Philosophical Studies (2006) 130:321–336 DOI 10.1007/s11098-004-4676-5
Ó Springer 2006
JOSEPH LAPORTE
RIGID DESIGNATORS FOR PROPERTIES*
ABSTRACT. Here I defend the position that some singular terms for properties are rigid designators, responding to Stephen P. Schwartz’s interesting criticisms of that position. First, I argue that my position does not depend on ontological parsimony with respect to properties – e.g., there is no need to claim that there are only natural properties – to get around the problem of ‘‘unusual properties.’’ Second, I argue that my position does not confuse sameness of meaning across possible worlds with sameness of designation, or rigid designation. Third, I argue that my position does not founder by way of failing to assign rigidity the work of grounding a posteriori necessity.
In an article in this journal (LaPorte, 2000), I have argued that there are rigid designators not only for concrete individuals but for kinds. Schwartz (2002) has published an interesting and detailed response in which he criticizes my position. Schwartz and I are in agreement on important points. I argue that the question of whether a term is rigid ought to be distinguished from the question of whether the causal theory of reference accounts for its behavior. The causal theory of reference accounts for how it is that the meaning of some terms is ‘‘outside the head,’’ as Putnam (1975) famously puts it. But contrary to Putnam, no appeal to rigidity is needed to account for this externalism about meaning: or so I claim.1 Schwartz agrees with my claim that securing externalism about meaning is not the work of rigidity, but he says that I should go on to say ‘‘that the notion of rigidity does no work at all ’’ when applied to kind terms (Schwartz, 2002, p. 273). While I do not think that Schwartz’s criticisms succeed in undermining my account of rigidity, I do think that Schwartz articulates well some serious and natural reservations. Those reservations merit a careful look. In this rejoinder, I will address Schwartz’s three main criticisms: first, that I cannot state
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my view by appeal to properties instead of kinds, unless I can somehow justify the position that there are only ‘‘natural’’ properties (Schwartz, 2002, section III); second, that I am confusing sameness of meaning across possible worlds with sameness of designation, or rigid designation (Schwartz, 2002, p. 272); and third, that rigidity as I understand it does not deserve to be called ‘‘rigidity’’ because it fails to perform important work required of rigidity, namely to ground a posteriori necessity (Schwartz, 2002, section IV). I will address these criticisms in order in sections (II)-(IV) after rehearsing very briefly in section (I) the basics of my position concerning rigidity, which position is under fire.
I
A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else.2 Kripke (1980) famously argues that because a rigid designator designates the same object in all possible worlds, an identity statement in which the identity sign is flanked by two rigid designators must be necessarily true if it is true at all, even if the statement is not a priori. His classic example is the identity statement ÔHesperus ¼ Phosphorus’, which is true, but which was discovered a posteriori to be true. ÔHesperus’ is a name that was given to a heavenly body seen in the evening, and ÔPhosphorus’ is a name that was, unknown to the first users of the name, given to that same heavenly body seen in the morning. The heavenly body is Venus. Since ÔHesperus’ and ÔPhosphorus’ are names rather than descriptions for the same object, both terms are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ÔHesperus’ and ÔPhosphorus’ name in all possible worlds is Venus. Since ÔHesperus’ and ÔPhosphorus’ both name Venus in all possible worlds, and since Venus ¼ Venus in all possible worlds, ÔHesperus ¼ Phosphorus’ is true in all possible worlds.
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A description like ‘‘the brightest non-lunar object in the evening sky’’ is, on the other hand, not rigid. That explains why the identity statement H. ÔHesperus ¼ the brightest non-lunar object in the evening sky’
is true but not necessarily true. While Hesperus is in fact the brightest object in the evening sky apart from the moon, Hesperus might have been dimmer: had, say, Hesperus been obscured by cosmic dust, Mars might have been the object designated by Ôthe brightest non-lunar object in the evening sky’ rather than Hesperus. In that case, the above identity statement (H) would have been false. So the reason that (H) could have been false is that Ôthe brightest non-lunar object in the evening sky’ does not designate Hesperus rigidly. It designates Hesperus in this world, which explains why (H) is true, but this description designates Mars in some other worlds, which explains why (H) could have been false: (H) would have been false had some other such world been actual. This is all familiar Kripkean territory. Both Kripke (1980) and Putnam (1975) extend the notion of rigidity to terms for natural kinds. Here controversy has ensued. What is rigidly designated by a term like ÔApis mellifera’? Certainly not particular honeybees, since those honeybees that presently go about their work might not have existed. Others that do not exist might have existed instead. I maintain that ÔApis mellifera’ designates the honeybee kind, an abstract object that has members or instances: particular honeybees. ÔApis mellifera’ designates the honeybee kind rigidly. Like ÔHesperus’, it is a name, and so a rigid designator. This name is properly contrasted with a non-rigid description like Ôthe species typically farmed for honey’. ÔThe species typically farmed for honey’ does designate Apis mellifera, because that is the species typically farmed for honey; but some other species could have been farmed for honey instead: ants are not honeybees or members of Apis mellifera, and honey-thieving ants could have been farmed for honey. Had ants been farmed for honey, Ôthe species typically farmed for honey’ would have designated a species of ant and not Apis mellifera. Hence, (A) is
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true but not necessarily true for reasons similar to those that explain why (H) is true but not necessarily true. A. ÔApis mellifera ¼ the species typically farmed for honey.’
