Beyond rigidity? Essentialist predication and the rigidity of general terms.
| Autor | Gómez-Torrente, Mario |
SUMMARY: I offer a brief formal exploration of a certain natural extension of the notion of rigidity to predicates, the notion of an essentialist predicate. I show that, under reasonable assumptions, true "identification sentences" involving essentialist predicates (such as 'Cats are animals') are necessary, and hence that the notion of essentiality is formally analogous in this respect to the notion of singular term rigidity.
KEY WORDS: Kripke, Soames, necessity, modal logic
RESUMEN: El artículo hace una breve exploración formal de una extensión natural de la noción de rigidez a los predicados, la noción de predicado esencialista. Muestro que, dados supuestos razonables, las "oraciones de identificación" verdaderas que contienen predicados esencialistas (por ejemplo, 'Los gatos son animales') son necesarias, y por tanto que la noción de esencialidad es formalmente análoga en este sentido a la noción de rigidez para los términos singulares.
PALABRAS CLAVE: Kripke, Soames, necesidad, lógica modal
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In his recent book Beyond Rigidity, Scott Soames has forcefully argued that there is no notion that immediately suggests itself as a natural extension of the idea of rigidity to general terms and that satisfies the following two Kripkean conditions: (i) it must apply to typical general terms for natural kinds, stuffs and phenomena, and fail to apply to many other general terms, and (ii) it must be usable in the derivation of the necessitations of true "identification sentences" containing general terms that the extended notion applies to (sentences such as Cats are animals, Water is [H.sub.2]O and Lightning is an electrical discharge ought to be examples). In particular, Soames has rejected the conjecture that a certain natural tentative notion of general term rigidity he himself considers, that of an essentialist predicate, satisfies (i) and (ii). He does not quarrel much with the idea that this notion satisfies (i) (or at least that it satisfies it to an extent compatible with the vagueness of 'typical' and 'many'); but he has argued that it certainly does not satisfy (ii). Space limitations force me to leave for another occasion a discussion of the extent to which the notion of an essentialist predicate satisfies (i), but I will argue here that, under reasonable assumptions, this notion does satisfy condition (ii). More precisely: the notion in question actually gives rise to at least three distinguishable notions of an essentialist predicate, which are analogous to three well-known distinct notions of singular term rigidity; and I will claim that these notions of an essentialist predicate satisfy condition (ii) to the same extent that the analogous notions of rigidity for singular terms satisfy the condition analogous to (ii) in the singular term case.
Before my disagreements with Soames, my numerous agreements. I agree with him about many of the claims he makes in the course of setting up the stage for proper discussion. He recalls that the general terms about which Kripke (1972) makes his key theoretical claims come in a variety of syntactic and semantic categories: they include common nouns (including "mass" common nouns), verbs, and adjectives. If they had all been singular terms or disguised singular terms, then we might have just wondered whether Kripke's notion of rigidity for singular terms applies to them, and if the answer were positive, explore its implications for the question of the necessity of the appropriate "identification sentences", which would then be mere identities. But given that many terms that interest Kripke (e.g., 'cat', 'animal', etc.) are not singular terms, this way of proceeding is not available to the Kripkean.
One possibility is that each general term can be associated in some natural way with a corresponding singular term. Then one might say that a general term is rigid when its associated singular term is rigid and "determine whether these singular terms are rigid. If they are, then true identity sentences involving them, as well as corresponding theoretical identification sentences containing the original [general terms], will be necessary" (Soames 2002, p. 249). In my opinion, Soames sufficiently discredits the feasibility of options of this type, basically because it is hard to see how to formulate one such option so that not all (or fewer than most) general terms come out rigid (pp. 259-262); notions of rigidity with this defect will fail to satisfy (i) (Soames does not stress that they will also fail to satisfy (ii), because of examples of contingently true "identification sentences" such as Popes are bishops).
Soames makes a reasonably good case that general terms are typically predicative, against views that see many of the grammatically singular ones (such as "mass" nouns like 'water', 'lightning' and 'heat') as semantically singular (Soames 2002, pp. 245-248). His main reasons are that the "mass" nouns occur naturally in predicate position (e.g., in That stuff is water), combine with quantifiers to form complex quantifier phrases (Some water) and have bare uses analogous to bare plural uses of predicates (Water is potable). I acknowledge that the claim that general terms are typically predicative deserves fuller discussion; I don't, however, think it's necessary to offer such discussion here. I will simply work under the assumption that the general terms relevant to our discussion are indeed predicative, sometimes availing myself of slightly artificial predicative phrases in the case of "mass" nouns which resist unmodified predicative use in some contexts ('sample of water', 'instance of lightning'); Kripke (1972) often resorts to similar phrases when this suits his purposes ('chunk of gold', 'flash of lightning', etc.). I will be perfectly happy --and probably Kripke would too-- if the Kripkean claims can be shown to hold for some notion of general term rigidity which applies to the slightly artificial phrases even if "mass" nouns are "really" semantically singular. I will thus speak from now on simply of "rigid predicates", "predicate rigidity", and so forth.
I also agree with Soames in thinking that, if general terms are predicative, it's natural to view the "identification sentences" Kripke is interested in (or many of them, at any rate) as having the form of universally quantified material conditionals or biconditionals; i.e., in symbolic notation, for predicates A and B, the sentences
[atañe a todos]x(Ax [reúne a] Bx);
[atañe a todos]x(Ax [flecha diestra y siniestra] Bx). (1)
Kripke too often phrases or rephrases his "identification sentences" in these forms. (2)
Soames says that the key Kripkean doctrine that the necessity of true "identification sentences" involving rigid predicates can be derived from them plus the appropriate rigidity claims --i.e., the Kripkean doctrine that the notion of predicate rigidity satisfies (ii)-- can be equated fairly with the thesis that the following basic argument schema, (P), is valid ('P' is for 'predicate'): (3)
(P)
(Pa) [atañe a todos]x(Ax [reúne a] Bx) is true / [atañe a todos]x(Ax [flecha diestra y siniestra] Bx) is true;
(Pb) the predicates A and B are rigid;
(Pc) [atañe a todos]x(Ax [reúne a] Bx) is necessary / [atañe a todos]x(Ax [flecha diestra y siniestra] Bx) is necessary --in other words, [??][atañe a todos]x(Ax [reúne a] Bx) is true / [??][atañe a todos]x(Ax [flecha diestra y siniestra] Bx) is true.
What the Kripkean needs, then, is to provide a characterization of the notion of predicate rigidity appearing in (claims of the form) (Pb) that makes (P) valid. I think Soames is again more of less right here, but not completely, and this is an important disagreement. As I will note later, a strict analogy with the singular term case ought to lead us to allow that, for some notions of an essentialist predicate, the conclusion of the appropriate argument be something...
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