The Logical Structure of English Quantifiers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper is a straight-forward collection of a number of results on quantification that Ed Keenan has produced over the years, which are scattered throughout the literature.  It is very pedagogical in nature, and is written engagingly and is easy to understand.  The abstract foreshadows the paper quite accurately.  These results are interesting, and underscore the message that object quantifiers might be more than just subject quantifiers which happen to be in object positions.  This is a message that is quite relevant to the field, despite the fact that most people simply assume it to be otherwise.  
* Minor errors:
- page 2 ::
  - line 68 :: there is a right bracket next to B, instead of the desired cardinality symbol
  - line 71 :: a closing parenthesis is missing after many
- page 3 ::
  - lines 91-93 :: why is the subject enclosed in brackets in 7a, but not in 7b or 7c?
  - line 99 :: open parenthesis before Paperno is never closed.
- page 13 ::
  - line 570 :: 'naturaleness' has one 'e' too many
- page 20 ::
  - line 897 :: (66a) should be (65a)
  - line 898 :: (66b) should be (65b)

Author Response

All 7 remarks were typographical in nature:  All have been handled in the corrected text consistent with the reviewer's recommendations (plus one other not noticed by any of the reviewers).

Reviewer 2 Report

Comments and Suggestions for Authors

If one accepts the paper's assumptions (about subject quantifiers), the argument against the textbook understanding of object quantifiers is rigorously and convincingly presented. It provides clear and detailed criteria (in eight points), a comparison class, and a plentitude of examples. I find the technical exposition excellent and the conclusion as far as object quantifiers are concerned convincing. 

What I miss, however (but this may go beyond what can be excepted of an article like this), is more of an engagement with critical literature that questions whether even an enriched Boolean model can adequately capture subject quantification. The article gives the impression that the subject side is ultimately unproblematic (overlooking that common usage of "overtly deviating" expressions often carries connotations that cannot even be captured by the enriched/extended analysis offered in the paper). By contrast, the treatment of quantifiers in object position seems to honour to a greater extent “ordinary usage” conditions. Because of this the paper’s claim of an „asymmetry" may reflect not so much a linguistic fact as a deficiency in the Boolean model itself: a reductive Boolean framework may already be too restrictive for the subject side, an aspect that becomes evident in its shortcomings on the object side. Having said this: 

The paper, as it is, is an interesting and very valuable contribution to the philosophical debate. For readers who accept the Boolean analysis of subject quantifiers, it should be utterly convincing; for those who question the starting point of the paper it raises important questions  concerning the actual source of the noted “asymmetry”.

Attention: "In the Einstein quote 'Raffiniert ist der herr gott…'(line 705)  there is a mistake. In German, nouns are capitalized, plus it seems that the quote should read: "Raffiniert ist der Herrgott … ."

 

Author Response

Remark 1:  Questions the adequacy of an enriched Boolean model for subject quantifiers, claiming that I give the impression that "the subject side is ...unproblematic".    Claims that the treatment of object quantifiers honors "ordinary usage" to a greater extent and "should be utterly convincing for those who accept the Boolean analysis of subject quantifiers" but that  But for those who don't it raises questions concerning the source of the subject/object quantificational asymmetry:  Might it not perhaps be due to deficiencies in the Boolean model itself?

 

   Responses to Remark 1:

1. I started to agree with Reviewer 2 on this point, and it's true that I do not question the adequacy of the treatment of subject quantifiers. But on rereading the paper I see that I provide a significantly greater range of subject quantifiers than of specifically object ones (roughly 15 pages as opposed to 9 pages).  I think that the classes of subject quantifiers I discuss is richer than anywhere else in the literature (though a few in Keenan's "Beyond the Frege Boundary" I haven't repeated. 

 

2. So I'm contrasting object quantifiers with the natural language quantifiers discussed in the literature (perforce subject ones). I am NOT arguing that the Boolean analysis in my work is a fully adequate treatment of natural language (nominal) quantifiers.  I'm merely supporting that from an extensional, type logical perspective, object quantifiers are much richer than subject ones.  Logicians (Mostowski, Lindstrom) are not primarily concerned to model natural language quantification and do not claim that there is no difference between subject and object quantifiers.  But as I note, linguists (Heim & Kratzer) do make such claims. 
3. I dispute that the Boolean perspective taken in the paper is in any way "reductive". The Subjects are Boolean theorem shows that given a domain E, ANY function of type (et,t) lies in the boolean closure of the generalized existential and universal functions.

   [Note the absence of a comparable theorem for objects!].  So this Boolean perspective does NOT eliminate any subject functions from consideration. 

                              But nothing prevents us from studying non-boolean properties of quantifiers  e.g. ones concerning the "topicality" or "definiteness" of subjects, ones concerning abstract nominalizations (of sentences, Pns, ...), ones concerning properly intensional properties, ones concerning their role in anchoring referentially dependent expressions,...  I am certainly NOT claiming that everything of interest re subject quantifiers can be stated in a boolean perspective.

4. The ultimate source of the subject/object quantifier asymmetry lies in the (obvious) fact that given a domain E with even just a few elements, object functions, ones that map binary relations to unary ones, MASSIVELY outnumber subject functions, ones that map unary relations to truth values. This not a specifically boolean fact, just a general combinatorial one.

                              NB: The reviewer refers to "the common usage of "overtly deviating" expressions".  I'm not sure what expressions these are, but I'd like to know.

