Summary of changes to Raising and Resolving Issues with Scalar Modifiers
Comments from the editor
1. The concerns raised by Reviewer B about “at most” and the scope facts are the most
significant at the empirical level. (77) should show formal representations and not simply
paraphrases; like Reviewer B, I find that the paraphrase for the authoritative reading does
not match my intuitions about what this reading entails, but without explicit
representations, we cannot be sure what your analysis exactly predicts. You need to work
through derivations for the scope facts, including with “at most”, in sufficient detail for
the reader to see that in fact your analysis works at least as well as or better than other
analyses on this point. Otherwise it is a bit odd to devote so much space to critiquing
Geurts & Nouwen's modal concord analysis.
Response: Thank you. This is partly related to the fact that we had made a mistake in our
inquisitive analysis of “at most”, and that is fixed now (section 3.3). We have also
discussed the interaction between “may” and “at most” in much more detail (section 3.5).
2. Reviewer C observes that your analysis and Büring’s are deeply similar but you seem
to derive the ignorance implicature in different ways. You suggest that your way of
deriving it is less stipulative. This may be true, but it is not obvious. You mention at the
end of 4.1. that you avoid having to posit a “specialized implicature schema for
disjunction”, but from what I know about the way implicatures are derived for
disjunction, the way in which it is done does not seem particularly stipulative. Perhaps I
am missing something here, but I do not think you can dispense with this issue as quickly
as you do in 4.1.
More generally, it would strengthen the paper significantly to contrast whatever
interesting advantages there might be between using Inquisitive Semantics to capture the
implicature over more classical pragmatic ways of doing so. If the two approaches end up
not differing in overall empirical adequacy, this would also be worth discussing – it
would mean that the decision as to which approach to adopt would depend on other
criteria, but it might also have interesting implications for the treatment of implicatures
more generally in Inquisitive Semantics. Either way, I think the paper needs to address
this general issue more explicitly in order to have more theoretical bite. Note as a detail
in relation to this general point that the account of the difference between “at most 5” and
“more than 4” is rather dense – it would help if you reminded your reader why (58)
comes out denoting a singleton.
Response: We have explained in more detail in Section 3.1 why Büring’s implicature
schema doesn’t actually work for “at least”. The problem is that the only level at which
“at least” sentences are disjunctions on Büring’s analysis is in the meta-language, and
implictures cannot depend on the syntactic formulation of the theory in the metalanguage. We have also clarified exactly in what sense our Maxim of Interactive
Sincerity is more general than Büring’s implicature schema (just underneath the
definition of the Maxim of Interactive Sincerity). This maxim is strictly more general
than Büring's implicature schema, because it applies not only to disjunctions, but to
anything that is interactive.
3. Reviewer B raises the question of whether your prediction about extensionality is a
good one. On this point I think you are both partly right. I share your intuition that, in
strictly truth conditional terms, your prediction is a good one, but I also share Reviewer
B’s intuition that the speaker’s epistemic state will not allow him/her to use the two
sentences in (21) in exactly the same contexts (though unlike Reviewer B, I would not
put this in terms of differences in truth). You should have something to say about this, if
only to acknowledge that there is an open issue here that merits a closer look.
Response: We need to distinguish between truth according to an agent and objective
truth. In the reviewer's example scenario, the agent knows that one of the sentences is
true but doesn't know that the other one is true because he/she has partial knowledge. But
given full knowledge of the situation, the sentences are both true; i.e., they are equivalent
vis-à-vis objective truth. We have attempted to explain this more carefully pp. 10-11.
4. At the rhetorical/organizational level, I sometimes had trouble feeling like I knew what
your primary goal in the paper really is. Are you most concerned about improving upon
existing analyses of “at least”/“at most”, or about showing how the Inquisitive Semantics
analysis can shed new light on these expressions? The answer to this question is
important because, while I understand that of course you are interested in achieving both
of these goals, choosing to prioritize one over the other will affect the details of how the
discussion proceeds.