Even though (A) is not necessarily true, ÔApis mellifera ¼ honeybeekind’ is necessarily true. ÔApis mellifera’ and Ôhoneybeekind’ are both names for the honeybee kind, and thus rigid designators; they are not non-rigid descriptions for the honeybee kind, as Ôthe species typically farmed for honey’ is.3 The significance of rigidity and non-rigidity for kind designators is the same as the significance of rigidity and non-rigidity for designators of concrete objects: in both cases, provided an identity statement is flanked by rigid designators, it is necessarily true if true at all. And in both cases, if an identity statement is flanked by a rigid designator on one side and a non-rigid designator on the other, the sentence is not necessarily true even if it happens to be contingently true. II
Schwartz reminds us that there is a complication for my account. Perhaps there are ‘‘unusual kinds,’’ such as the kind species-typically-farmed-for-honey. This is not identical to the honeybee kind because, had some species of honey-thieving ants been farmed for honey more often than honeybees, the metaphysical extension of the honeybee kind would have contained all and only individual honeybees just as it does in fact; but the metaphysical extension of the unusual kind speciestypically-farmed-for-honey would have contained some species of ant instead of honeybees.4 Suppose there is a kind speciestypically-farmed-for-honey. Why should not Ôthe species typically farmed for honey’ be said to designate this unusual kind rigidly, rather than, as I would have it, to designate the honeybee kind non-rigidly? Schwartz notes that I do propose a resolution to this problem, but he misreads that resolution. Schwartz writes: ‘‘LaPorte recognizes that his preferred account will be trivialized if we allow what he calls the abstruse kind insect species that is
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typically farmed for honey. Consequently he denies that there are such kinds’’ (p. 268). On the contrary, I do not deny that there are such unusual, non-natural kinds. In the paper Schwartz cites, I take no position on whether there are or are not any such kinds, arguing only that if there are such kinds, they present no trouble for my account of rigidity. But for the record, I do think that there are such kinds. They are artificial kinds. Had my response to the problem of unusual kinds been simply to deny that there are any unusual kinds like the kind species-typically-farmed-for-honey, as Schwartz supposes it is, then I would have had a lot of explaining to do concerning what makes some apparent kinds genuine and others not only unnatural or unusual but non-existent. I do no such explaining, as I have said. So Schwartz has good reason to be dissatisfied with the response that he takes me to provide to the problem of unusual kinds. He objects that such an account would rely on obscure ideas about kindhood. I agree. Although Schwartz is appropriately unhappy with the response that he takes me to provide to the problem of unusual kinds, he is incorrect to suppose that no other response to the problem will do: for Schwartz, the problem is fatal for any account that ascribes rigidity to kind terms. He explains that the ‘‘difficulties come out more clearly if we focus on properties’’ (p. 268). The problem is that, ‘‘as standardly understood there is a property for just about every possible description and every boolean function of descriptions, and there are still a lot more. When considering possible worlds, properties are not limited to robust things like causal powers’’ (p. 268). Hence, we cannot say that Ôthe color of my car’ is a non-rigid designator for the color red, because there is also the property of being the color of my car, which the expression Ôthe color of my car’ could rigidly designate: ‘‘the property Ôbeing the same color as my car’ is the same relational property in every possible world’’ (p. 269). Schwartz challenges me to state my view in terms of the designation of properties: if I can do that, I will have shown my position to be tenable (Schwartz, 2002, pp. 272–273). I am happy to state my position in terms of the designation of properties.5 My position is not that only ‘‘natural’’ properties
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exist, so that there is no property of being the same color as my car or, alternatively, being the color instantiated by my car (cf. Schwartz, 2002 p. 269). I acknowledge that there is a property of being the color instantiated by my car, which is distinct from the property redness. So why does Schwartz’s problem not arise? Do I not end up without principled grounds for saying that Ôthe color instantiated by my car’ non-rigidly designates redness instead of saying that that expression rigidly designates the relational property of being the color instantiated by my car? No, there are principled grounds for saying that Ôthe color instantiated by my car’ non-rigidly designates redness on at least some uses, in at least some contexts, even if there is a relational property of being the color instantiated by my car that could be designated by the same expression on other uses of that expression in other contexts. The expression’s non-rigid designation of redness in some contexts is enough for my purposes. A speaker who believes of two cars that both instantiate redness might use Ôthe color instantiated by my car’ non-rigidly when affirming, say, C. ÔThe color instantiated by my car ¼ the color instantiated by your car’
