Kripke on the Structure of Possible Worlds

Richard Brown 9 Comments

Yesterday I attended Saul Kripke’s talk at the Graduate Center (there are quite a few interesting talk coming up…also looking good are the cogsci talks). The title of the talk was “The Structure of Possible Worlds: a Preface to a statement” and was subtitled, “Prolegomena to a talk on possible worlds, some considerations” so maybe I didn’t really attend a talk. Much of the talk, um preface to a prolegomena to a talk, consisted of Kripke going over the history of his thinking on modality, punctuated with his usual wit and humor. My two favorite moments were (a) the one where, after talking for an hour (the scheduled length of the talk), he stops and says “I may have to go over because I haven’t come to the main point yet” and (b) the one where, while discussing modal realism, he says “what does God have to do to make a really existing merely possible world actual; give it a kiss?” Ah, that Kripke should have his own reality show…I bet it’d be really popular!

As to the content of the talk, or whatever, he seemed to be indicating that (he may have) changed his mind about how he conceives of possible worlds. Here is how he put it in the handout,

I used to think that a sufficient account of my view of what a possible world is might be given by something like a Russellian structured proposition describing it. Now i think that one cannot give an account of what a possible world is in and of itself, but only as part of the structure of all possible worlds, or at least that modal logic cannot rule this out. (Even if there is not a unique structure of all possible worlds, structures where the problem I have just described arise cannot be ruled out philosophically.)

A structured Russellian proposition is an abstract entity that has as its constituents the actual objects in the proposition. So, to modify the classic example, the proposition that Jennifer Aniston loves Brad Pitt has Jennifer Aniston (the actual person), Brad Pitt (the actual person), and the relation of loving as constituents and these constituents are ordered by the loving relation such that Jennifer loves Brad (which is a different ordering from Brad loving Jennifer). This is just a more refined way of putting the basic point of Naming and Necessity. When we ask if Al Gore could have won the election we are asking a question about the actual Al Gore. We are not talking about some distinct object which merely resembles Al Gore (or which merely has many of the same descriptions true of it). There is therefore no issue of how we re-identify Al Gore in various possible worlds; it is the actual Al Gore.

So why does he now think that we can’t do this? (Of course, he hasn’t really come to this conclusion officially. What he said was that it might be true and he sort of leaned towards thinking that it is true). The basic reasoning he employed relies on his argument that there can be objects which are indistinguishable in every way which are none the less distinct. There is no criterion of identity that distinguishes these objects; as Kripke put it “the only difference between them is that there is a difference.” His favorite example is the square root of -1, known as i. i is equal to whatever number equals -1 when multiplied by itself. This number is not on the real number line and so is known as an imaginary number. The problem comes when we realize that i and -i are distinct numbers and that everything that is true of the one is also true of the other. i and -i are distinct yet have no clear criterion of identity.

The problem that Kripke sees is that something like this might be true for possible worlds. To see this he talks about what he calls ‘grounded’ objects. So, let’s imagine a world where there is an person, let’s call him George, who does not exist in the actual world. Let’s say that George is the son of two people who actually exist but do not actually have kids. In the actual world the sperm and egg that come together to form George never meet, but they do in some possible world. So George is grounded in the actual gametes that he could be the product of. But there is also the possibility of ungrounded objects. So consider Georgette. Georgette is a women who does not exist in the actual world but does at some possible world, yet unlike George, Georgette is not the related to any past, present, or future actual person. The sperm and egg which come together to form Georgette at no time exist in the actual world; they are the products of an alternate history which does not overlap with the actual world (in this respect). Georgette is ungrounded.

So if there can be ungrounded entities then we can see that the following situation is possible. Imagine that there are two possible worlds each which has an extra hydrogen atom which is not related to anything that actually exists. These two extra hydrogen atoms are thus ungrounded. We can furthermore imagine that these two hydrogen atoms are indistinguishable from each other. Now if this is the case then the two possible worlds we are imagining are indistinguishable yet distinct. There is nothing that we could say about the possible world in and of itself that could distinguish between these two worlds. The only way that we could distinguish them is by noting their relative positions to each other in the overall space of possible worlds. Thus Kripke concludes that we cannot talk about individual possible worlds except in relation to the entire structure of modality, or to be more modest, he concludes that there is no a priori consideration that would rule this kind of automorphism out.

