Friday, 1 November 2013

On Kripke's "Identity and Necessity"

In this blog post, I will like to consider the implications (if any) of the intelligibility of the following scenario for Kripke’s claim that identity statements involving rigid designators are necessarily true.  Suppose that the Messenger space probe were to send back pictures revealing that “Venus” is actually a binary planetary system—two planets orbiting around a common gravitational midpoint.  Moreover, as luck would have it, when viewed from the northern hemisphere on any given morning, one of the twin-planets (let’s call it V1) would stand perfectly in front of the other (let’s call the second V2), so that only V1 could be seen.  But in the evening, the planets would switch positions so that V2 would obscure V1 such that only the former would be visible.  The upshot of this is that the heavenly body that was visible (from Greece or Italy) in the morning and that was “tagged” with the name Phosphorus would actually be distinct from the heavenly body seen in the evening and which was “tagged” with the name Hesperus.  Now such a scenario is clearly fictional and may, given what we know about the laws of planetary motion, even be physically impossible.  However, it certainly strikes me as intelligible and I wish to consider what follows (in anything) from the simple fact that it is intelligible. 

Suppose, after considering the above scenario, I were to say something to the effect: “If Phosphorus and Hesperus turned out to be different heavenly bodies, then Kripke would be left without a cogent illustration for his identity thesis.”  Presumably, Kripke would hold that it is impossible for the antecedent of the above counterfactual statement to be true.  Moreover, the kind of impossibility that Kripke would have in mind would be logical and not merely physical.  In brief, Kripke holds that both names, Phosphorus and Hesperus, are rigid designators.  Even so, this does not impugn the intelligibility of anything said thus far since we do often employ counterfactuals in which the antecedent is logically impossible (such as in reductio arguments). 

In Kripke’s version of the Phosphorus-Hesperus scenario, the gravitational influence of a passing comet causes Venus to be moved from its normal position and Mars to take its place.  He then suggests that under such circumstances, the thing to say would not be that Phosphorus is not Hesperus (i.e., the two names designate different heavenly bodies), but that Phosphorus has been moved so that it no longer occupies its normal position in the night sky.  Now, it does not seem to me that this reply works in the case as I have described it.  This is because in the binary-planet case we are not simply imagining a case in which another heavenly body, say Mars, is occupying the position we once thought was occupied by Venus.  Rather, we are imagining a case in which what we took to be a single object, Venus, actually turns out to be two distinct objects.  What would Kripke say in response to the above example?

In attempting to answer this question it may be helpful to consider the following question:  “In the aforementioned counterfactual, which of the two heavenly bodies, V1 or V2, should we identify with Venus?”  Given the parity between the two cases (we can suppose that in astronomical observations V1 was identified as Venus just as often as V2) it would seem arbitrary to say that one, and not the other, ought to be identified with Venus.  Since both could not be Venus (personally I’m not convinced of this, but it seems like the position that Kripke would hold) then the only available option would be to say that neither heavenly bodies are to be identified with Venus.  If this is right, then the proper name “Venus” would cease to refer to anything.  (This conclusion seems to jive with Russell’s requirement for successful reference.)

Let us suppose that in the binary-planet example, the proper name “Venus” ceases to refer.  What about the status of the proper names “Phosphorus” and “Hesperus”?  Stated in the terminology of possible worlds, a rigid designator is defined as one that designates the same thing in all possible worlds in which it designates.  Suppose that the names “Phosphorus” and “Hesperus” are both rigid designators, and that “Phosphorus is Hesperus.”  (Strictly speaking, there is no need for imagination here, since this is what Kripke takes to be the case in the actual world.)  Since they are rigid, they each designate the same thing in all possible worlds in which they both designate. That is to say that “Phosphorus is Hesperus” is true in all possible worlds in which “Phosphorus” and “Hesperus” both designate, and hence that “Phosphorus exists & Hesperus exists → Phosphorus = Hesperus” is true in all possible worlds, and is therefore necessarily true.  This, according to Kripke, is all we mean when we say that “Phosphorus = Hesperus” is a necessary truth. 

