One reason to think that names rigidly designate individuals, and that this rigid designation does not reduce to some kind of description, is because you think that the identity of objects is necessary and a posteriori. I have already shown how that argument has flaws, so let me turn instead to another argument for rigid designation, namely that we refer to objects, or that we seem to be able to refer to objects, even in counterfactual situations. For example, if I say “if Bob hadn’t gone to the store then he would be out of milk” I am discussing a possible situation, that could have happened. But more importantly I am talking about Bob, the same Bob, it would seem, that I refer to when I use the name regularly. But in counterfactual situations we can suppose that any properties that are true of Bob are not in fact true. For example I can consider the situation in which Bob was not in fact named “Bob”. And thus it would seem that there is no description that will pick out Bob in these counterfactual situations, since I could always suppose that the description didn’t hold of Bob. Thus we must be referring rigidly to Bob, without the use of a description, in these counterfactual situations.
I think this argument is a bit too hasty. Before we can draw any conclusions from considerations concerning counterfactual claims we must first analyze those claims, and determine how they really work. Only then can we proceed to draw conclusions from them. And I think that there are basically two ways to analyze counterfactual claims: in terms of counterparts and in terms of possible properties, neither of which requires rigid designation.
Let’s start with counterparts. One way to analyze counterfactuals is by thinking of them in terms of possible worlds. Thus when we consider the counterfactual “if Bob hadn’t gone to the store …” what we are thinking about is a possible world in which things were the same as our world up until the point where Bob decided to go to the store. At this point the possible world diverges from ours, differing from ours in all the ways that would be a consequence of Bob’s altered choice. But, as David Lewis has argued, when we speak of other possible worlds there is no need to assume that those worlds overlap, such that our Bob is somehow in both worlds. Rather Bob has a counterpart in that world, and our counterfactual considerations are about this counterpart, who we simply call Bob for convenience since he is so Bob-like. Thus this Bob could indeed be picked out by a description, specifically “the counterpart of Bob”, assuming the name Bob also reduces to a description. Now the argument for rigid designation assumed that every property could be taken away in counterfactual situations, but now we see that that is not quite true. It wouldn’t make any sense to consider the case where Bob is not the counterpart of Bob, because that would mean considering the case where the counterpart of Bob is not the counterpart of Bob, which is equivalent to denying that the object is identical to itself, which is ridiculous. And thus we do not have to appeal to rigid designators in order to explain counterfactual considerations.
Of course there are two objections that can be raised to this analysis. One is to deny that individuals in possible worlds are counterparts of each other, and instead hold that they really are the same individual in some way. But why should we accept that characterization of possible worlds? Since everything we want to talk about with possible worlds can be put in terms of counterparts there seems to be no need to invoke this more complicated structure. And moreover assuming that the same individuals are in different possible worlds is to endorse a specific analysis of necessity, which by its nature entails several questionable consequences, including that names are rigid designators. Which is not to say that this analysis of necessity must be in error, just that it is no less questionable than the conclusions that are trying to be proven using it. The second possible objection is to insist that we are talking about the same individual in counterfactual situations, and moreover that we simply aren’t thinking about possible worlds, but rather certain possible re-arrangements of properties and their consequences. Honestly I can’t think of a reason to say that counterfactuals must be analyzed in this way, since generally the analysis of the content of what we are saying comes apart from what we intend when we make those statements. (For example, if I say that As are B then I am really saying that everything which is an A is also a B. But even though that is the logical content of my assertion I certainly didn’t think of myself as quantifying over everything when I said it.) But I can’t think of a reason to reject this alternate way of looking at the matter either, so let us simply see where it takes us.
So we must assume that when I consider the situation “if Bob hadn’t gone to the store …” I am really talking about Bob. But then it doesn’t seem as if I am ascribing to Bob the property of really going to the store. Certainly I would deny that Bob really went to the store if you asked me, even in the middle of my counterfactual construction. Thus we seem to be considering Bob having certain possible properties. So if we denote a real property of Bob as Pb let us denote the corresponding possible property as P◊b. Furthermore, let us denote property of having gone to the store as S and the property of having milk as M. Thus our assertion is that ~S◊b → ~M◊b. But how did we derive that conclusion from our premises? Well the rules of deduction for possible properties are as follows: We start with a set of objects having various properties, rules of deduction, and possible properties of those objects by assumption. We then create a set of rules for the deduction of facts about possible properties simply by taking our normal rules of deduction and replacing all their references to actual properties with the possible versions of those properties. And in addition to the possible properties the object has or lacks by assumption we will say that the object has or lacks the possible version of any property that it has actually has or lacks, assuming that having that possible property doesn’t contradict any possible property that the object already has, by assumption or by deduction from the assumptions, and that no contradictions can be derived from having that possible property. In our case with Bob the facts about Bob are Mb, Sb, and our rule of deduction is Sb ≡ Mb. Our assumption is ~S◊b. Given these facts we have a rule of possible property deduction: S◊b ≡ M◊b, which allows us to deduce that ~M◊b. And given this deduction we can’t say S◊b or M◊b, even though Bob actually has those properties, because they would contradict the possible properties Bob already has. And thus we have way of talking about counterfactual situations that doesn’t invoke possible worlds and allows us to be discussing the same individual. But neither does it force us to conclude that we are rigidly designating Bob, because even in our counterfactual discussions Bob has all the real properties he always had, and so we can’t rule out the possibility that we are referring to Bob in virtue of some description in terms of those real properties.
Thus counterfactual considerations, although interesting, do not force us to conclude that proper names rigidly designate their referents, given that we have two perfectly consistent ways to analyze counterfactual situations that don’t lead to that conclusion.