This lack of clarity manifests itself in an especially visible way in the discussion up to
section 3. If your main goal is to make a case for an improved analysis of superlative
quantifiers, the result is not very convincing insofar as you do not discuss any alternative
analysis in enough detail to make it clear exactly what the fundamental problems are. If
your goal is to make a case for an Inquisitive Semantics account, then a better
introduction to this framework and a general characterization of how it will improve the
analysis of superlative quantifiers should be presented much earlier, so as to orient the
reader. A clearer and more explicit exemplification of how the analysis works in sections
3.4 and especially 3.5 is also necessary. Whichever goal you are ultimately most
interested in, I find that the early part of the paper is too heavily focused on “only”, when
“only” is only relevant to the extent that it serves to motivate your analysis of “at least”
and “at most”. But you could just as easily start with the latter analysis as a given and
refer to the work on “only” that motivates it, rather than discussing the latter.
Response: The goal is to give the best possible analysis of “at least” (and we think that
Inquisitive Semantics does that...) To make this clearer, we have included an overview of
the data to be accounted for in the introduction, and made the relationship between only
and superlative modifiers less prominent. We have also added more detail regarding other
theories in the “comparison with other theories” section.
Some more minor comments:
1. About (22): Though their dynamic semantics is obviously different, I actually have
some trouble imagining how someone who responds, “That’s false” to them would then
continue so as to make clear what the differences in truth conditions are. “I disagree”
seems like a much more natural response. You might think a bit more about this.
Response: Interesting. This seems to be because what "should" and "shouldn't" be the
case is more a matter of opinion than a matter of objective truth. Sentences with deontic
modals may be interpreted more like statements of moral judgments and sentences with
predicates of personal taste, where faultless disagreement is possible. Such sentences may
have only agent-relative truth conditions, as the relativists would say. Nevertheless, such
sentences do seem to give rise to logical entailments, which can be brought out by the
following contrasts.
John should at least invite [the postdoc]_F to lunch.
Hence, John should invite someone to lunch.
#Hence, John should invite the postdoc to something.
John should at least invite the postdoc to [lunch]_F.
#Hence, John should invite someone to lunch.
Hence, John should invite the postdoc to something.
The fact that their entailments are different shows that their (possibly agent-relative) truth
conditions are different.
2. First sentence of 3.2: Instead of “Traditionally”, I would say something like “Under
most analyses” (which is not the same thing). I would not characterize e.g. Jonathan
Ginzburg’s approach to questions in the terms that you refer to as “traditional”, though by
now it has quite a long history.
Response: The distinction we are getting at here is the distinction between "classical"
and "inquisitive" semantics for declarative sentences; we should have used the term
"classical" instead. That is changed now.
3. Below (61), though I suppose you mention Kennedy’s (2012) analysis because you are
using it, it seems odd that it is the only two-sided analysis of numerals that you cite in
this part of the discussion, given the huge debate that numerals have generated in the
scalar implicature literature and the existence of other two-sided analyses.
Response: Point taken! We have now just cited Kennedy (2012) for an overview of the
one-sided/two-sided issue. (Furthermore, we don't even rely on the two-sided analysis.
We have changed the rhetoric to show that our analysis works whether we take a onesided or two-sided analysis.)
4. Re (67): Intuitively, it’s not obvious to me that the themes are “John should at least
invite someone to lunch” and “John should at least invite the postdoc to something”.
Couldn’t the themes be these without the “at least” in them? And if so, would that make a
difference?
Response: Thank you, that must be right, because the QUD that “at least” relates to
consists of answers that do not consist of “at least”. Fixed.
5. Here’s a data point to think about. My intuitions are that “at most” is not as
polymorphic as “at least” – I have trouble with it in combination with adjectives, e.g.
“She will be at most satisfied with the results”, though I can say things like “At most she
will be satisfied with the results” (though curiously the effect of the superlative on the
interpretation is rather different from what you get in “At least she will be satisfied with
the results”: with the latter, I can’t get association with a focus on “satisfied”). I’m not
sure how significant these differences are, but given that you defend a fully generalized
analysis of these expressions, you should take a stand on them, if only in a footnote. Note
also that, though it addresses a different issue, you might find the reply to Nouwen 2010
by Schwarz, et al. in the most recent volume of S&P relevant reading.
Response: We do not know how to explain this contrast, unfortunately. We have
admitted this in footnote 4.