An interesting argument, and there is a lot more to say about it but I will come back to that later.

I’m Back, Baby!

Richard Brown 5 Comments

Wow, it’s already September! I have had a very busy summer. I have just recovered from a massive hard drive failure which has cost me all of my photos and three new papers that I have been working on. Damn you Dell!! I know, I know; I should have backed it up. I don’t know what happened. I moved the damn thing to my new house (closer to LaGuardia) and it was working fine (so it didn’t break in the move) then it just stopped working. They tell me that no data can be recovered from it unless I am prepared to pay in excess of $2,000!! So that stuff is as good as gone. I should have been working on that stuff here instead of in a word file!!!! I did print out a hard copy of some of it, but even so I have substantially revised it since then…Oh well, live and learn. I am now the proud owner of a macbook pro and loving it…though I have Pages instead of Word and I am wondering if I should get MS Office. At any rate,  I am planning on posting the rework so I should be posting more often.

On a personal note, I got married! I just returned from my honeymoon (a seven day cruise to Mexico) and am trying to get my life back together again. Between the moving, the computer dying, and the two weeks out of town for the wedding/honeymoon, and the semester starting, I feel like everything is ass over teakettle.

I also recently became the editor of the Higher-Order Theories of Consciousness category over at PhilPapers, which I am loving. This is a fantastic resource that makes research in philosophy the way it should be: fun and exciting. And finally some exciting things are in the works for this year’s Consciousness Online and the official call for papers should be going out in the next week or two.

Zoombie Round-Up

Richard Brown 3 Comments

There has been a bit of discussion of zoombies in the blogosphere of late and I want to keep track of them all so that I can respond to them so I am posting links to them.

1.) Intentional Objects‘ David Gawthorne

Richard Brown’s Zoombies and Shombies

2.) Brain Scam‘s Tony Alterman:

Zombie, Scmombie –Richard Brown’s Efforts to Ressurect Materialism

(and his reply to my reply) Return of the Zombie

3.) And then there’s Richard Chappell’s responses.

In our latest exchange he has acknowledged that the primary and secondary intensions of statements in Q may diverge but seems to think that translating those statements into “semantically neutral” language will still let the argument go through. So, just was “the watery stuff isn’t H2O” comes out true at Twin Earth, “the painful stuff isn’t C-Fiber firing” comes out true at the zombie world. But this move won’t work. Here is what Chalmers has to say about this:

Given the discussion above, one might try generating an anti-materialist argument by simply substituting primary possibility for metaphysical possibility in the original argument.

(1) P&~Q is conceivable

(2) If P&~Q is conceivable, P&~Q is 1-possible

(3) If P&~Q is 1-possible, materialism is false.

_______________

(4) Materialism is false.

On this reading, (1) and (2) are both plausible theses, but (3) is not obviously plausible. The reason is that materialism requires not the 1-impossibility of P&~Q but the 2-impossibility of P&~Q. That is, materialism requires that it could not have been the case that P were true without Q being true. This is a subjunctive claim about ordinary metaphysical possibility, and so invokes 2-impossibility rather than 1-impossibility.

A materialist might reasonably question (3) by holding that even if there is a world W verifying P&~Q, W might be a world with quite different ingredients from our own. For example, it might be that W does not instantiate true microphysical properties (those instantiated in our world), such as mass and charge, but instead instantiates quite different properties: say, pseudo-mass and pseudo-charge, which stand to mass and charge roughly as XYZ stands to H2O. Likewise, it might be that W does not lack true phenomenal properties, but instead lacks quite different properties: say, pseudophenomenal properties. If so, then the possibility of W has no bearing on whether true microphysical properties necessitate true phenomenal properties. And it is the latter that is relevant for materialism.

Still, it may be that the gap between 1-possibility and 2-possibility could be closed. In particular, when a statement S has the same primary intension and secondary intension, then a world will verify S iff it satisfies S, so S will be 1-possible iff it is 2-possible. If P and Q both have primary intensions that coincide with their secondary intensions, then so will P&~Q, and we could run the following argument:

 

(1) P&~Q is conceivable

(2) If P&~Q is conceivable, P&~Q is 1-possible

(3) If P&~Q is 1-possible, P&~Q is 2-possible.

