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.

The 46th International Philosopher's Carnival

A NARROW CROSS-SECTION OF PHILOSOPHY
FROM ACROSS THE WEB

A Philosophy (Pseudo) Conference
Hosted by the Space of Reasons
Monday, April 23rd, 2007

Welcome to the 46^th instalment of the Philosopher's Carnival, which takes the form or a philosophy pseudo-conference, showcasing a narrow cross-section of philosophy on the web. A special thank you goes out to Professor Daniel Dennett for his submission, which raises important questions with regards to what constitutes a worthwhile philosophical research program. In the three "presentations" immediately following the "keynote address" (under the heading of METAPHILOSOPHY), two philosophy students and one non-philosopher share their views on the status and role of philosophical theories. We then turn to the heart and soul of the Carnival which features a number of “presentations” that fall under the heading of Language, Epistemology, Metaphysics and Mind (or LEMMINGS). Finally, we top it all off with a sprinkling of ETHICS and a brief IN DISCUSSION section. Enjoy!

KEYNOTE ADDRESS

Topic: Higher Order Truths about Chmess
Presenter: Daniel C. Dennett


METAPHILOSOPHY

Topic: Theory and Philosophy
Presenter: Peter Schombe

Topic: Thoughts on Theories
Presenter: Adrian Tan

Topic: The Role of Philosophy
Presenter: Quincy Faircloth


LEMMINGS

Topic: Evidence and Armchair Access.
Presenter:Clayton Littlejohn

Topic: A Problem for Externalist?
Presenter: Michael Horton

Topic: Jackson's Mary and Complete Physical Knowledge
Presenter: Ignacio Prado

Topic: Luminosity, Coziness and Borderline Cases
Presenter: Aidan McGlynn

Topic: The Modified Turing Test
Presenter: Christopher Anderson

Topic: Are Causal Facts Observable?
Presenter: Gualtiero Piccinini

Topic: Lewis on Non-Trivial Counterpossibles
Presenter: Joe Salerno

Topic: Infinite Regress and Geisler on Infinite Regress
Presenter: Bryan Norwood

Topic: Libertarian Compatibilism
Presenter: Kenny Pearce

Topic: Arguments for Compatibilism
Presenter: Jeremy Pierce


ETHICS

Topic: Second-Person Reasons and Causally Amorphous Aid.
Presenter: Brian Berkey

Topic: The necessary-condition interpretation of the subjectivity of welfare
Presenter: Michele Loi

Topic: Thom Brooks on “Is Bradley a Retributivist”
Presenter: Thom Brooks


IN DISCUSSION

Our Carnival's discussion section features a brief exchange between Jeremy Stangroom and Richard Chappell on what constitutes "brainwashing"?

Causal vs. Rational Explanations (Part 2)

In my previous post on this topic, I briefly touched on a common reply to Lehrer’s Gypsy-Lawyer type cases—namely, the suggestion that a belief need not have its ‘causal origin’ in a reliable process, so long as it is ‘causally sustained’ by such a process. On this more moderate view, Tom’s belief can be seen as ‘causally sustained’ by the discovery of the spyware in the sense that if Tom were to give up his fanatical religious views, he would still continue to believe that ‘the NSA is spying on US citizens’ (henceforth ‘SPY’).

In this post I will examine one way of unpacking the concept of what it means for a belief to be causally sustained by some bit of evidence (whether propositionally or non-propositionally understood)—namely, Marshall Swain’s notion of a counterfactual cause. We may define a counterfactual in terms of possible world semantics. Following Lewis let us say that the truth of the statement A > B consists in the fact that, among possible worlds where A holds, there is at least one world where B holds and which is more similar to our world than any world where A holds but B does not. (For the sake of simplicity, I will just speak in terms of the closest possible world.)

Roughly, the idea is that a belief, B, is based on a reason, R, if R is either the non-deviant cause or counterfactual cause of B. R counterfactually causes B if in the closest possible world where the actual cause, C, is missing, R causes B. Thus, causal theorists maintain that the underlying intuition behind the causal theory can be preserved by insisting that if the justifying evidence does not actually cause belief, it must counterfactually cause belief. Applied to the ‘Fanatical Tom’ counterexample, we may say that in closest possible world in which Tom’s belief that SPY is not caused by his fanatical religious views, it is caused by the spyware evidence. Thus, the spyware evidence is the counterfactual cause of Tom’s belief.