6. Finally, as someone who is not particularly a specialist in this literature, I found the
paper unnecessarily difficult reading in several places. At various points you make use of
notation from other work without defining it (Reviewer B points out a couple of
examples, to which I would add the notation for the semantics of the modal in (29-30)),
and in a few places you make rather cryptic references to analyses in other works (e.g. the
reference to Beaver and Clark in footnote 1, the initial mention of Büring at the top of p.
6, or the discussion of highlighting in section 3.4.2, where clarification is essential to the
intelligibility of the argumentation). You also start using various assumptions about focus
and the QUD without making any initial presentation whatsoever of these notions;
overall, the notion of QUD gets rather short shrift in the paper, considering the
importance you seem to give it. Here, some clear, formal definitions would help. Note
also the comments made by Reviewer A concerning the non-standard or simply not
explicitly defined terminology and notation related to the Inquisitive Semantics part of
the paper. These points should be clarified, both to avoid confusion and to make the
paper more accessible to a broader audience.
Response: We have introduced the notion of QUD and explained how it relates to focus
earlier on in the paper, and we have significantly revised our terminology regarding
inquisitive semantics, which was actually not correct in the previous version. We have
made an effort to explain all of the other notation in the “comparison to other
approaches” section as well.
Reviewer A
Overall recommendation. The paper presents a new account of at least and at most. The
account brings together ideas from recent work on exclusives with ideas from inquisitive
semantics, in an original and insightful way. The paper seems well-situated in the
existing literature on at least and at most (although I must note that I am not a specialist
in this area), and to improve considerably on previous accounts. Both in terms of topic
and in terms of approach and methodology, the paper is likely to be of interest to many
S&P readers. Thus, my overall recommendation is to accept the paper for publication,
modulo some minor revisions. Some more specific comments are provided below.
10. p.10 I have one worry here that may be quite serious: if you need to give at least
three books wide scope with respect to the modal in order to get the speaker insecurity
reading, aren’t you bound to end up with a de re reading (there are at least three books
such that. . . )? This is also a possible reading, but you should also be able to get the de
dicto reading. How are these two readings derived?
Response: Good point. We have to assume Kennedy’s degree-quantifier analysis of
numerals, and let “at least three” undergo QR in order to avoid the de re reading. We
have spelled this out in the present version.
14. p.12 the term ‘issue’ is used here for a proposition containing more than one
possibility. In other work on inquisitive semantics where the term ‘issue’ is used as a
technical term, it is used differently. See for instance Ciardelli et al. (2012). It would be
preferable to avoid this incompatibility of terminology.
Response: Thanks. Done.
15. p.12 Sentences are defined here to be inquisitive just in case they express a
proposition consisting of more than one possibility. In previous work on inquisitive
semantics, a sentence φ is normally defined as being inquisitive just in case info(φ) ∈
[φ], which is not equivalent with the definition assumed here. It would be good to adopt
the standard definition, or to argue explicitly that a different notion than the standard one
is needed.
Response: Thank you. We have made it clear that we are using the “unrestricted” version
of inquisitive semantics and have attempted to make our terminology consistent with
those definitions. We have also introduced the term “interactive” as a cover term for
“inquisitive” and “attentive”, since that is really what we were getting at.