In my binary-planet example, the antecedent of the conditional (Phosphorus exists & Hesperus exists) is true and the consequent (Phosphorus = Hesperus) is false.  It therefore appears to represent a counterexample to Kripke’s claim that Hesperus and Phosphorus are rigid designators.  Now, I have already conceded that the situation described in the antecedent may be impossible.  Moreover, perhaps Kripke should be interpreted as allowing that even a rigid designator may designate different things in impossible worlds.  If so, then perhaps there is also an expectation on Kripke’s part, that we restrict ourselves to counterfactuals with possible antecedents whenever we unpack the definition of rigid designator in terms of possible worlds. 

However, on pain of circularity, such a move seems illegitimate at this stage.  Kripke is supposed to be offering us an argument for necessity of identity from his definition of rigid designation.  But if Kripke’s definition of rigid designation already required us to omit impossible worlds, it would be to argue for the conclusion that a certain identity is necessary from the starting assumption that the identity failing to hold is impossible.  But that would be to settle before hand the position one wished to achieve by argument.  If Kripke’s argument is to be cogent, it must be possible to begin with the initial supposition that the antecedent it possible.  Then if the argument is successful, we would be led to reject our initial supposition.  But once we grant that the antecedent is possible (i.e., that Phosphorus is not Hesperus), it is not clear that any argument can be given to show that the possibility that has been assumed for the sake of argument should be rejected.  In sum, without some independent argument showing that the binary-planet counterfactual, in which the names “Phosphorus” and “Hesperus” designate different objects, is impossible, it is not clear that Kripke’s argument that the names are rigid designators gets off the ground.

14 comments:

mao said...

This really does seem to show that rigid designators don't do very well in accommodating changes in what we know about the singular objects. Also it seems to require a very "decided" view on what constitutes the identity of an object (e.g. Phosphorus). Just not very intuitive imo...
Anyway, this is a great thought-provoking post!

Philip Cartwright said...

I don't think Kripke could complain about the impossibility of your scenario, since his own scenario (involving H2O and XYZ) has the unfortunate consequence of destroying the periodic table and the atomistic theory which underpins it. Far from proving that "water=H20" his example fatally undermines the very concept of "H" and "O".

And, of course, Kripke's argument is completely circular. He says that if we discovered XYZ we would have to conclude that it wasn't water. But we'd only have to conclude that if we were already committed to the notion of rigid designators. Otherwise we could simply decide to say "there are two forms of water: H2O and XYZ".

Tristan Haze said...

I find this post confusing, but I think it does draw attention to the need to make sense of talk along the lines of 'What would have happened if Hesperus had turned out to be distinct from Phosphorus'. How such talk works is a delicate matter not settled by Kripke, and how (or whether) it can be squared with some of Kripke's main claims, e.g. that names are rigid designators, and that true identity statements involving names are necessary, is a difficult matter.

I want to focus on this paragraph near the end of your post:

'In my binary-planet example, the antecedent of the conditional (Phosphorus exists & Hesperus exists) is true and the consequent (Phosphorus = Hesperus) is false. It therefore appears to represent a counterexample to Kripke’s claim that Hesperus and Phosphorus are rigid designators. Now, I have already conceded that the situation described in the antecedent may be impossible. Moreover, perhaps Kripke should be interpreted as allowing that even a rigid designator may designate different things in impossible worlds. If so, then perhaps there is also an expectation on Kripke’s part, that we restrict ourselves to counterfactuals with possible antecedents whenever we unpack the definition of rigid designator in terms of possible worlds.'

Firstly, and I'm not saying you've failed to do this, but it's important to distinguish the question at issue here - whether 'Hesperus' and 'Phosphorus' are rigid designators, and whether you have a counterexample to this claim - from the question of whether Kripke has a non-circular argument for the necessity of identity. He may not, and yet names (like 'Hesperus' and 'Phosphorus') may still be rigid designators - and furthermore, true identities like 'Hesperus is Phosphorus' may still be necessary.

I am puzzled by your claim that the binary-planet example is an apparent counterexample to the claim:

(A) that names like 'H' and 'P' are rigid designators

especially given that you concede that a situation in which Hesperus is distinct from Phosphorus may be impossible in a strong sense (e.g. logical or metaphysical).

