogger Richard said...

"If William Bynoe did not exist then it would be impossible that he is now standing."

There are two readings of this:

(i) (WB does not exist) and (WB is now standing) are incompatible propositions. That is, the 'impossibility' claim is (despite appearances) wide scope.

(ii) If WB did not exist then the proposition (WB is now standing) would have been metaphysically impossible.

Only the first reading is "straightforwardly true", but the conclusion doesn't follow, because wide-scope operators don't allow for conditional detachment as modus ponens requires (see my linked post for explanation).

The second reading is the one you require for validity. But it's false (or so most philosophers would claim).

More generally: the intuition that there could have been nothing is surely just the intuition that there could have been nothing physical. Who has the intuition that there could have been no numbers, possible worlds, or other abstracta? That doesn't sound at all intuitive to me. (Philosophers are usually happy to assume that abstract objects exist necessarily!)

8:25 PM  
Blogger Brandon said...

So WN provides a counterexample to equivalence and reflexivity.


I don't see any particular reason for taking either equivalence or reflexivity to be generally true (my own view is that taking any such principles as generally true involves a misunderstanding of what one is doing with modal logic), but I also don't see how WN would be a counterexample to either. For if WN is the actual world, there is something actual that could ground the truth of the possibility of other worlds, namely, the actuality of WN itself (which we have assumed). A similar point could be made about reflexivity. (I suppose this is related to the point Richard makes about abstracta.)

9:44 PM  
Blogger bloggin the Question said...

Hi Richard. Yes it is the second reading, which you call wide scope, that I intend. The first is trivial and makes no possible worlds accessible from any other. I didn't cover it in the post very well, but the first premise of Will's argument was that claims about metaphysical possibility are grounded in the actual world. He thought that this was controversial, but I think it must be a requirement otherwise disagreements about modal claims are baseless. Iterated possibility then surely transfers this requirement onto the possible world. So, in clumsy world speak, if in the actual world x doesn't exist, then any proposition that rigidly designates x is not possible. So x is F can be actually true but not necessarily possible.
I guess the response to this would be, well if WB didn't exist, then it would stillbe possible that he did. But that's just to reassert an instance of the claim that I am rejecting. The second appearance of "WB" or "he" is non refering. It cannot be a definite description and it cannot rigidly designate.
Brandon, if you don't take them to be generally true then I am with you. As for your comment about WN, I find the whole WN thing too wierd to get a grip on. My basic intuition is that if you have a world with just a blue square and green circle then it is possible to have a blue circle, but to have a shrill scream would not be grounded in the actual world. So if WN were the actual world then other empty worlds would be possible, but nothing else.

10:56 PM  
Blogger Richard said...

BTQ - note that, on the second reading, the argument is question-begging. Nobody who doesn't already agree with your conclusion is going to grant that premise. We think the conditional in question is false, not "straightforwardly true".

"I guess the response to this would be, well if WB didn't exist, then it would still be possible that he did. But that's just to reassert an instance of the claim that I am rejecting. The second appearance of "WB" or "he" is non refering."

Hold on, the consequent is still being spoken in our language, in which 'WB' straightforwardly refers to WB. Perhaps you mean to defend instead the meta-linguistic counterfactual claim:

(ML) If WB didn't exist, then the sentence 'WB possibly exists' would not express a truth.

Maybe that's so, but it's irrelevant. If the world were different, then sentences would express different propositions than they actually do. But that doesn't affect what propositions are necessarily true. In particular, it doesn't change the fact that WB possibly exists is a necessary truth -- that is, the proposition actually expressed by 'WB possibly exists' is not false at any world, even though that string of symbols may of course fail to express this proposition at some worlds. (Note that it may still be expressible in other terms, e.g. give a complete qualitative description of our world, and then say something like, "It is possible that the person named 'WB' [fill in any further identifying features] in the described world, exists.")

"I didn't cover it in the post very well, but the first premise of Will's argument was that claims about metaphysical possibility are grounded in the actual world. He thought that this was controversial, but I think it must be a requirement otherwise disagreements about modal claims are baseless."

This is the core of the disagreement. It is a controversial claim, and the alternative does not make modal claims "baseless". Instead, they are grounded in necessarily existing abstracta, viz. the space of possible worlds.

1:51 AM  
Blogger bloggin the Question said...

You see, how I look at it is this, William Bynoe is a person, not a necessarily existing abstracta. This should be apparent if you consider the possibility that William Bynoe was very different from how he is. Now we have two worlds, W1 and W2, in both there exists William Bynoe, but the two WB's are not identical to each other, nor satisfy some set of descriptions. In W2 william could have possibly been the way he is in W1 and vice versa. But if there existed a person in W1 who fitted the description of William Bynoe in W2 then he wouldn't be identical with William Bynoe in W1, he wouldn't even be a doppleganger and may not resemble William Bynoe at all. But now let us take W3 where William doesn't exist at all. If there existed an person in W3 that was atom for atom identical to any William Bynoe in any possible world where William Bynoe existed, this person would still not be identical with William Bynoe. So however the world was, it would be impossible that William Bynoe was now standing.
Although I maybe begging the question against people who have various what I consider to be crazy commitments, I am appealing to common sense. If William Bynoe was actually sitting, he could be standing. But if he didn't exist at all, then it would be impossible that he was standing. To say that it is possible for someone to stand up who doesn't exist just doesn't seem sensible to me. The necessarily existing abtracta must be more than infinite in number if they are to contain all the things that don't exist. In fact they must surely include all the contingently existing abstracta and perhaps even the abstracta that don't actually exist at all. If someone says that denying all this is BTQ then he should get his beard cut at Occams. ;)

3:12 AM  
Blogger Richard said...

"To say that it is possible for someone to stand up who doesn't exist just doesn't seem sensible to me."

Well, we both agree it's trivial that existing is a precondition for standing up. But it's surely possible that there could have existed people besides those of us who actually exist. And those non-actual people could have been standing up. Simple.

3:35 AM  
Blogger bloggin the Question said...

"It is possible that there could have existed people besides those of us who actually exist"
I agree with this statement since I can make particular use of it. Had I had a child with my first girl friend then I might have had a son, or daughter who does not exist. Now we have someone non existent to talk of, for convenience let's call it F. Is it possible that F could have been crippled at birth? Yes. Is it possible that F could have been a girl? Yes. Is it possible that F could have been a boy? Yes. Is it possible that F could have no personhood, in other words to have been born without a brain say? Yes, why not? It seems clear to me that F is in no way self identical. Clearly in some cases it was possible that F is now standing, and some cases not. So it is contingent that it is possible that F is now standing. In other words it is not necessary that it is possible that F is now standing. We are using our actual world language like you recommend, but there is no way to tie down the reference for F. This may seem like a linguistic thing, but it is not. "F" is not a bit of language.
Lets take this: it is possible that someone who does not exist could now exist. It is possible that that someone could be called "Freddy Fierce". It is possible that Freddie Fierce is now standing. It is possible that Freddie Fierce was called something else.!!!!!???? It is possible that Freddie Fierce does not exist!!!!???? It is possible that Freddie Fierce is not Freddie Fierce at all but an atom for atom replica????!!!!
I hope I'm getting something across. There is such a thing as contingent possibility is all I'm trying to say. To talk about some possibilities, we need an organic public thing to tie down what the possibilities are about. Non existent people don't provide this anchor, so what is possible of them is contingent.

1:58 PM  

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