I will now turn to the view that is by far most commonly held (or implicitly assumed) on this question. The view I have in mind is the “simple proposal” (henceforth: SP), versions of which are held by a number of authors (LaPorte 2000, 2004, 2006; Martí 2004; Salmon 2005; Linsky 2006; López de Sa 2008; I’m taking the label for the view from López de Sa). While the views of the proponents of SP diverge on some important issues, they agree on roughly the following definition of rigidity for general terms:
Something like this view seems to be often assumed in discussions of natural kinds and the necessary a posteriori, and it would be hard to deny the attractiveness of this proposal. Moreover, it is easy to come up with examples which seem to support SP (such as “red” vs. “Mary’s favourite colour”, to take a well-worn example).
However intuitive SP may seem, it has been subject to heavy criticism. I will now take a brief look at two existing objections that have been raised against SP. I do not think they succeed in refuting SP, but a quick review of these problems will be useful in bringing out commitments and consequences of the view; these will play a role in my own argument against SP, which I will present in Sect. 2.2.
Old Objections to SP: trivialization and over-generalization
The first objection is that SP trivializes the notion of rigidity, by making all kind terms rigid (Schwartz 2002; Soames 2002). After all, unless we place restrictions on which kinds are real kinds (and thus legitimate), there will be a kind corresponding to any kind term. Consider the example mentioned above, “Mary’s favourite colour”. Proponents of SP would naturally want to say that it is non-rigid, because it might designate one colour in this world and another colour in another world. But why say this? Why not say, instead, that it designates the same kind in all worlds: the kind Mary’s-favourite-colour?
Defenders of SP have sought a reply along the following lines (I am here mostly following Martí 2004). First, we are to suppose that general terms designate, when evaluated at a world, a function from possible worlds to objects. Rigid general terms will then be the ones which designate the same function at all worlds. On this elaboration of SP, “Mary’s favourite colour” would be non-rigid, because, at w1, it might designate the function from worlds to the red objects, whereas at w2, it might designate the function from worlds to the blue objects, and so on.
In fact, it turns out that this commitment alone will not save SP from the trivialization objection (see López de Sa 2007)—SP also needs to provide linguistic data of a certain sort to avoid a further problem. But in fact data of the sort needed does seem to exist (LaPorte 2006; Martí and Martínez 2007). I will not discuss this issue here, but merely assume that this line of response will work. It is worth noting, however, that to deal with the trivialization objection SP needs to assume that general terms designate abstract objects such as functions (rather than their extensions, as some would like to hold on independent grounds). This assumption will play a role in my own argument against SP.
The second objection is that, even if SP does not trivialize the notion of rigidity by making all kind designators rigid, it will still over-generalize by making far too many of them rigid. For example, it seems to follow straightforwardly from SP that terms such as ‘bachelor’ and ‘hunter’ are rigid. ‘Bachelor’ rigidly designates the kind bachelor—the function from worlds to all and only the bachelors—and similarly for ‘hunter’, and any other simple general term. For some (e.g. Soames 2002; Schwartz 2002), this is reason enough to reject SP, but the proponents of SP are quite happy to accept the consequence. On SP, rigidity is not a feature that is exclusive to natural kind terms (and perhaps a few others). Most general terms are rigid (indeed, it appears that only unrigidified definite descriptions of kinds will turn out non-rigid.) It does not seem very fruitful to carry on a debate about whether this is an acceptable conclusion. For my purposes here, it is enough that we make note of this conclusion, because it will play a role in my argument against SP, to which we shall now turn.
A new objection to SP: theoretical role
My own objection to SP could be called the objection from theoretical role. The notion of rigidity for general terms was supposed to play a central role in explaining the necessity of a posteriori identifications between rigid general terms. And mostFootnote 5 proponents of SP claim that their view does just that. LaPorte, for example, gives a nice example of an a posteriori identity between kind terms: “Brontosaurus = Apatosaurus”. This example has a history quite similar to “Hesperus is Phosphorus”: Brontosaurus and Apatosaurus were first thought to be two distinct species of dinosaur, but this was later empirically disconfirmed (see LaPorte 2004, p. 37).Footnote 6 LaPorte claims that rigidity, as elaborated in SP, plays a role in explaining the fact that this identity is necessary, even though it is a posteriori. “Brontosaurus” and “Apatosaurus” were discovered to denote the same kind, and because they are rigid, they denote the same kind in all worlds, and the identification is shown to be necessary (LaPorte 2004, p. 40).