(4) If P&~Q is 2-possible, materialism is false.

_______________

(5) Materialism is false.

Here, the truth of (3) requires that both P and Q have primary and secondary intensions that coincide. (from The 2-D Argument Against Materialism)

The Contestability of (P & ~Q)

Richard Brown 37 Comments

The discussion of Richard Chappell’s post Understanding (Zombie) Conceivability Arguments: Part II over at Philosophy, etc has prompted me to clarify the sense in which I take (P & ~Q) to be contestable and the reasons whyI take  the primary and secondary intensions of statement in Q not to be  identical; as it turns out the two claims are related.

We first start with the primary and secondary intensions of a statement. Let’s take our old standby ‘water is H2O’ and our two ways of considering possible worlds as either actual or counter factual. So, ‘water is H2O’ is true when we consider any possible world as counter factual. This is because  ‘water is H2O’ is an a posteriori necessity. There are no worlds, considered as counter-factual, where water isn’t H2O. But there are possible worlds, which if we consider as actual instead of counter factual, ‘water is H2O’ comes out false. So, take Twin Earth. On Twin Earth ‘water is XYZ’ is true and so when we consider Twin Earth as actual ‘water is H2O’ is false. That is to say that if Twin Earth were the actual world ‘water is not H2O’ would be true (because ‘water is XYZ’ is true there). What we have here is the makings of the distinction between primary and secondary intensions. The primary intension of a statement is given by asking whether it is true or false at possible worlds considered as actual while the secondary intension of a statement is given by asking whether it is true or false at possible worlds considered as counter factual. In effect then the primary intension of a statement is given by some kind of reference fixing description and then we determine whether the statement is true or not by taking a possible world and letting the description fix the reference at that world and the secondary intension of a statement is given by assigning the actual reference of the terms in question and holding that fixed as we vary our counter factual worlds.

Primary and secondary conceivability are then defined in terms of the kind of intension at work. So, take ‘water is not H20’. Chalmers accepts that there is a sense in which this is not conceivable. This is the sense in which we give ‘water’ the reference that it actually has. Then ‘water is not H20’ is equivalent to saying ‘H20 is not H20’ which is a contradiction. But this is to use secondary conceivability. ‘Water is not H2O’ is still primarily conceivable since if we consider Twin Earth as actual it will be true. This is because we assign ‘water’ just the reference fixing description and so to say that water is not H2O is just to say that ‘the stuff picked out in the same way we pick out H2O is not H2O’ which is true at Twin Earth. This captures Kripke’s way of putting it. When we think that we are conceiving of water not being H2O were are really conceiving of a person who is in the same epistemic situation as we are when we pick out H2O but isn’t picking that stuff out (i.e. Twin Earth).  Now, Chalmers continues, the zombie argument relies only on primary conceivability, not secondary conceivability; in fact Chalmers himself accused my zoombie argument of relying on secondary conceivability and not primary conceivability. I think my response at the time isn’t as good as it could be because it focused on P and not Q So let me try and restate the case.

A crucial premise of Chalmers’ argument is that when it comes to pains and other phenomenal properties their primary and secondary intensions are identical. What that means is that the statements in question pick out the same property no matter whether we consider the world as actual or counter factual. This is supposed to capture Kripke’s claim that it is impossible for there to be someone in the same epistemic situation as someone who was in pain and yet for that person not to be in pain (and that it is impossible for there to be a person who was in the same epistemic situation as someone who wasn’t in pain and yet to be in pain. There is no appearance/reality distinction when it comes to pains. So then the upshot here is to try to show that there is a difference between the way ‘water is not H2O’ works and the way ‘pain is not C-fiber firing’ works that preserves Kripke’s general idea but is made precise by the 2-D framework. Kripke’s basic idea was that when we think that some identity is contingent what is really going on is that there is some identity statement involving a description that is contingent but this can’t be the way we explain away the seeming contingency of ‘pain is C-fiber firing’ since there  is no alternate contingent identity involving a description in the case of pains.  This translates into the 2-D framework as the claim that Kripkean a posteriori necessities have a contingent primary intension (i.e. ‘water isn’t  H2O’ comes out true at some possible world considered as actual) but ‘pain isn’t C-fiber firing’, according to physicalist, has a necessary primary intension (there are no worlds considered as actual where this comes out true).