 

PS I rather enjoyed thinking out this issue.

 

               Remark 2:  Corrections to the Einstein quote have been made per the reviewer's observation.

Reviewer 3 Report

Comments and Suggestions for Authors

Please see the attachment.

Comments for author File: Comments.pdf

Author Response

Remark 1

               The paper is insufficiently contextualized, making it difficult to decide which claims are the author's and which are due to the literature.

 

Response 1

               In the abstract and introduction I cite specific works that relate to my claims (Most were cited already but later in the article, and one is new).  I assume the paper that the reviewer read did not have my name as author, and a significant amount of the references include me (often as joint author), which should remove worries about distinguishing claims that are mine vs ones given independently in the literature.

 

Remark 2

               The author takes for granted a WYSIWIG approach to syntax  [Me: more exactly to semantic interpretation]. 

 

Response 2

               That is correct, I do, and consonant with the reviewer's recommendation I have made such a claim explicit in the Introduction.

 

Remark 3

               The paper needs a proper introduction  the current introduction presents the structure without contextualizing it and "setting its agenda".  Also at the beginning of each section we need more pointers indicating where we are going.

 

 

 

Response 3

               I have modified the Introduction (slightly) to include explicit references to the literature and added one "pointer" in the subcategory of Unary Comparatives which just started with unintroduced examples.  (But in the subcategories of object quantifiers the bolded subheadings announce what is going to be discussed, so I don't see what further "agenda" I should set).

 

Remark 4:  Function Composition is not limited to adjacent expressions. 

 

Response 4:  Reviewer is correct, FC does not require adjacency and I have modified the text eliminating reference to 'adjacent' and introducing an example of FC (Right Node Raising) which syntactically forces the use we see in the SNS reading above it.  This is a clear improvement over the original text.

 

Remark 5: 

               Reviewer notes that P2s and P1s are not argument-distinct in all respects   unaccusative subjects of some P1s and direct objects of some P2s are comparable (in terms of theta roles).

 

Response 5

               For purposes of logical expressive power the structural difference between P2s and P1s is that P2s have two arguments, whence quantified objects, which take P2s as arguments, may be sensitive to e.g. the one-to-oneness of a P2 interpretation.  P1s only have one argument, so they lack the two arguments necessary to define one-to-oneness conditions, as in Different reporters interviewed different candidates, or Every one likes someone and no two people like the same person.  The actual theta roles of the arguments in my examples are irrelevant.  [Fully comparable to our illustration that the Ss formed from likes can force infinite models, so also can Ss built from P3s like show.  Further, the arguments go through just the same with the passive P2, was shown, even though the subject theta role of was shown is the same as that of one of the objects of show). 

               To respond to Reviewer's query here, nothing in my paper supports that the distribution of quantifiers should be constrained by the theta role of the argument quantified (Actually I never thought about the issue, Hmmm).

               However, the reviewer's remarks here make me realize that, as in Keenan and Westerståhl, I am ultimately treating DPs as functions from the union of n+1 place predicates (sets of n+1-tuples) to the union of n-place predicates (sets of n-tuples) which map each Pn+1 to a Pn.  So a DP like every student takes Pn+1s to Pn's, all n; but a DP like every student but himself maps Pn+2s to Pn+1s, but doesn't map P1s to anything, that is, P1s are not in its domain.  I make this more explicit in the text (Again, thanks for pushing me to make this explicit).

               I might also note that when I say that subject quantifiers extend to object ones I mean "extend" in the mathematical sense in which a function is extended by adding new objects to its domain and saying what the values of the function at the new objects are. I have included this in the text.  (I have lectured in the States at institutions that are supposedly mathematically sophisticated where they thought I contradicted myself when I applied e.g. every student first to laughed and later to praised and I had to explain that if I define the squaring function on the natural numbers I can, without contradiction, extend it to the fractions).  So every student applies, as subject, to both intransitive and transitive verbs (both P1s and P2s).

 

Minor comments

 

1. Abstract: The sense of "extend" has now been explicated in the body of the paper (slightly in the abstract, more thoroughly later, per Response 5 above.

 

2. p. 1: type frequency is intended. I replaced "quantifiers" with "quantifier types in the mathematical literature"
   
   
3. p.3: I inserted ("non-interrogative"), the latter term having already been used.

 

4. p.5: brief raison d'être for the discussion of Existential There contexts added to paper above example (17).

 

5. bottom p. 5: changed "marginal" to "limited" + McCloskey reference. Thanks for the reference (which I read). 

 

6. p.11: I have a slight preference for my (cumbersome) order over that of the reviewer. I find it slightly less incomprehensible. 

 

7. Appendix [1]: The reviewer is correct, the trees I define are the standard ones except they allow for discontinuous constituents. But many of my (American) colleagues and students could not come up with a definition of such trees without study, and I want them to realize how simple it is to simply weaken the definition of the sorts of tree they are used to using to get ones with discontinuous constituents.

 

Typos:

 

The reviewer notes about 20 "typos".  Only two involve more than just brief notational changes, which I have made in accordance with the reviewer's suggestions.  The two are:

 

p.14:  The sentence beginning "Worth emphasizing..." has been slightly simplified. (I didn't find it hard to follow).

 

22. 22. My original sentence was only marginally processable. I have rephrased it.  Thanks

 

                              I'd like to thank Reviewer 3 for a thorough and careful review.  His/her observations clearly improved the readability of the paper.