2 S. Kripke, Naming and Necessity (Cambridge, MA: Harvard University Press 1980); H. Putnam, The Meaning of Meaning, in H. Putnam, Mind, Language, and Reality: Philosophical Papers Volume 2 (Cambridge: Cambridge University Press 1975) 215-71, first published in Language, Mind, and Knowledge (Minneapolis, MN: University of Minnesota Press 1975)

3 This account of rigidity and non-descriptionality for singular terms is meant to be suggestive, not definitive. See D. Kaplan, Afterthoughts, in J. Almog, H. Wettstein, and J. Perry, eds., Themes from Kaplan (Oxford: Oxford University Press 1989) 565-614, for elaborations.

4 Putnam shies away from calling (1) a definition, preferring instead to call it a 'definition. As I point out below, certain units of measure are defined by similarity to a standard and Putnam's Principle is analogous to such a definition.

5 H. Putnam, Meaning and Reference, Journal of Philosophy 70 (1973) 699-711, 702f.

6 In Montague's semantics, proper names of individuals denote sets of properties (R. Montague, The Proper Treatment of Quantification in Ordinary English, in R. Thomason, ed., Formal Philosophy: Selected Papers of Richard Montague [New Haven, CT: Yale University Press 1974]247-70; first published in J. Hintikka, J. Moravcsik, and P. Suppes, eds., Approaches to Natural Language [Dordrecht: Reidel 1973]).

7 A more general notion of a frame takes it to include a binary (accessibility) relation defined on W. For present purposes we will not need this more general notion.

8 The first of these follows from the other two.

9 By adding an existence function to the semantics which assigns to each world the set of objects existing at that world, we can say that I represents an essential property of y iffy ∈ l(w), for each world w at which y exists. This might seem to be a more plausible definition than the one given in the text, but the difference does not affect the point I wish to make.

10 N. Salmon, Reference and Essence (Princeton, NJ: Princeton University Press 1981)

11 H. Deutsch, Essentialism and the Theory of Reference, in preparartion

12 The notion of a classification could be generalized to include families of non-overlapping relation intensions. Are there relational natural kinds?

13 This is solely for simplicity. The semantics can be developed with other interpretations of the modal operators and quantifiers.

14 Nor are they necessarily desirable. Most predicates are associated conceptually with many classifications and classifying relations. For example, consider the geometrical predicate has a smooth boundary. Both of the following arguments are intuitively valid: (1) x has a smooth boundary, x and y have the same shape, hence, y has a smooth boundary. (2) x has a smooth boundary, x and y have the same kind of boundary, hence, y has a smooth boundary. So there is no unique classifying relation associated with the predicate has a smooth boundary which accounts for all inferences of this sort.

15 Kripke subscribes to the essentialist view that natural kind words express essential properties of individuals. That is the reason for the qualification (completely) necessary truth in the above statement. The qualification can be omitted if essentialism (as regards individuals) is false. As already observed, NK verifies that essentialism as regards individuals is not a consequence of the basic Kripke-Putnam view.

16 See the references in Reference and Essence, 163f.

17 Let F and G be one-place predicates, and let S be a family of non-overlapping property intensions such that g(F) E S. Assume that g(G) is an Rs-closed property intension, then

is interesting to note, however, that this is not a stronger result than Proposition 3. The latter cannot be obtained from the above without the help of Proposition 2. I mention this fact since some readers of this paper have claimed otherwise. Note also that the necessitation of Kripke's Principle (i.e. the result of placing the whole of the formula following the turnstile within the scope of a necessity sign) does not follow from the hypotheses of Proposition 3. Of course, given the additional assumption that, we get an exact analogue of Proposition 3 for the predicates F and G.

18 See Reference and Essence for an acute discussion of the status of (Salmon's counterparts of) these assumptions.

19 Naming and Necessity, 53-6

20 See A. Sidelle, Necessity, Essence, and Individuation: A Defense of Conventionalism (Ithaca, NY: Cornell University Press 1989) for a general discussion of this challenge.

21 See E. Zalta, Logical and Analytic Truths that are not Necessary, Journal of Philosophy 85 (1988) 54-74 for an especially lucid account of contingent logical truth.

22 Stephen Schwartz criticizes Kripke's view that natural kind properties are essential properties of individuals in Formal Semantics and Natural Kind Terms, Philosophical Studies 38 (1980) 189-98.

23 Necessitation is the principle that if a formula ϕ is valid in a modal system, then ϕis also valid therein.

24 Demonstratives, in Themes from Kaplan, 481-564

25 See my Contingency and Modal Logic, Philosophical Studies 60 (1990) 89-102 and 'Logic for Contingent Beings, Journal of Philosophical Research, forthcoming 1993.

26 The Contingent A Priori, preprint, 1990

27 B. Abbott, in Nondescriptionality and Natural Kind Terms, Linguistics and Philosophy 12 (1989) 269-91, however, makes a nice start. See also G. Chierchia and 5. McConnell-Genet, Meaning and Grammar: An Introduction to Semantics (Cambridge, MA: MIT Press 1990), 63-86.

28 See L.T.F. Gamut, Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar (Chicago: University of Chicago Press 1991), 173-4.

29 See Salmon's Reference and Essence, ch. 4 and B. Linsky, General Terms as Designators,' Pacific Philosophical Quarterly 65 (1984) 259-76 for discussion of these and related issues.

30 Despite the fact that the concepts of rigid designation and non-descriptionality are general theoretical notions, there is a tendency - especially prevalent among linguists- to view the Kripke-Putnam insights as having no potential effect on the basic apparatus of model-theoretic semantics. The idea seems to be that the KripkePutnam insights have only to do with the nature of the referential link between words and the world: proper names and natural kind words are linked to the world causally rather than conceptually, and this doctrine does not have ramifications for the way in which truth-conditions for sentences containing proper names and/or natural kind words are formulated. This view is expressed very clearly in Chierchia and McConnell-Genet's Meaning and Grammar: From the perspective of our semantics there are certain general consequences that it might be tempting to draw from Kripke's and Putnam's work. Maybe what Tarski-style truth definitions accomplish is the reduction of the notion of meaning to the notion of reference (via the notion of truth). The reduction succeeds where other previous attempts have failed because it can provide a compositional account of sentence meaning, a characterization of notions like entailment, and a plausible account of the meaning of function words, among other things. Reference is then to be understood along the lines that Kripke and Putnam have independently argued for, namely as a direct causal link of words to objects and classes of objects that propagates through the language community by means of various conventions (86).

This view overlooks the fact that if for certain words the word/world link is a 'direct causal one, then this introduces new entailments and new logical phenomena such as those having to do with contingent logical truth and a posteriori necessity. New entailments, new logical phenomena, require a new modelling, a substantial revision of our semantics.'