Consider the last sentence of the paragraph I am concentrating on:

'If so, then perhaps there is also an expectation on Kripke’s part, that we restrict ourselves to counterfactuals with possible antecedents whenever we unpack the definition of rigid designator in terms of possible worlds.'

I'm not sure what to make of this. Here's an unpacking of the definition of 'rigid designator' in terms of possible worlds:

A term is a rigid designator iff it designates the same object in all possible worlds in which that object exists.

This doesn't on the face of it involve any counterfactuals, and so it's unclear why Kripke would expect us to 'restrict ourselves' to counterfactuals with possible antecedents. We don't seem to need any counterfactuals at all.

And since Kripke's definition of 'rigid designator' *is* given in terms of *possible* worlds, I don't see how there's a counterexample here. It seems very clear that the claim that 'Hesperus' and 'Phosphorus' are rigid designators in this (the intended) sense *is* compatible with a rigid designator designating something other than what it actually designates in some *impossible* situation.

So, I don't think the paragraph I have quoted shows that there is a counterexample to the claim (A). Furthermore, the paragraph following it is about a different thing, namely whether Kripke has a non-circular argument from one thesis to another. Accordingly, I don't think any counterexample to (A) has been given here. Your thoughts?

AVERY ARCHER said...

Great catch, Tristan! I think your criticism is on point. What I should have said (in the passage you cite) is that the binary-planet example is a counterexample to the following conditional:

(B) Phosphorus exists & Hesperus exists → Phosphorus = Hesperus

That the binary-planet example is a counterexample to (B) is straightforwardly true since it describes a situation in which the antecedent of the conditional is true, and the consequent is false. However, it does not follow from this that the terms ‘Hesperus’ and ‘Phosphorus’ are not rigid. This is because the possible world described in the binary-planet example (assuming that there is such a possible world), is not one in which the object designated by the terms ‘Hesperus’ and ‘Phosphorus’ (in the actual world) exists. Hence, given the definition of a rigid designator as a term that designates the same object in every possible world in which that object exists, the possible world corresponding to the binary planet example (i.e., one in which the object, Venus, does not exist) poses no challenge to the claim that the terms ‘Hesperus’ and ‘Phosphorus’ are rigid. The upshot, as you point out, is that the binary-planet example fails to constitute a counterexample to the following claim:

(A) that names like 'H' and 'P' are rigid designators.

(I recognise that the way I just sketched the worry differs slightly from yours, but I think it is getting at the same basic point.) I haven’t had time to work through the implications of this objection for the various points adumbrated in this post. As you rightly observe, there are some difficult questions relating to the nature of proper names lurking in the background. However, the basic point of your objection strikes me as a good one.

Thank you for the helpful feedback.

Tristan Haze said...

Thanks, this is helpful. I agree that there is reason to think that (B) comes out false on a certain, natural-enough reading or class of readings - namely, to invoke a broadly Lewisian framework, where the "relevant A-worlds" which are required to be C-worlds in order for the counterfactual to be true include worlds where Hesperus is distinct from Phosphorus. (For Kripkean reasons, I think such worlds are metaphysically impossible, but contra Lewis I think counterfactuals can non-vacuously involve these.)

It is perhaps worth noting, however, that since the counterfactual is a flexible device (as Lewis held, but even moreso, since counterpossible scenarios/worlds can be made relevant on some readings), the sentence (B) could be given another reading, where the relevant A-worlds are more similar to ours, and all metaphysically possible. On such a reading, I think (B) comes out true.

(This ambiguity makes the claim that the binary-planet example 'straightforwardly' constitutes a counterexample to (B) seem a little strong perhaps. Still, I agree that given a certain reading of (B), which seems quite natural to me but does make trouble for some prominent theories of counterfactuals, e.g. Lewis's, the binary-planet situation is a counterexample.)

AVERY ARCHER said...

