This is a preview of subscription content, log in via an institution to check access.
Notes and references
P. F. Strawson, “On Referring,”Mind 59 (1950), pp. 324–344.
B. A. W. Russell, “Mr. Strawson on Referring,”Mind 66 (1957), pp. 385–389.
K. Donellan, “Reference and Definite Descriptions,”Philosophical Review 75 (1966), pp. 281–304.
S. A. Kripke, “Speaker's Reference and Semantic Reference,” in P. French, T. Uehling, and H. Wettstein, eds.,Contemporary Perspectives in the Philosophy of Language (Minneapolis: University of Minnesota Press, 1979).
G. M. Wilson, “Reference and Pronominal Descriptions,”Journal of Philosophy 88 (1991), pp. 359–387. Wilson's argument, like Hans Kamp's “Discourse Representation Theory,” focuses on semantic features of discourse that go beyond sentence boundaries.
W. V. Quine, “On What There Is,”Review of Metaphysics 2 (1948), pp. 21–28; most familiar reprinting in Quine'sFrom a Logical Point of View (Cambridge MA: Harvard University Press, 1953).
Question for historians of ideas: is it conceivable that the Ramsey who introduced Ramsey sentences might have been influenced in his logical thinking by Russell?
Cf. D. M. Armstrong,A Combinatorial Theory of Possibility (Cambridge UK: Cambridge University Press, 1989), which, however, only defends the thesis for alethic modalities.
In Appendix A to his “Opacity,” in E. Hahn and P. A. Schupp, eds.,The Philosophy of W. V. Quine (La Salle: Open Court, 1986). For the development of Montague's thought on unicorns, see under “unicorn” in the index toFormal Philosophy.
Footnote 12 to “Bob and Carol and Ted and Alice,” in K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes, eds.Approaches to Natural Language (Dordrecht: Reidel, 1973). At the time, I wrote to Kaplan asking for more details on the general theory of quantifying out, which I thought might be relevant to the semantics of donkey sentences, and he wrote back that he had no general theory beyond that of actuality operators.
Various of Quine's papers have been reprinted inFrom a Logical Point of View and hisWays of Paradox (New York: Random House, 1966); his earliest publication on the subject seems to be the 1943 “Notes on Existence and Necessity” (Journal of Philosophy 40, pp. 113–127), which was reprinted in Leonard Linsky's early and influential anthologySemantics and the Philosophy of Language (Urbana, University of Illinois Press, 1952).
For treatments of the actuality operator and related devices, see the three papers by H. Hodes inJournal of Philosophical Logic 13 (1984) or, for a brief summary, A. P. Hazen, “Actuality and Quantification,”Notre Dame Journal of Formal Logic 32 (1991), pp. 498–508. For a short and well-motivated introduction to two-dimensional modal logic, see B. C. Van Fraasen, “The Only Necessity is Verbal Necessity,”Journal of Philosophy 74 (1977), pp. 71–85.
This is most plausible when the intensional operator is an impersonal one like (alethic) possibility. Since it is not at all obvious that we humans can understand (quantifications of) infinite conjunctive propositions, doxastic analogues of (A) are more problematic.
And similar devices, like the “actuality quantifiers” discussed in Hazenop. cit. Published proposals for eliminating actuality operators in favor of something like infinite conjunction include P. Bricker, “Quantified Modal Logic and the PluralDe Re,” in P. A. French, T. E. Uehling, and H. K. Wettstein, eds.,Midwest Studies in Philosophy XIV: Contemporary Perspectives in the Philosophy of Language II (Notre Dame: University of Notre Dame Press, 1989), and R. Teichman, “Actually,”Analysis 50 (1990), pp. 16–19.
A. McMichael, “A Problem for Actualism about Possible Worlds,”Philosophical Review 92 (1983), pp. 49–66; M. J. White, “Harmless Actualism,”Philosophical Studies 47 (1985), pp. 183–190, and M. Losonsky, “No Problem for Actualism,”Philosophical Review 95 (1986), pp. 95–97. The “stipulational semantics” outlined in the appendix to A. P. Hazen, “Counterpart-Theoretic Semantics for Modal Logic,”Journal of Philosophy 76 (1979), pp. 319–338 offers (for those actualists willing to accept the ontological commitments of set theory) a treatment of iterated modalities that escapes the ontological objections to possible worlds with non-actual constituents. Apart from extreme complexity, however, it makes the interpretation of a clause depend on the number of operators in whose scopes it is embedded in ways that neither Russell nor most contemporary actualists have considered.