While this explanation—which is clearly an instance of the schema (NAP)—may seem to work, and even be obvious, I will argue that it in fact fails.Footnote 7 But first, we should note that in the case of kind terms, the identity discovered in (NAP1) can be understood in two very different ways. This is perhaps easiest to see with the most common example of such an identity statement, “Water is H2O”. This statement can be read in two ways: as a quantified biconditional, or as a true identity statement between kinds. I will now look at each reading and claim that SP fails to play the required role in delivering the necessary a posteriori status of these identities, regardless of which reading we adopt.
First, suppose that the purported identity is read as a quantified biconditional (or as a quantified conditional; this is the natural reading of another common example, “tigers are animals”):
$$ \forall x\;(x{\text{ is water}} \leftrightarrow x{\text{ is H}}_{ 2} {\text{O}}) $$
On this reading, the kind terms function as predicates, and the discovery in (NAP1) will be a discovery about actual co-extension: we discover that, in the actual world, anything composed of water is composed of H2O, and vice versa.
It is fairly easy to see that, on this reading of theoretical identities, SP runs into problems. Recall that, as we saw in connection with the overgeneralization problem, according to SP most kind terms are rigid. For example, “renate” and “cordate” will quite obviously come out rigid on SP, rigidly denoting the properties of having a kidney and having a heart, respectively.Footnote 8 But now, if in the actual world all and only renates are cordates, (NAP) should apply to the biconditional “renates are cordates” as well: (NAP1) and (NAP2) are satisfied, so it should follow that it is a necessary a posteriori truth. But that cannot be right: even if all and only renates should actually turn out to be cordates, it appears obvious that there could be creatures that only have a kidney or a heart, but not both. “Renates are cordates” is contingently true (if true at all). The upshot is that SP’s notion of rigidity cannot play the role of delivering, via schema (NAP), the necessity of true theoretical identifications of the quantified biconditional type, since it would confer necessity to biconditionals which quite clearly are contingent.
Suppose, on the other hand, that the identity in (SAP1) is a true identity between kinds (This reading seems natural with some standard examples, such as “heat is mean molecular kinetic energy”). Now the kind terms function as names for kinds, and “Water is H2O” expresses something like the following:
$$ \text {Waterkind} = {\text{H}}_{2} {\text{O-kind}} $$
We saw earlier that, to deal with the trivialization objection, SP needs to commit itself to the view that kind terms designate, at worlds, functions from worlds to objects. So, on SP, kinds presumably should be identified with such functions.
On this reading of theoretical identities, then, the empirical discovery in (NAP1) would be an identity between kinds (construed as functions from worlds to extensions). From this, rigidity (in the sense of SP) would indeed deliver the necessity of the identity: if we can find out empirically that the kinds designated by A and B are identical, and we know that A and B are rigid (in SP’s sense), we can conclude that the identity statement A = B is necessary a posteriori. On the surface, then, SP seems to do the work required. But when we look at the case more closely, two problems arise.
Firstly, we should note that the kind terms are now really functioning as names for abstract objects. In other words, SP is succeeding in delivering the necessity of a posteriori identifications involving kind terms only by giving them a reading on which they are, in fact, singular terms. This is not what we were originally looking for: what we wanted is a notion of rigidity for general terms.
A second problem concerns the putative status of the identity as an empirically discovered fact. The identity mentioned in (NAP1) is now interpreted as holding between abstract objects, such as functions from worlds to objects. But how do we empirically observe such an identity? We cannot observe functions—they are causally inert. In the case of an identity statement between singular terms, things are fairly straightforward. We observe spatiotemporally located objects and find reason to suppose that the object with which we have been in causal contact on one occasion is in fact the same object with which we have had dealings at another. But since kinds are, on SP, assumed to be abstract objects such as functions, we cannot have been in causal contact with them. The things we observe are members of kinds, not the kinds themselves.
Hence, the sense in which kind identities such as “Brontosaurus = Apatosaurus” are empirically discovered must be more indirect. We somehow reason to the identity, based on our empirical observations about members of the kinds in question. However, it is not immediately obvious how we do this. In the next section, I will take a closer look at this issue and claim that SP’s notion of rigidity in fact plays no role at all in explaining the necessity of kind identities; the work expected of rigidity is really done by a notion I will introduce and label actuality-dependence.