After reading your most recent comments, I am not quite sure that we are on the same page regarding the rhetorical structure of my argument (though I am nevertheless inclined to agree with the main thrust of your criticism). Just to be clear, the counterfactual to which I refer in the passage you cite is not (B). Of course, Kripke does think that (B) is true in all possible worlds. However, that does not mean that (B) is itself a modal claim. The difference is like the difference between saying

(C): “Necessarily, 1 + 1 = 2”

and saying

(D): “1 + 1 = 2”.

Of course, we do think that (D) is necessarily true. But that does not make (D) a modal claim. Rather, it is a non-modal claim that happens to be true in all possible worlds. Likewise, I take (B) be a straightforward material conditional, albeit one that Kripke takes to be true in all possible worlds. Consequently, when I refer to a counterfactual in the passage you cite, what I actually have in mind is the following claim:

(E): “If Phosphorus and Hesperus turned out to be different heavenly bodies, then Kripke would be left without a cogent illustration for his identity thesis.”

The question I then go on to consider is whether or not there is a possible world corresponding with the antecedent of (E). Now (if I may briefly lay my cards on the table), it seems to me that antecedent of (E) describes something intelligible (which is what my binary-planet example is meant to illustrate), and that its intelligibility is sufficient to establish that there is a possible world corresponding with the antecedent of (E). However, since it would be begging the question against Kripke to simply assume that this is so, I frame my argument as a dilemma. Kripke can either affirm that there is a possible world corresponding with the antecedent of (E), or he can deny that there is. I then attempt to argue that there are unfavourable consequences for Kripke either way.

AVERY ARCHER said...

First off, if there is a possible world corresponding with the antecedent of (E), then such a possible world would represent a counterexample to (B). Notice, we are here simply assuming that there is such a possible world in order to instantiate one horn of a potential dilemma. Of course, I was proceeding under the assumption that this would not be the horn on which Kripke would fall given his characterisation of rigid terms. In short, my claim that the binary-planet example is a straightforward counterexample to (B) is predicated on the assumption that the binary-planet world is among the set of possible worlds (an assumption that is only being made in order to satisfy one horn of a dilemma).

With this first horn out of the way, I then turn my attention to the second horn, which is to assume that there are no possible worlds corresponding with the antecedent of (E). My complaint about this second horn is that it is not one that Kripke seems entitled to on pain of circularity or being question begging. Given that he is supposed to be offering an argument in favour of the thesis that identity statements involving rigid designators are true in all possible worlds, it seemed to me that it would be question begging to exclude the binary-planet world from the set of possible worlds based on the thesis that rigid designators (like the terms 'Hesperus' and 'Phosphorus') must designate the same object in all possible worlds in which they designate. This is because the claim that rigid designators (like the terms 'Hesperus' and 'Phosphorus') must designate the same object in all possible worlds is part of what is supposed to be at issue, in the context of making sense of (E) in light of the intelligibility of the binary planet example. This then leads me to conclude not that 'Hesperus' and 'Phosphorus' are not rigid designators, but that there is a need for some independent grounds for thinking that they are, in light of the intelligibility of the binary-planet example.

Now, I agree that your observations present a challenge to a crucial move I make in my argument. However, I hope it is at least a bit clearer how the argument is supposed to go.

Richard Chappell said...

Hi Avery, aren't you conflating Hesperus with what 'Hesperus' denotes in your binary world case?

Kripke would say there are three ways of elaborating upon your case:

(1) Stipulate that neither of the two planets is (identical to) the actual object Venus, and hence it's false to say that Hesperus exists or that Phosphorus exists in the counterfactual scenario (though of course there are distinct planets that the twin-Earthlings talk about using the terms 'Hesperus' and 'Phosphorus')

(2) Stipulate that Venus (=Hesperus = Phosphorus) is visible in the evening, such that the twin-Earthlings use 'Phosphorus' to denote the new planet (which is not actually Phosphorus) visible in the morning.

(3) Stipulate that Venus (=Hesperus = Phosphorus) is the planet visible in the morning, such that the twin-Earthlings use 'Hesperus' to denote that new planet (not Hesperus) which is visible in the evening.

In none of these explications do Hesperus and Phosphorus exist as distinct entities. (For how could they? That would be for a single object, Venus, to be distinct from itself.)