Fans of the sperm- and-egg tradition of essentialism argument will enjoy constructing examples in which it is metaphysically impossible for there to be a Russellian proposition for the embedded operator to apply to.
D. K. Lewis,On the Plurality of Worlds (Oxford: Blackwell, 1986), pp. 158–165.
Cf. H. Kamp and U. Reyle,From Discourse to Logic, forthcoming.
Cf. the discussion in F. B. Fitch,Symbolic Logic: An Introduction (New York: Ronald Press, 1952), pp. 76–77, where an account of counterfactual conditionals as nomically necessary material ones with false antecedents is suggested.
For relevance logics this has been proven: cf. R. K. Meyer, “Entailment is not Strict Implication,”Australasian Journal of Philosophy 52 (1974), pp. 212–231. I don't know of a corresponding impossibility proof for the counterfactual logics, but it seems overwhelmingly unlikely that the features of the “variably strict” conditionals of these logics could be captured through the use of any monadic operator applied to any truth function.
Anyone wishing to interpret my use of the wordsituation here as constituting a generalized reference to the works of Barwise and Perry is free to do so. This treatment of (C) could also be taken as inspired by D. K. Lewis, “Adverbs of Quantification,” in E. L. Keenan, ed.,Formal Semantics of Natural Language (Cambridge: Cambridge University Press, 1975).
Cf. Edelberg's discussion of the (G) examples, below, which has influenced my thinking about the (D) examples.
A. Bressan,A General Interpreted Modal Calculus (New Haven, Yale University Press, 1972). For another discussion of the role of individual concepts in modal semantics, cf. R. H. Thomason, “Modal Logic and Metaphysics,” in K. Lambert, ed.,The Logical Way of Doing Things (New Haven: Yale University Press, 1969).
For (E), cf. his “A New Puzzle about Intentional Identity,”Journal of Philosophical Logic 25 (1986), pp. 1–25; for (G), his “A Case for a Heretical Deontic Semantics,”Journal of Philosophical Logic 20 (1991), pp. 1–35.
What does it mean to classify a non-alethic operator as necessity-like? Devotees of possible-worlds semantics will note that they are the operators whose satisfaction clauses involve universal quantification over accessible worlds; more syntactically minded logicians will note that they are the operators that distribute over conjunction. There is a deep connection between the two characterizations: cf. J. M. Dunn, “Gaggle Theory: an Abstraction of Galois Connection and Residuation with Applications to Negation and Various Logical Operations,” inLogics in AI, Proceedings European Workshop JELIA 1990 (LNCS v. 478) (Berlin: Springer-Verlag, 1991).
A comprehensive bibliography would be out of place and a non-comprehensive one invidious. T. Parsons,Nonexistent Objects (New Haven: Yale University Press, 1980), probably did as much as any one publication to convince the general logical public that such ideas were not the exclusive property of a lunatic fringe and might have applications.
I am not convinced that objects individuated by their properties are appropriate to some of the other tasks Meinongiana have been invoked for, either. It is, for example, not clear to me that we would want to say of two cultures which have evolved their religions independently of one another that they worship the same god, even if their theologies/mythologies attribute precisely the same list of properties to their deities.
The similarity between the Fregean and Meinongian “disorderly elements” is underlined by E. Zalta's proposal, in hisIntensional Logic and the Metaphysics of Intensionality (Cambridge MA: MIT Press, 1988), to construe them as species of a common genus.
As to applications elsewhere: the direct reference theorists hold that neitherLondres norLondon has a characterizing, Fregean,Sinn, but Descartes, who was happy to admit to having two ideas of the sun, one derived from the senses and one from astronomical theory, would surely have been willing to allow Puzzling Pierre two ideas of an English city.... My student Stephen Barker has also pointed out that there are resemblances between the individual concepts invoked in treating quantifying out and the arbitrary or generic objects of K. Fine'sReasoning with Arbitrary Objects (Oxford: Blackwell, 1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hazen, A.P. On quantifying out. J Philos Logic 24, 291–319 (1995). https://doi.org/10.1007/BF01344205
Issue Date:
DOI: https://doi.org/10.1007/BF01344205