 But what are we to make of this claim? Is it really the case that the primary and secondary intensions of ‘the painful stuff is C-fiber firing’ are  identical? Or another way of asking the question; can the painful stuff fail to be c-fiber firing at some possible world considered as actual even though the painful stuff picks out C-fiber firing here? The answer is arguably yes! This is something that may be surprising but it is arguably shown to be true by empirical results. In particular cases of Dental Fear show that we can pick out mental states as painful which are not pains. Pain Asymboilia also, arguably, shows that we can pick out pain states without picking them out as painful. So the primary intension of ‘pain is not C-fiber firing’ is contingent. There is a possible world, say, where the painful stuff is ABC, where ABC is some distinct property from C-fiber firing, and if that world were actual it would be true that pain is not C-fiber firing. But does that world threaten physicalism? Obviously not. It is not physically identical to our world so is no threat. What needs to be shown is that there is a possible world where you have C-fiber firing and no painful stuff. Is there one? Well, obviously there might be one that is physically distinct from ours (that is, a world that was NOT a micro-physical duplicate of ours, say with different laws of physics there, might have C-fiber firing and no painful stuff and if that world were actual then it would be true that ‘c-fiber firing isn’t pain’) but again this world is not threat to physicalism. But of course (P & ~Q) is supposed to describe a world that IS micro physically identical to ours and which lacks qualitative properties. But this clearly isn’t conceivable on the present account. To see this, compare the water=H2O case. Given that the watery stuff is H2O in the actual world we know that in a world micro-physically identical to ours is a world in which H2O is picked out by ‘the watery stuff’. So too, then, if pain=C-fiber firing in the actual world then we know that any world micro-physically identical to ours is a world in which C-fiber firing is picked out by ‘the painful stuff’. So IF physicalism is true of our world then zombies are not conceivable. But this is not to rely on secondary conceivability. This is to rely of the non-identity of the primary and secondary intensions of ‘pain is not C-fiber firing’ in just the same way as we do in the water/H2O case. This is why my view is in the Kripkean-tradition, and so akin to type B physicalism but not wholly so.

Notice that the upshot of this is that when the dualist says that (P & ~Q) is semantically neutral they are either wrong or do not threaten physicalism. When they go to explicitly fill in the place holder ‘~Q’ with statements like ‘RB is consciously having a pain’ they assign a semantics to terms like ‘pain’ where the primary and secondary intensions are identical, whereas a physicalist like me will assign those terms a semantics just like other natural kind terms (where these intensions are not identical). If you really were to remain neutral on this semantic issue the conceivability of (P & ~Q) is no threat to physicalism (since you need the premise (PI=SI) to make the argument go through). So to get the zombie argument off the ground you must assume a certain semantics for the terms in Q, just as to get the zoombie argument off the ground you have to assume a certain semantics for NP (namely one that stipulates that there are no qualitative properties in NP. This nicely mirrors the zombie argument where the dualist has to stipulate that there are no physical properties in Q). It may be the case that this is more obvious in the zoombie case but it still helps to expose the same flaw in teh zombie argument.

Happy Birthday!!

Richard Brown 1 Comment

It has now officially been two years since I started Philosophy Sucks! I have had 300 posts, 1,714 comments, and 75,000 hits. Thanks to everyone who has stopped by and especially those who have stayed to engage in discussion, most of which has been challenging, thought provoking, and fun!

Ut vos es Bellator Victus Mortuus Tempus Fugit

Richard Brown 22 Comments

Yes, indeed, time does flee when you are fighting the living dead!

It has been a year since the original zombies wars broke out around here, which led to all of the zoombie and shombie action. I was recently looking over some of these old posts and the debate between Richard Chappell and myself as I get ready to do the re-write for the Journal of Consciousness Studies (where this paper and others from Consciousness Online are slated to appear).