Jason Zarri said...

Hi Avery,

I had thoughts similar to Richard's. Also, I wonder what you think about this:

Distinctness is correlative to identity, so if identity is contingent then distinctness is too. So, what would a scenario opposite to yours be like? Would there be possible words where Jupiter and Saturn are the same planet? If counterpart theory is true that makes sense; otherwise, things are less clear.

AVERY ARCHER said...

Richard,
I take myself to be making a claim about the ordinary proper names ‘Hesperus’ and ‘Phosphorus’. I do not take myself to be making a claim about the object the proper names designate. Inter alia, I am questioning whether Kripke has provided us with cogent (i.e., non-question-begging) grounds for thinking that the ordinary proper names ‘Hesperus’ and ‘Phosphorus’ are rigid designators.

In describing these terms as rigid designators, I take Kripke to be saying that the terms ‘Hesperus’ and ‘Phosphorus’ refer to Venus not only in this world, but in all possible worlds. (On this much, we seem to agree.) However, in my post, I have been urging that this conclusion does not come for free. Insofar as Kripke purports to be making a claim about ordinary proper names (as opposed to some technical terms he has invented and is therefore free to operationalize as he chooses), then we (as inhabitants of Earth and users of language) do seem to have some stake in the matter. He owes us an explanation of why we should believe that the terms that we all use behave in the way he says that they do. Whether or not my argument succeeds (and in the light of Tristan’s comments, I am beginning to have my doubts), this is how I would describe its intent.

If Kripke’s claims about ordinary proper names is to be factive, it must match certain fundamental features of ordinary usage. Suppose I were to utter the following counterfactual:

(F) If Hesperus and Phosphorous turned out to be different astronomical bodies, then Mars would not exist.

I think there is an intuitive sense in which we would say that (F) is false. If we were to attempt to make good on this intuition in terms of a possible world analysis, we would have to conceive of a possible world in which the antecedent of the conditional is true, and the consequent is false. (Sufficiently described, the “possible world” described in the binary-planet example would be just such a world.) Hence, insofar as we seem to think that it is possible to assign a truth-value of false to (F), we seem to have some motivation for thinking that there is a possible world that makes the antecedent of (F) true. Since, according to Kripke’s account, the antecedent of (F) is false in all possible worlds, one very natural way of preserving the intuition that (F) may be false is lost on Kripke’s account.

AVERY ARCHER said...

(Reply to Richard Continued)

I think there is an intuitive sense in which we would say that (F) is false. If we were to attempt to make good on this intuition in terms of a possible world analysis, we would have to conceive of a possible world in which the antecedent of the conditional is true, and the consequent is false. (Sufficiently described, the “possible world” described in the binary-planet example would be just such a world.) Hence, insofar as we seem to think that it is possible to assign a truth-value of false to (F), we seem to have some motivation for thinking that there is a possible world that makes the antecedent of (F) true. Since, according to Kripke’s account, the antecedent of (F) is false in all possible worlds, one very natural way of preserving the intuition that (F) may be false is lost on Kripke’s account.

Of course, this is not even close to being the final word on the matter. In assessing what kind of conception of proper names we should adopt, we must weigh the costs and benefits of various alternative conceptions against each other. For example, there seems to be an intuitive sense in which the following counterfactual is also false:

(G) If ‘2 + 1= 6’ were true, then mars would cease to exist.

But clearly, ‘2 + 1 = 6’ is necessarily false. So if we happen to think that (G) could be false, and if we also think that (G) can be false only if there is some possible world that makes its antecedent true and consequent false, then so much for our ordinary intuitions.

But the above dismissal of our ordinary intuitions seems to move too fast for me. There seems to be a sense in which we can make the antecedent of (G) false, a sense that is compatible with the claim that ‘2 + 1 = 6’ is false in all possible worlds. We can imagine a possible world in which numeric symbols ‘2’, ‘1’ and ‘6’ pick out different numbers from the ones they do in the actual world. Here, we are imagining a case in which the meaning (in some intuitive sense of the word) of the symbols have changed. This seems to go hand in hand with your point that we have ceased to use the terms in the same way that Earthlings do, and are now using the terms in the way that twin-Earthlings do. And this, of course, is no challenge to Kripke since he grants that the inhabitants of other worlds may use the same words that we do in different ways. Why not simply say the same thing about the terms ‘Hesperus’ and ‘Phosphorus’ as they appear in (F).