where what the speaker intends is that the identity relation holds between the first color and the second.6 To make the exposition easier, in view of the indexicals in (C), I will suppose that I am the speaker and that you are my audience. Given these intentions and the relevant use of the definite descriptions, (C) would be true if my car instantiates redness and your car also instantiates redness, as I the speaker believe. Let us suppose, for simplicity, that our cars do both instantiate redness.7 In that case, (C) is true on the relevant reading set by the context. Clearly I the speaker could and here would avoid using Ôthe color instantiated by my car’ to designate the relational property of being the color instantiated by my car; otherwise the statement would be false, despite our cars’ both instantiating redness. So I would not use Ôthe color instantiated by my car’ to designate the relational property of being the color instantiated by my car in the context; I want to say something true.
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Why would (C) be false if Ôthe color instantiated by my car’ designated the relational property of being the color instantiated by my car? For this reason: Ôthe color instantiated by your car’ would presumably designate the relational property of being the color instantiated by your car, and that property is not identical to the relational property of being the color instantiated by my car even though redness is identical to redness and both cars instantiate redness. If, on the other hand, Ôthe color instantiated by your car’ designates redness, then again, the property of being the color instantiated by my car, a relational property, is not identical to redness, as I indicate above when discussing unusual kinds. So (C) has no reading on which it is true unless Ôthe color instantiated by my car’ can designate redness rather than the relational property of being the color instantiated by my car. On the true reading of (C), Ôthe color instantiated by my car’ and Ôthe color instantiated by your car’ both designate redness, since by supposition our cars both instantiate redness. The sentence is true on that reading because redness is identical to redness. It is correct, in the assumed circumstances concerning the speaker’s intentions and the way redness is instantiated by our cars, to say, ‘‘The color instantiated by my car is identical to the color instantiated by your car,’’ only because Ôthe color instantiated by my car’ is used to designate redness. Of course, Ôthe color instantiated by my car’ does not rigidly designate redness; it can only designate that color non-rigidly. In some worlds, my car is turquoise, and in such worlds Ôthe color instantiated by my car’ designates turquoiseness, not redness. Hence, Ôthe color instantiated by my car’ is a non-rigid designator of redness on the above use. ÔThe color instantiated by my car’ would be a non-rigid designator of redness on the above reading of (C), which is a natural reading of (C). If there are other possible readings owing to other possible uses for Ôthe color instantiated by my car’, that is irrelevant. For all I will contest here, there could be bizarre contexts in which someone would assert a false and indeed necessarily false proposition by (C) by using Ôthe color instantiated by my car’ to designate rigidly the relational property of being the color instantiated by my car and by using
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Ôthe color instantiated by your car’ to designate rigidly the relational property of being the color instantiated by your car. These properties are not identical whatever the color of our cars, so the use of (C) to assert that they are identical would result in (C)’s being false. On such a use, (C) would be necessarily false since the designators would be used rigidly for the respective properties and thus, with respect to any possible world, (C) would say of these same properties that they are identical, which they are not. Such an unlikely use of Ôthe color instantiated by my car’ to express a necessary falsehood by the utterance of (C) would not cause paradox for my position that (C) could be used in other contexts and indeed typically would be used to say something true. Kripke would apparently agree: addressing another, similar phenomenon, he writes ‘‘That more than one proposition may be expressed by [a sentence] is irrelevant: the question is whether each such proposition is evaluated as I describe, or is it not.’’ (1980, p. 10). I suppose that a defender of the objection from unusual universals might still protest that it is impossible to keep distinct the two possible uses that I have described for Ôthe color instantiated by my car’, in which case (C) is neither true nor false. But why think that? I can surely distinguish between the two possible uses: I just did distinguish between them when elaborating on the difference between them. III
Schwartz rightly insists that we must distinguish sameness of meaning across possible worlds with sameness of designation, or rigid designation (Schwartz, 2002 p. 272). He supposes that I am confusing these two distinct phenomena: ‘‘LaPorte is confusing rigidity with consistency of meaning,’’ he suggests. This confusion has allegedly misled me into thinking that my observations reflect the rigidity of certain terms, when really my observations reflect not rigidity but only ‘‘the obvious and rather uninteresting fact that words have the same meaning when talking about other possible worlds as they do when talking about the actual world’’ (p. 272).