We may add one important restriction to the idea of a counterfactual cause. First, it is crucially important that we limit ourselves the closest possible world. Otherwise, the notion of a counterfactual cause would become much too broad; allowing beliefs to be based on reasons when it is obvious that they are not so based in the actual world. (Presumably, it is such considerations that prompt Swain to limit the application of the concept of a counterfactual cause to the reason next in line to the reason that actually causes the belief.) Thus, Swain’s view may be put as follows:

S1: Subject S bases her belief that p on R IFF S’s having R is either (i) a cause of S’s believing that p in the actual world, or (ii) S’s having R is a counterfactual cause, such that R causes S’s believing that p in the closest possible world in which the actual cause, C, is absent.

If we accept the restriction on what constitutes a counterfactual cause imposed by S1, we seem able to adjust the ‘Fanatical Tom’ counterexample so that the spyware is no longer the counterfactual cause of Tom’s belief. For example, we could imagine that Tom is not only a religious fanatic, but that he is also a member and ardent believer in a webring devoted to conspiracy theories. Thus, holding all other parts of the ‘Fanatical Tom’ counterexample constant, we may stipulate that in addition to his fanatical religious views, he has also read about the NSA’s surveillance activities on the internet, before actually discovering the spyware evidence in Fred’s home. On this revised version of ‘Fanatical Tom’ case the closest possible world in which Tom’s belief is not based on his religious views, it would actually be based on his reading the conspiracy theory webring. Thus, according to S1, the spyware no longer constitutes a counterfactual cause for Tom’s believing that SPY. Since in the re-described case, Tom’s belief seems no less justified than it is the original case, the introduction of counterfactual causes fails to resolve the present difficulty.

But perhaps Swain is being unnecessarily conservative when he restricts the notion of a counterfactual cause to the closest possible world. Perhaps it would be sufficient to restrict ourselves to nearby worlds in which Tom both finds the spyware and believes SPY. On the present proposal, we might be able to rescue Swain’s theory by widening the scope of what counts as counterfactual cause to all worlds sufficiently close to the actual world. Thus modified, Swain’s counterfactual cause may be summarised thus:

S2: Subject S bases her belief that p on R IFF S’s having R is either (i) a cause of S’s believing that p in the actual world, or (ii) for some set, C, of possible counterfactual causes of S’s belief that p, R is a member of C.

On S2, R need not be the next in line to the actual cause, C, such that in the closest possible world in which C is not the actual cause R causes S’s belief that p. It is sufficient that R be the cause of S’s belief that p in some nearby world. As with most talk of nearby worlds, there is an obvious difficulty regarding how one delineates which worlds count as nearby and which do not. Or, to put the problem differently, how do we determine (in a non-arbitrary manner) which reasons, out of the maximal set of possible reasons, ought to qualify as counterfactual reasons.

One plausible criterion would be to restrict ourselves to reasons that are occurrent to the subject in the actual world. Thus, we may add to S2 the clause that for some possible reason, R, to be included in the set, C, of possible counterfactual causes, it must be occurrent to S in the actual world. Assuming that this provides a plausible and sufficient restriction on which worlds ought to count as nearby, we seem to have a working definition of a counterfactual cause. S2 provides us with a reply to the ‘Fanatical Tom’ example since it allows both the conspiracy webring and the spyware (along with any other potential reasons occurrent to Tom in the actual world) to be considered a counterfactual cause of his belief.

Unfortunately, this still is not sufficient for rescuing the notion of a counterfactual cause. An even more decisive objection to the Swainesque reply to the ‘Fanatical Tom’ problem is that it allows the spyware to be the counterfactual cause of Tom’s belief even when it seems obvious that it is not justified. For example, suppose that Tom’s religion teaches him to reject all evidential relations and that only beliefs based upon ‘faith’ are justified. However, Tom realises that his neighbour, Fred, still buys into ‘the whole evidence thing’ and appeals to the spyware solely for the purpose of converting Fred. The idea is that Tom does not see the spyware as genuine evidence himself. In such a case, Tom’s belief would clearly be unjustified. However, in such a scenario, the spyware would still be the counterfactual cause of Tom’s belief by Swain’s lights. In the closest possible world in which Tom no longer has his religious beliefs, and in which he still believed SPY, his belief would be based on the spyware. This is because in that world, the religious belief would no longer prevent Tom from recognising the spyware as a reason for believing SPY. Thus, Swain’s notion of a counterfactual cause allows the spyware to causally sustain a belief even when it is clear that the belief is not justified.

