0. abstract
My thesis is that all semantically unstructured predicates are rigid designators; it is developed in response to a thread running through Chapters 9-11 of Soames (2002). I’ll argue that any intuitions to the contrary are accommodated by a proper understanding of Russell’s (1905) referring/denoting distinction, as it pertains to predicates. That is, just as in the case of individuals, properties (or sets) can be designated in two ways: they can be denoted (e.g., ‘Dan’s favorite color’) and they can be referred to (e.g., ‘yellow’). Denoting expressions can either be rigid (e.g., ‘the element with atomic number 79’) or nonrigid (e.g., ‘the element most highly prized by local jewelers’). However, any expression that refers to a property designates it rigidly, and all semantically unstructured predicates refer to properties.
After arguing for this thesis I will: [1] briefly explore some of the differences between natural kind predicates and other predicates, that many are tempted to (mis)characterize in terms of rigidity, [2] compare Lewis’ view that such terms as ‘pain’ and ‘heat’ are nonrigid designators—cf., e.g., Lewis (1994: 304), and [3] address arguments given by Schwartz (2002) that are in tension with this thesis.
1. some background
‘Rigid designation’ is Kripke’s name for a concept that has been in the air at least since the development of quantified modal logics: a designator is rigid if and only if one and the same individual is relevant to the possible-worlds truth-condition of propositions expressed by sentences in which the designator occurs. The concept of rigidity might have been baptized by Smullyan (1948), as it affords a neat way to state his refutation of Quine’s (1947) argument against the intelligibility of quantified modal logic. Rigidity, unbaptized, is very much there in Kripke’s (1959, 1963) semantics for modal logic; and lies just beneath the surface of much other logical and semantic work in the 1950s and 1960s. Kaplan (1968: 379) perhaps comes closest to explicitly defining the concept, in his search for a kind of designator whose “reference is freed from empirical vicissitudes”. However, like Smullyan, Kaplan’s interests are more narrow, his goals less comprehensive, than Kripke’s. Rigid designation is first baptized, in print, by Kripke (1971, 1972), in the course of his developing a wide range of arguments about reference and content.
Although Kripke develops some analogies between proper names and natural kind terms, and argues that such terms as ‘gold’, ‘pain’, and ‘tiger’ are rigid designators, Kripke nowhere gives a definition of rigidity that applies to general terms or predicates. One of Soames’ (2002) focal projects of is to rectify this, by characterizing a more general definition rigidity. Toward that end, Soames does some groundbreaking work on such questions as: What is it for a general terms, or predicates, to be rigid? Precisely which predicates, then, are rigid?
At one point (pp.259-63), Soames argues that it is desirable to arrive at a definition according to which natural kind terms like ‘gold’ count as rigid but expressions like ‘bachelor’ do not, because the thesis that natural kind terms are rigid designators would be trivial if we defined the notion of rigidity such that what he calls ‘ordinary descriptive predicates’—examples he gives include ‘philosopher’ and ‘bachelor’—count as rigid. (Schwartz (2002) gives some complementary arguments, more on which below.) I will contest this. I will show why, despite the hard work that had to be done to identify and characterize the concept of rigidity, it is trivially true that all semantically unstructured terms are rigid designators.
First I’ll work though three preliminaries:
[1] In what sense are ordinary predicates ‘descriptive’?
[2] What should we take the designatum of a predicate to be, for our purposes here?
[3] How does Russell’s (1905) referring/denoting distinction apply to predicates?
2. all semantically unstructured expressions are rigid designators
Here is a sketch of the argument:
A singular term’s being
descriptive does entail that it might be a nonrigid designator, but this does
not hold for semantically unstructured descriptive general terms or predicates.
The reason is that whereas descriptive singular terms (mediately, or
indirectly) denote individuals, such descriptive predicates refer to
descriptive properties. While you cannot rigidly designate an individual via
its contingent accidental properties, you can rigidly refer to manifest
descriptive (contingent, accidental) properties, and that’s what ordinary
predicates (including ‘bachelor’ and ‘philosopher’) typically do.
I’ll argue that semantic structure is a necessary condition for nonrigidity; it follows that all semantically simple expressions are rigid designators. (Alternatively, in Bach’s (1987) terms, an expression has to designate satisfactionally in order for the question of nonrigidity to arise, but the link between any simple predicate and the property is designates, be it ‘bachelor’ or ‘gold’, is relational, not satisfactional).
3. what is special about the predicates which some are tempted to single out as rigid?
I explore briefly two significant, relevant differences between natural kind terms and ordinary descriptive terms: [1] natural kind terms are thought to refer to the properties that are essential to their instances, whereas ordinary descriptive predicates designate more superficial, perceptually salient, typically accidental properties, and [2] we do not divide up the linguistic labor (at least not in the same way) for ordinary descriptive terms—i.e., ordinary adult speakers are experts about the criteria of correct application of most ordinary descriptive predicates, but this is not the case for natural kind terms.
4. Lewis and Schwartz
I
compare Lewis’ view that such general terms as ‘pain’ and ‘heat’ are
nonrigid—cf., e.g., Lewis (1994: 304). I explain how Lewis’ view of these terms
is rather akin to Russell’s view of ordinary proper names—i.e., Lewis holds
that such terms are semantically equivalent to denoting expressions, of the
form ‘the occupant of the causal role R’. Thus, just as in the case of
Russell’s view of ‘
Schwartz (2002) argues that not all semantically unstructured predicates are rigid because they do not all give rise to the phenomenon of necessary a posteriori statements. I point to some flaws in his argument, and sketch an alternative explanation of why only some sorts of term give rise to this phenomenon. (In general, that two types of term are both rigid designators is compatible with there being all manner of important semantic differences between them.)
5. conclusions
Here are two further reasons in favor of the thesis that all semantically unstructured predicates are rigid: [1] Both Soames (2002) and Schwartz (2002), in trying to avoid this thesis, get tied up in irrelevant metaphysical questions. This risks losing some hard won ground, by adding currency to vague and mistaken objections that rigidity is an obscure essentialist doctrine. Rigidity is a semantic thesis about the relation between ‘D’ and D, not a metaphysical thesis about the essence of D. [2] This thesis offers an illuminating picture of the historical continuity, of the progress in philosophical logic, from Mill through Frege and Russell on into Kripke and Kaplan.
6. Works cited
Bach, K. (1987) Thought and Reference.
Kaplan, D. (1968) “Quantifying in,” Synthese 19.
Kripke, S. (1959) “A completeness theorem for modal logic,” Journal of Symbolic Logic 24.
(1963) “Semantical considerations for modal logic,” Acta Philosophia Fennica 16.
(1971) “Identity and necessity,” in Identity and Individuation, ed.
(1972) Naming
and Necessity.
Lewis, D. (1994) “Reduction of mind,” in Papers in Metaphysics and Epistemology.
CUP, 1999.
Quine, W.V. (1947) “The problem of
interpreting quantified modal logic,”
Journal of Symbolic
Logic 12.
Russell, B. (1905) “On denoting,” Mind 14.
Schwartz, S. (2002) “Kinds, general terms,
and rigidity: a reply to LaPorte,” Philosophical
Studies 109.
Smullyan, A. (1948) “Modality and description,” Journal of Symbolic Logic 13.
Soames, S. (2002) Beyond Rigidity.