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I agree with Schwartz that it would be a confusion to say that an expression is rigid just because it keeps the same meaning from world to world. My own account does not fall into this confusion. In my view Ôredness’ is rigid, while Ôthe color instantiated by my car’ is not. But both Ôredness’ and Ôthe color instantiated by my car’ keep the same meaning when we talk about counterfactual situations. ÔThe color instantiated by my car’ is non-rigid because it designates redness in this world, but not in some other worlds, where my car is black or some other color and so instantiates blackness or some other color instead. Yet Ôthe color instantiated by my car’ has the same meaning as always when we are discussing worlds in which I paint the car black, so that Ôthe color instantiated by my car’ designates blackness instead of redness. ÔThe color instantiated by my car’ designates, in this or any other possible world, whatever satisfies the description on its present meaning. On my account, one could understand the meaning of each of the above designators as a function taking possible worlds as arguments and yielding abstract objects (properties or kinds) for values.8 A rigid designator for an abstract object like a property is one whose meaning is a constant function, yielding the same abstract object, the relevant term’s designatum, for every possible world. A non-rigid designator for an abstract object, by contrast, yields different abstract objects, or designata, at different worlds. The meaning of Ôredness’ is a constant function: hence, Ôredness’ designates redness in any possible world and is rigid. The meaning of Ôthe color instantiated by my car’ is a function that yields a different value depending on the possible world. ÔThe color instantiated by my car’ designates redness in this possible world but blackness in others: it is non-rigid.9 So the designatum of Ôthe color instantiated by my car’ varies from world to world. But the designatum is the value of the relevant function for any possible world, not that function itself. Although the designatum, or the value of the relevant function, varies from world to world, the function itself, which is the meaning of the expression, does not. ÔThe color instantiated by my car’ has just one meaning as it denotes different colors at
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different worlds: the meaning is a non-constant function that remains the same non-constant function regardless of the value of the function at a world. Notice that, in spite of Schwartz’s focus on general terms, here and in my earlier paper, I attempt to elaborate on the rigidity of singular terms for properties, not general terms.10 Schwartz prefers to paraphrase away apparent uses of singular terms for kinds (see note 6). His preferred paraphrases, if successful, would allow him to avoid talking about kinds and properties as objects, albeit abstract ones, which can themselves be described as having contingent properties. An account like mine, on the other hand, is committed to talking about properties as objects and so appears, at least at first sight, to be committed to realism about properties (again, see note 6). Is this a drawback for my rendering? I cannot see that it is. I have aimed to provide a more explicit working out of Kripke’s suggestive but inchoate claim that terms for kinds and properties are rigid. I count it against my interpretation if I saddle Kripke with extra metaphysical commitments concerning which his account was supposed to remain neutral. However, it seems to me that Kripke’s initial idea is explicitly committed to speaking of kinds and properties as objects. So an elaboration like mine of Kripke’s idea of rigidity does not saddle the idea unnecessarily with extra metaphysical baggage by taking properties as objects that can themselves be described as having contingent properties. Here is a representative passage from Kripke: So we use the description, Ôthat which causes such and such sensations, or that which we sense in such and such a way’, to identify heat. But in using this fact we use a contingent property of heat, just as we use the contingent property of Cicero as having written such and such works to identify him. We then use the terms Ôheat’ in the one case and ÔCicero’ in the other rigidly to designate the objects for which they stand (Kripke, 1971, p. 160; I have added the emphasis to Ôobjects’).