I believe the above analysis suggests that all attempts to cash out the idea of a belief being causally sustained by evidence in terms of counterfactual causation is moribund. In my next post on this topic I will present what I believe is a successful reply to Lehrer Gypsy-Lawyer type scenarios.

Gettierising Nozick

Over at The Web of Belief, I lay out a Gettier case against local reliabilism (which is itself based on an earlier post of mine, Undescriminating Reliabilism). Let's call my proposed Gettier case against local reliabilism GLR. The version of local reliability I took as my target was admittedly quite simple, so here I will attempt to apply GLR to a much more sophisticated version of local reliability—namely, Nozick’s counterfactual account. Nozick [1981, p. 179] argues that the true belief that p is knowledge only if:

(N1) If p were true, then S would believe that p
(N2) If p were not true, then S would not believe that p¹

Following David Lewis [1973] we may say that (N1) and (N2) are true, as counterfactual statements, iff in possible worlds near to the actual world, if p is true, S believes that p, and if p is false S does not believe that p. Nozick recommends that we assess (N1) and (N2) by reference to what is the case in all nearby possible worlds. Roughly, a world may be described as ‘nearby’ if it is only slightly different from the actual world and ‘distant’ if it is radically different.

The following reply to GLR seems available to Nozick. Let us suppose that the set of nearby possible worlds include ones in which the computer is running a different program or is missing altogether. In such nearby worlds, although there is a red cube in the box, there is no hologram of a red cube. Since in such a world the subject would not believe that (a) although (a) is true, (N1) has not been satisfied.

One initial difficulty with this reply is that it is not immediately clear that worlds in which the computer is running a different program or is missing altogether should be considered nearby. But let us, for the sake of argument, assume that such worlds are in fact nearby.

Even so, Nozick’s strategy for responding to GLR proves too much, since it also impugns cases in which the subject intuitively has knowledge.

The ‘Jesse James’ Counterexample:
Consider the case of the Jesse James Bank Robbery, as described by Craig [1990]:

Jesse James, the reader will recall, is riding away from the scene of the crime with his scarf tied round his face just below the eyes in the approved manner. The mask slips, and a bystander, who has studied the ‘wanted’ posters, recognises him. The bystander now knows, surely, that it was James who robbed the bank. But Nozick has a problem: there is a possible world, and a ‘close’ one, in which James’ mask didn’t slip, or didn’t slip until he was already past the bystander; and in that world the bystander wouldn’t believe that James robbed the bank, although it would still be true that he did. So Nozick’s condition [N1] is not satisfied, and he is threatened with having to say that the bystander doesn’t know that it was James, even though the mask did slip. So his analysis looks like ruling out something which is as good a case of knowledge as one could wish for [p. 22].

Nozick is already equipped with a reply to the ‘Jesse James’ counterexample, akin to that employed in the Grandma case [See endnote 1]. In brief, he may simply argue that in worlds in which the mask did not slip, the method employed by the bystander would be different. Thus, given the version of Nozick’s counterfactuals revised to include the subject’s method, worlds in which the mask did not slip would not be included in the relevant nearby possible worlds.

However, to the extant that this reply is effective in preserving the bystanders knowledge in the Jesse James case, it is also effective at preserving the GLR subject’s ‘knowledge’ that (a). In GLR, the computer program, as the locus of reliability, constitutes part of the method by which S arrives at her belief that (a). Thus, by (N1*), all worlds in which the computer program is different or the computer is missing, a different method is being used and that world eo ipso fails to count as nearby.


Endnote:

1 Counter examples such as the Grandma case has prompted Nozick [1981, p. 179] to revise (N1) and (N2), limiting them to the same method (i.e., vision):

(N1*) If p were true, S (using M) would believe that p

(N2*) If p were not true, then S (using M) would not believe that p

References:

Craig, E. [1990], Knowledge and the State of Nature. Oxford: Clarendon Press.

Lewis, D. [1973], Counterfactuals. Oxford: Basil Blackwell.

Nozick, R., [1981], Philosophical Explanations, Cambridge: Cambridge University Press.