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Generality

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Abstract

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the designatum of a predicate is a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn.

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Notes

  1. I owe to David Kaplan the insight that the word ‘horse’ functions as a kind name rather than a predicate whereas the phrase ‘is a horse’ functions as a predicate rather than a name. Cf. his “Afterthoughts” (1988a) to “Demonstratives” (1988b).

  2. The adjectival term τ may be an adjective phrase, as for example, ‘sleepless in Seattle’.

  3. Does ‘x is a horse’ stand for anything absolutely, i.e., not relative to a value-assignment? One could say (as some do) that the open sentence stands for a function from value-assignments to truth-values. This manner of speaking is misleading at best. It is better to say that an open expression designates only under an assignment of values to variables (or at least of values to the formula’s free variables).

  4. Cf. my “Naming, Necessity, and Beyond” (2003); and “Are General Terms Rigid?” (2005).

  5. In R&E I raised the question, but remained neutral, whether kinds having the same metaphysical intension are ipso facto the same kind (p. 53, n. 9). Teresa Robertson has formulated an interesting puzzle in “A Puzzle about Kinds” (unpublished). Robertson’s observations have helped to persuade me that there are numerically distinct kinds that exactly coincide in metaphysical intension. (R&E adopted an artificial use of ‘designate’, which I do not now favor, according to which a general term, τ, designates each of the kinds, categories, etc. whose metaphysical intensions coincide with the semantic intension of the corresponding predicate ⌜is τ⌝.).

  6. Putnam (1975).

  7. Kaplan (1973).

  8. Cf. my “Are General Terms Rigid?” at footnote 23.

  9. Cf. my “The Logic of What Might Have Been” (1989).

  10. Cf. R&E, pp. 42–48, and passim; Salmon (1986/1991).

  11. Kaplan (1978); and my “Demonstrating and Necessity” (2002); also in Davidson (2007).

  12. As should be obvious (notwithstanding modern-day attempts to assimilate the two), the demonstrative use of ‘that’ is very different from the ‘that’-clause-forming use, certainly as far as their logic is concerned.

  13. Cf. my “Demonstrating and Necessity.” It is controversial that demonstratives are directly referential, but it should not be.

  14. Cf. my “A Theory of Bondage” (2006).

  15. For reasons related to this, Alonzo Church’s lambda-abstraction operator, as it occurs in ⌜(λα)[\( \phi_{\alpha } \)]⌝ where \( \phi_{\alpha} \) is an open sentence, is susceptible of a contextual definition. The latter is defined to be just this: ⌜ is-a{(θα)[\( \phi_{\alpha } \)]}⌝. It thus emerges that the theta-abstraction operator is a more basic variable-binding operator than the predicate-abstraction lambda operator. The predicate-abstraction use of ⌜(λα)[…]⌝ amounts to ⌜ is-a{(θα)[…]}⌝. Cf. R&E, p. 51.

References

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  • Kaplan, D. (1973). Bob and Carol and Ted and Alice. In K. J. J. Hintikka, J. M. E. Moravcsik, & P. Suppes (Eds.), Approaches to natural language (pp. 490–518, at p. 518, n. 31). Dordrecht: D. Reidel.

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Authors and Affiliations

  1. Department of Philosophy, University of California, Santa Barbara, CA, 93106, USA

    Nathan Salmon

  2. Program in Philosophy, The Graduate Center, City University of New York, New York, NY, USA

    Nathan Salmon

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Correspondence to Nathan Salmon.

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The present paper was delivered as a “magisterial lecture” at the XV National Congress of Philosophy in Buenos Aires, Argentina, December 2010. I am grateful to the conference hosts and for my audience’s reactions. I am especially grateful to Teresa Robertson for extremely fruitful discussion, and for much else.

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Salmon, N. Generality. Philos Stud 161, 471–481 (2012). https://doi.org/10.1007/s11098-011-9772-8

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