The basic claim that Chappell makes is that the zoombie argument is not really a parody of the zombie argument. The basic reason for this is his claim that there is an important dis-analogy between the zombie argument and the zoombie argument. This dis-analogy arises because the completed micro-physical description of the world contains qualitative facts, if it does at all, only implicitly. This opens up the conceptual gap between the physical and the qualitative in a way that leaves the physicalist susceptible to the conceivability argument.

The dualist on the other had think that the qualitative facts are primitive and must be added to a completed micro-physics explicitly. Since the qualitative is not reducible to any base facts that are not themselves qualitative the dualist is not susceptible to conceivability arguments in the same way that the physicalist is. Another way to make the point, and a way that I think Richard prefers to make the point, is in terms of asking what follows from a completed micro-physics. The original zombie argument tries to show that the qualitative facts do not follow from the complete physical facts. The zoombie argument doesn’t work this way. We do no build up the non-physical facts and then ask whether or not the qualitative facts follow from them. This is because the dualist claims that the qualitative facts have to added explicitly. There is no issue of whether the follow from any other kind of fact since they are taken to be primitive.

Now, clearly, there is this dis-analogy between the two arguments. But does it follow, as Chappell alleged, that this dis-analogy makes it “daft” to mount a conceivability argument against the dualist? Or, another charge from Chappell, does this dis-analogy make the zoombie argument a bad parody of the original zombie argument (actually he said that it was irrational to think so, but let’s not dredge that stuff up) or show that I have misunderstood the original zombie argument (yet a further gem from Chappell)?

To start with the first question, the answer is obviously ‘no’.  A conceivability argument just starts from the claim that something is conceivable and reasons to that thing’s being possible. If something follows from that possibility then fine.If not fine. In this case it is conceivable that NP, being the complete set of non-physical facts about the actual world, obtain without any qualitative properties included in NP. If this is conceivable then it is possible and if it is possible dualism is false. Is this a bad parody of the zombie argument? Only if you think a parody must be identical in every respect to the original. The point is that zoombie argument is like the zombie argument in the right respects; in particular in asserting the conceivability of p and reasoning from there. The fact that what is at issue in the zoombie argument is not “what follows from what” but is rather “what must be included in the complete non-physical description of a world that is non-physically identical to the actual world?” is irrelevant. All that maters is that the possibility of zoombies shows that qualitative properties are not non-physical properties.  Finally, does this show that the proponent of the zoombie argument misunderstands the zombie argument? I don’t think so. The zombie proponent holds that zombies are conceivable because there is a gap between our physical/functional concepts and our qualitative concepts; or in other words that there is no reason as of now to think that qualitative properties are physical properties. The physicalist like me will claim that this gap will be abolished as we reach the ideal limit and so zombies are prima facie conceivable but not ideally conceivable. The zoombie proponent holds that zoombies are conceivable because there is no reason to think that qualitative properties are non-physical and so no reason to think that they must be included in a complete description of a non-physical duplicate of our world. Clearly both of these (zombies and zoombies) can’t be ideally conceivable so a priori arguments won’t help us decide between theories of consciousness.

Two Questions Regarding Hume’s Account of Relations of Ideas

Richard Brown 8 Comments

I have always had two interpretational questions about Hume’s account of relations of ideas. These issues come up in my into class all the time and I am constantly foiled in my attempt to locate an exact answer either in Hume’s corpus or in the secondary literature. Maybe someone else knows where I should look…

The first question is about Hume’s account of our ideas of numbers. Locke is very clear that the ideas of numbers are what he calls modes. We start with our simple idea of a unity and then form the complex ideas of 2, 3, 4, 5…etc by combing this idea with itself. So the idea of the number three is a complex idea composed of three of the simple ideas of a unity (‘III’). Does Hume accept this account of our ideas of numbers? Or does he have some other account of them? I somehow started to think that he had a set-theoretic accoount but I may be turning him into a logical positivist…

The second question is about the possibility of change in relations of ideas. If the mathematical truths are simply definitional truths defined in such a way as to exclude contradictions then it seems that it should be possible for us to change these definitional relations. Is this what Hume actually thinks or am I turning him into Quine? If he doesn’t think this, then how do the relations get set? And what makes it the case that they can’t be changed?

Does anyone know where in Hume’s work he is more explicit about these issues than he is in the Enquiry? Or the name of a good secondary source that addresses these issues?