If Kripke’s initial but primitive idea is committed to speaking of kinds and properties as objects, then surely an elaboration like mine of that initial idea is not at fault for sharing that initial idea’s commitments.
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IV
I have addressed a couple of Schwartz’s chief objections. There is a remaining worry that figures prominently in Schwartz’s mind, a worry that is, as Schwartz properly suggests (p. 271), independent of the above considerations: this worry is that rigidity as I understand it fails to do important work it would have to do, namely to ground a posteriori necessity just as the rigidity of singular terms for concrete objects does (Schwartz, 2002, section IV). That Hesperus ¼ Phosphorus was a discovery and an unanticipated one at the time. Announcing that these sorts of identities are necessarily true (if true at all) and a posteriori and thus not analytic was a remarkable advance in semantics and made Saul Kripke justly famous. Now consider ÔThe honeybee ¼ Apis mellifera’. In order for LaPorte’s point to be effective this claim must be not only necessarily true but a posteriori – a discovery (p. 270).
Schwartz complains that ÔThe honeybee ¼ Apis mellifera’ is analytic, and that we did not need Kripke to show us that it is necessarily true (p. 271). He is right that the necessity of sentences like this was recognized by those working before Kripke: the logical positivist Hans Hahn (1959, p. 152), for example, discusses sentences just like this, counting them analytic.11 So the example that I have chosen does not head off this worry. But although this is a natural worry to raise in the face of my example, the worry turns out, on inspection, to be groundless. First, it is not true that every identity statement whose necessity is guaranteed by its containing only rigid designators is a posteriori: Kripke himself discusses identity statements that are not a posteriori yet that contain two uncontroversially rigid designators for concrete objects. Second, there are necessarily true statements containing rigid designators for kinds that are a posteriori. Schwartz sees no problem with Kripke’s application of rigidity to terms for concrete objects: so Kripke’s application of rigidity to terms like ÔCicero’ and ÔTully’ is okay even by Schwartz’s reckoning. Kripke (1980) maintains that ÔCicero ¼ Tully’ is necessarily true as a result of containing two rigid designators for the same person. The truth of this
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statement might be a posteriori for some people, such as people who have never heard the name ÔTully’. But it could also be a priori and presumably it would be a priori for Tully’s parents or whoever baptized him ÔMarcus Tullius Cicero’. Hence, the necessity associated with rigidity need not be a posteriori. Further, there are necessarily true statements containing rigid designators for kinds that are, like ÔHesperus ¼ Phosphorus’, a posteriori. Here a word of caution is needed for the sake of maintaining desirable neutrality. Millians (e.g., Soames, 2002, pp. 240 and 243) insist that the truth of the proposition that Hesperus ¼ Phosphorus is knowable a priori. They therefore inherit the job of explaining how it is that competent speakers could sincerely deny the truth of the sentence ÔHesperus ¼ Phosphorus’. I will not comment here on whether Millians have succeeded in this job. Nor will I comment on whether the proposition that Hesperus ¼ Phosphorus is a priori, as Millians claim. Kripke himself, who initially suggests that such propositions are a posteriori (1980, e.g., p. 160), later professes agnosticism about the matter (Kripke, 1979, pp. 269f. and 281, note 44). When I say that ÔHesperus ¼ Phosphorus’ is a posteriori, though necessary, I mean to be understood to say not that the truth of the proposition expressed by the sentence is knowable only a posteriori but rather something like this: a competent speaker of the language who understands and can competently use the sentence ÔHesperus ¼ Phosphorus’ is nevertheless not in a position to know a priori whether the sentence, on its present interpretation, is true. It takes a posteriori investigation to determine that. Such a claim is consistent with the Millian position that the truth of the proposition that Hesperus ¼ Phosphorus is knowable a priori. A Millian cannot say with a non-Millian that (i) a competent speaker knows that the proposition expressed by ÔHesperus ¼ Phosphorus’ is the proposition that Hesperus ¼ Phosphorus, but that (ii) such a speaker must check the world to see a posteriori if this proposition is true. But a Millian can concede that a competent speaker is not in a position to know a priori whether the sentence, on its present interpretation, is true because a Millian can say that a competent speaker would need a posteriori investi-
