David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 20 (2):205 - 223 (1991)
Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the “one quantifier at a time” way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed “treat one quantifier at a time”, if not “in first-order fashion”: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the “depending only on” idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB See  for a start on a semantics aspiring to handle sentences like (6) without invoking abstract objects. See also my comments on its notion of dependence, in . . So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim
|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
No citations found.
Similar books and articles
G. Y. Sher (1997). Partially-Ordered (Branching) Generalized Quantifiers: A General Definition. [REVIEW] Journal of Philosophical Logic 26 (1):1-43.
Nina Gierasimczuk & Jakub Szymanik (2009). Branching Quantification V. Two-Way Quantification. Journal of Semantics 26 (4):329-366.
Jon Barwise (1979). On Branching Quantifiers in English. Journal of Philosophical Logic 8 (1):47 - 80.
Thomas Müller (2012). Branching in the Landscape of Possibilities. Synthese 188 (1):41-65.
Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
Michael Hand (1993). A Defense of Branching Quantification. Synthese 95 (3):419 - 432.
Jiri Benovsky (2005). Branching Versus Divergent Possible Worlds. Kriterion 19 (1):12-20.
Tom Patton (1989). On Humberstone's Semantics for Branching Quantifiers. Mind 98 (391):429-433.
Charles F. Kielkopf (1977). Quantifiers in Ontology. Studia Logica 36 (4):301-307.
Gila Sher (1990). Ways of Branching Quantifers. Linguistics and Philosophy 13 (4):393 - 422.
Added to index2009-01-28
Total downloads3 ( #344,841 of 1,692,491 )
Recent downloads (6 months)1 ( #184,284 of 1,692,491 )
How can I increase my downloads?