David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 5 (1):25--46 (1976)
The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Alessandro Torza (2013). How to Lewis a Kripke-Hintikka. Synthese 190 (4):743-779.
Allen P. Hazen, Benjamin G. Rin & Kai F. Wehmeier (2013). Actuality in Propositional Modal Logic. Studia Logica 101 (3):487-503.
I. L. Humberstone (1982). Scope and Subjunctivity. Philosophia 12 (1-2):99-126.
Harold T. Hodes (1984). Some Theorems on the Expressive Limitations of Modal Languages. Journal of Philosophical Logic 13 (1):13 - 26.
Lloyd Humberstone (2008). Béziau's Translation Paradox. Theoria 71 (2):138-181.
Similar books and articles
Ernst Zimmermann (2003). Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12 (1):99-117.
Paolo Gentilini (1993). Syntactical Results on the Arithmetical Completeness of Modal Logic. Studia Logica 52 (4):549 - 564.
J. F. A. K. Benthem (1980). Some Kinds of Modal Completeness. Studia Logica 39 (2-3):125 - 141.
D. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.
George Gargov & Valentin Goranko (1993). Modal Logic with Names. Journal of Philosophical Logic 22 (6):607 - 636.
Balder Ten Cate (2005). Interpolation for Extended Modal Languages. Journal of Symbolic Logic 70 (1):223 - 234.
Patrick Blackburn & Maarten Marx (2002). Remarks on Gregory's “Actually” Operator. Journal of Philosophical Logic 31 (3):281-288.
Wiebe Van Der Hoek & Maarten De Rijke (1993). Generalized Quantifiers and Modal Logic. Journal of Logic, Language and Information 2 (1):19-58.
Maarten De Rijke (1992). The Modal Logic of Inequality. Journal of Symbolic Logic 57 (2):566 - 584.
Added to index2009-01-28
Total downloads59 ( #25,428 of 1,098,973 )
Recent downloads (6 months)8 ( #27,099 of 1,098,973 )
How can I increase my downloads?