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gation to determine that the sentence ÔHesperus ¼ Phosphorus’ expresses the proposition that Hesperus ¼ Phosphorus. With this clarification, I agree with Schwartz that Kripke has shown that ÔHesperus ¼ Phosphorus’ is necessarily true but a posteriori. Not all identity statements whose necessity is guaranteed by rigidity are a posteriori, but some such statements are a posteriori: ÔHesperus ¼ Phosphorus’ is one such statement that is. Kripke presents no analogous sentences for kinds, it is true.12 And I do not present analogous sentences for kinds, either, in the article Schwartz cites: he is right about that. ÔThe honeybee ¼ Apis mellifera’ is not analogous, for the reasons Schwartz gives. However, other sentences are analogous. I argue at some length elsewhere that ÔBrontosaurus ¼ Apatosaurus’ is relevantly just like ÔHesperus ¼ Phosphorus’. ÔBrontosaurus ¼ Apatosaurus’ contains two rigid designators for the same kind, although earlier speakers did not know this: it took scientific investigation to figure it out, and the scientist who dubbed the terms never realized that the sentence is true even though it is necessarily true. Because I discuss this matter in detail elsewhere, there is no need to go into the matter here; I refer the interested reader to my discussion in a recent monograph (LaPorte 2004, chapter 2).13 V
In conclusion, Schwartz does an admirable job of articulating natural reservations concerning my account of the rigidity of kind terms. Even so, those reservations may be laid to rest by the observations of sections (II)–(IV). NOTES * I thank Steve Schwartz and Bernard Linsky for helpful feedback on this paper. 1 Here I merely summarize. For details and development, see LaPorte (2000, 2004, chap. 2). 2 Again, I am content here to refer the reader to other publications (see note 1) for qualifications.
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Actually I am inclined to think that vernacular terms like ‘the honeybee kind’ or ‘honeybeekind’ do not precisely match their scientific correlates like ‘Apis mellifera’ in reference conditions (LaPorte, 2004, chapter 1); even so, there is nothing to stop an individual, in a given context, from employing an expression like ‘honeybeekind’ for the object of scientific investigation, Apis mellifera. So there is no need to replace this example with another in order to circumvent this minor irritation, though I could easily perform such a replacement, as will become clear below from my use of other examples. 4 Following Salmon (1981, p. 46), I call the class of a kind’s members or instances its ‘‘metaphysical extension.’’ The same class that serves as the metaphysical extension of a kind serves as the semantic extension of a general term for that kind. 5 On my account, for every kind there is a corresponding property, and for every property there is a corresponding kind, so it would appear reasonable to say that there is an identity between kindhood and propertyhood. At the very least, kinds and properties seem analogous with respect to this issue of designation. I discuss the relationship between kinds and properties in LaPorte (2004, chap. 1). 6 Schwartz would apparently prefer to paraphrase away singular terms for abstract objects and the sign for the identity relation as he construes sentences of English that on first blush seem to be identity statements containing abstract singular terms (Schwartz, 2002, p. 276, note 2). Without commenting on specifics about the kinds of sentences for which Schwartz’s style of paraphrasing may or may not work (Swoyer, 2000, section 4.2 offers comments to this effect), let me just note that I have precluded by stipulation any attempt to read (C) in such a way that there is no use of singular terms or appeal to identity. (More precisely, I have precluded any reading that cannot tolerate either singular terms or general terms that can appear as subjects: if we wish to use second order logic to represent sentences like (C) then ‘the color of my car’ and like terms can occur in the position of a subject or in a predicate. Since such terms could appear in a predicate, they are general terms. But the identity relation could still be expressed using these general terms, which terms can also appear as subjects. I will be ignoring this option of using second order logic for representing sentences like (C): see note 10.) Barring a better tactic for demonstrating otherwise than the unavailable one of paraphrasing away the use of singular terms and talk about the identity relation, the identity statement (C) would seem to be doomed to something short of truth in the event that nominalism is true and there are no abstract objects. Perhaps better tactics for a nominalism-friendly reduction than the one that I have just rejected are available, but whether or not they are will not concern me in this paper, for reasons that I discuss at the end of section (III). I will be assuming realism for simplicity here: the problem of unusual universals that I address in this section remains to be addressed, because the worry is that if properties like redness exist, as they