AVERY ARCHER said...

(Reply to Richard Continued)

However, the above line of thought seems to overlook what some would consider an important disanalogy between the antecedents of (F) and (G). The only way to make the antecedent of (G) true would be to alter one or more of the intentional objects picked out by the numeric symbols ‘2’, ‘1’, and ‘6’. In other words, when we imagine a possible world that makes ‘2’, ‘1’, and ‘6’ true, we are imagining a world in which any inhabitants of twin-Earth who has an adequate conceptual grasp of ‘2’, ‘1’ and ‘6’ are ipso facto in a different mental state when they think of ‘2’, ‘1’ or ‘6’, than the mental state of inhabitants of Earth who have an adequate conceptual grasp of ‘2’, ‘1’, and ‘6’. The notion of “adequate conceptual grasp” is in need of serious unpacking. But the basic idea I have in mind has to do with the intention of the agent(s) who baptised the terms. In short, an inhabitant of a possible world that makes the antecedent of (G) true must be in a different mental state (i.e., have a different intentional object before her mind) to an inhabitant of Earth.

The same isn’t true of (F). The terms ‘Hesperus’ and ‘Phosphorus’ may have exactly the same intentional object in (F) as they did when the Greek astronomers first baptised the term (I am here assuming that the Greek astronomers in question did not know that Hesperus and Phosphorus were in fact the same object—to wit, the object that we, today, call ‘Venus’). In the case of both the Greeks and the person who utters (F), the intentional object of the term ‘Hesperus’ (i.e., the first or brightest heavenly body visible in the evening), and the intentional object of the term ‘Phosphorus’ (i.e., the last or brightest heavenly body visible in the morning) may be the same.

The question then becomes do we (or must we) individuate proper names by their extension (such that, to change the object a proper name designates just is to switch to a different proper name), or can we (at least in certain cases) individuate proper names by their intentions (such that, we can change the object of a proper name without switching to a different proper name, so long as the intentional description remains the same). The more I think about it, the more I like Kripke’s proposal. That’s unsurprising because there is so much to like about it. However, it will help me further appreciate the attractions of his view to hear more about why it would be a bad idea to individuate certain kinds of proper names in terms of their intentional objects. This comports with the conclusion of my post, which is not that Kripke is mistaken, but that more needs to be said to convert the unconverted.

P.S.: I plan to also respond to Jason’s comments. (Thanks for joining the conversation, Jason!) However, I have two stacks of papers and a looming grade-submission deadline demanding my immediate attention.

Jason Zarri said...

No problem, I can understand. I look forward to your response.

AVERY ARCHER said...

Jason,
I believe that the beginnings of an answer to your question is already contained in my response to Richard. I am not committed to the claim that identity is contingent. This is because I am not making a metaphysical claim at all. Rather, I am making a claim about the behaviour of a certain class of words (i.e., ordinary proper names). There therefore seems to be a broad sense in which Lewis’ work on convention is more relevant to the questions I take up in my post than his work on counterfactuals. That said, I would be quite curious to hear more about why you think that counterpart theory allows for the possibility that Jupiter and Saturn are the same planet.

By my lights, the salient question is this: could the terms ‘Jupiter’ and ‘Saturn’ both designate the same object? Consider the following counterfactual claim:

(H): If Jupiter and Saturn were the same planet, then Mars would cease to exist.

If we take the framework I introduced in my response to Richard seriously, then the question becomes is there a possible world that makes the antecedent of (H) true, and which does not require that we alter the intentional content with which the terms ‘Jupiter’ and ‘Saturn’ were first baptised? My inclination is to think not. It seems to me that the intentional content attached to the terms ‘Jupiter’ and ‘Saturn’ at their baptism entails that they are mutually exclusive of each other. If this is right, then (H) is more like (G) than it is like (F) in the relevant respect.