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do for the realist, ‘the color instantiated by my car’ could not non-rigidly designate such a property, contrary to what I maintain, in view of rival candidates vying to be the designatum of that expression. 7 Or, if you prefer, suppose that our cars instantiate the very same shade of redness. See note 6 and section (III) for discussion of the apparent commitment here to abstract objects. 8 ‘Meaning’ is often used in a richer way. Thus, the present account of meaning will not allow meaning to distinguish between necessarily co-designative expressions. This bare-bones account of meaning could certainly be supplemented: but though one might hope to see it succeeded by something structurally richer, it will suffice for present purposes. Kripke suggests that this is how he would account for ‘sense’ or ‘meaning’ (1980, p. 59n.). 9 At least ‘the color instantiated by my car’ is non-rigid on a typical use. As I indicate in section (II), we must limit ourselves to discussing the meaning of a term on a given use if a term is ambiguous. 10 LaPorte, 2000, p. 312, note 4 is explicit about this, leaving only a promissory note suggesting that my treatment of singular terms has analogous application, which I say that I will not specify in any detail in that article, to general terms or kind terms in predicative position. I still think that an application to general terms is possible, but I am content here to limit the discussion to my earlier position with respect to singular terms. I follow rather loosely, then, in the tradition of Donnellan (1973) and others who discuss the rigidity of terms like ‘redness’, ‘wisdom’ or ‘bachelorhood’ rather than terms like ‘red’, ‘wise’, and ‘bachelor’. Schwartz’s criticisms, if effective, would undermine not only my account of the rigidity of singular terms for kinds but also the main account now in the literature for how general terms can be rigid: this brilliant account, which recognizes some definite descriptions (or ‘‘definite ascriptions’’) as non-rigid general terms for kinds, traces to Bernard Linsky and earlier (Heintz, 1973; Linsky, 1984; Salmon, 2003). The relationship of my account to an account like Linsky’s deserves consideration; but to elaborate on that relationship would take me beyond my ambitions here, where my aim is to defend the cogency of my account (and, with only minor modifications to the defense, the cogency of Linsky’s account too) against the natural objections raised by Schwartz. 11 For critical discussion of Hahn’s position, see Bolton (1996, pp. 155–157). 12 Sentences like Kripke’s ‘Heat ¼ the motion of molecules’ present complications absent from the likes of ‘Hesperus = Phosphorus’. This is not an issue between Schwartz and me so I set it aside here. (I take it up in LaPorte, 2004, chap. 2.) 13 I wrote this chapter before I saw Schwartz’s criticisms of my (2000). In the chapter I go on to endorse the claim, also endorsed by Schwartz (p. 274), that rigid designation cannot underwrite the necessity in case of truth of all of the various sentences that Kripke takes to be necessarily true. I offer quite
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distinct arguments to support the necessity of sentences like ‘Cats are animals’, which do not assert anything about the identity relation. REFERENCES Bolton, C.J. (1996): ÔProper Names, Taxonomic Names and Necessity’, The Philosophical Quarterly 46, 145–157. Donnellan, K. (1973): ÔSubstances as Individuals’, Journal of Philosophy 70, 711–712. Hahn, H. (1959): ÔLogic, Mathematics, and Knowledge of Nature’, in A.J. Ayer (ed.), Logical Positivism, New York: Free Press, pp. 147–161. Heintz, J. (1973): Subjects and Predicables, The Hague: Mouton. LaPorte, J. (2000): ÔRigidity and Kind’, Philosophical Studies 97, 293–316. LaPorte, J. (2004): Natural Kinds and Conceptual Change, New York: Cambridge University Press. Linsky, B. (1984): ÔGeneral Terms as Designators’, Pacific Philosophical Quarterly 65, 259–276. Kripke, S. (1971): ÔIdentity and Necessity’, in M.K. Munitz (ed.), Identity and Individuation, New York: New York University Press, pp. 135–164. Kripke, S. (1979): ÔA Puzzle About Belief’, in A. Margalit (ed.), Meaning and Use, Dordrecht: D. Reidel, pp. 239–283. Kripke, S. (1980): Naming and Necessity, Cambridge, MA: Harvard University Press. Putnam, H. (1975): ÔThe Meaning of ÔMeaning’’, in Mind, Language and Reality, New York: Cambridge University Press, pp. 215–271. Salmon, N. (1981): Reference and Essence, Princeton: Princeton University Press. Salmon, N. (2003): ÔNaming, Necessity, and Beyond’, Mind 112, 475–492. Schwartz, S.P. (2002): ÔKinds, General Terms, and Rigidity: A Reply to LaPorte’, Philosophical Studies 109, 265–277. Soames, S. (2002): Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity, New York: Oxford University Press. Swoyer, C. (2000): ÔProperties’, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, URL=http://plato.stanford.edu/archives/win2000/entries/properties/.
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