1. p.1 are inquisitive ⇒ as inquisitive [done]
2. p.4 rephrase second sentence of second paragraph
3. p.4 just define states as partially ordered sets of possibilities (partial orders are
reflexive, transitive and anti-symmetric). [done]
4. p.6 and it not ⇒ and is not [done]
5. p.8 the Focus Principle should be stated earlier, as part of the account,
not when the account is evaluated [done]
6. p.8 CQ ⇒ QUD [done]
7. p.10 The parts of the paraphrases in (28) that are in brackets are unclear. [fixed]
8. p.10 More detail is needed in deriving the readings in (29) and (30). It is not exactly
clear how the syntax is supposed to be mapped to the given semantic values, and how
these values correspond to the intended readings. [done]
9. p.10 when when ⇒ when [done]
12. p.12 to explain it ⇒ to explain the contrast [done]
13. p.12 it is nonsense to ⇒ it does not make sense to [done]
16. p.13 useful propositions ⇒ useful possibilities [done]
17. p.14 multiple possibilities, therefore inquisitive ⇒ see remarks above [done]
18. p.15 The text refers to the informative content of a sentence, but this notion has not
been defined. The standard definition from inquisitive semantics can be adopted. [done]
19. p.15 definition (48). I think that k ∪ q should be k ∩ q. It is unclear to me why p
should be non-empty. An easier formulation of P restricted to k would be {p ∩ k | p ∈ P
}. [done]
20. p.16 The formulation of the inquisitive sincerity maxim is slightly different from the
formulation of this maxim in previous work (if φ is inquisitive relative to the current
common ground, then it should also be inquisitive relative to the speaker’s information
state). [done]
21. p.16 So we will use ⇒ We will use [done]
22. p.17 for our inquisitive setting, like so ⇒ for our inquisitive setting [done]
23. p.17 The notions of drawing attention to a possibility and highlighting a possibility
are used exchangably here. In previous work on inquisitive semantics, these are two
distinct notions. Both may be relevant for the purposes of the present paper, each in their
own way. [done]
24. p.18 denied on the grounds ⇒ can be denied on the grounds [done]
25. p.19 such that w contained ⇒ such that w is contained [done]
26. p.20 ‘the truth conditions are the same’ ⇒ it is crucial here that the notion of
informative content is explicitly introduced and discussed earlier, also see comments
above. [done]
27. p.20 captures this focus-sensitivity ⇒ captures focus-sensitivity [done]
28. p.23 fact superlative modifiers ⇒ fact that superlative modifiers [done]
29. p.25 the paraphrases in (78a) and (79a) are unclear [removed]
30. p.25 The discussion below (78-79) is very difficult to follow. I think some cross
references are off, and the speculative account of (79) is too sketchy in its current form.
Perhaps it would be better to explicitly acknowledge that there is an open issue. [fixed]
31. p.26 they say that the conjuncts ⇒ G&N say that the conjuncts [done]
32. p.26 toward and explanation ⇒ toward an explanation [done]
33. p.27 Geurst notes ⇒ Nouwen notes 34. p.28 acknoledging ⇒ acknowledging [done]
35. p.28 quantity implicatures ⇒ exhaustivity implicatures [done]
36. p.28-30 several references are incomplete
Reviewer B
I've enjoyed reading this. The paper offers an exciting thought: superlative quantifiers are
not just focus-sensitive rank-order operators, they are furthermore inquisitive. This is a
fun route to take, and the authors have succeeded in convincing me that this line of
analysis is worth considering. However, the paper ultimately fails to deliver, given that
the analysis of some crucial aspects of superlative quantifiers are not worked out. In
particular, the authors do not show when ignorance implicature appear and when they
disappear, nor do they show how the interaction with modals works in the inquisitive
framework. My conclusion is that some more research is needed. Having said that, this
work packs a lot of promise, is of commendable clarity and steers the superlative
quantifier discussion in an interesting direction, especially given the emphasis it lays on
information structure. So I do hope that this material will ultimately be published.
I have two major issues, followed by some minor comments.
1. Extensionality
On page 7, the authors state that one of the advantages of their proposal is that it is
extensional. They support extensionality being a desideratum by claiming that 21a and b
are equivalent:
21a. Mary petted at least three magical beings.
b. Mary petted at least three rabbits.
As far as I can see, whether or not 21 a equals 21 b is very much an empirical question. In
fact, my own intuition is that these sentences are not straightforwardly equivalent in the
situation described on p7. Let me explain why I think they are not: Say that I think that
horses and rabbits are magical animals, but in fact (as on p7) only rabbits are magical
animals. Also, I'm sure that Mary petted three rabbits, but I am not sure whether Mary
petted a horse or not. In that case, to my intuitions at least, 21a is true, but 21b is false
(or, rather, inappropriate, given the ignorance implicature). The fact that in the actual
world rabbits and magical animals pick out the same set seems irrelevant. Such reasoning
actually speaks in favour of the Geurts and Nouwen analysis the authors intend 21 to
argue against.
Response: We need to distinguish between truth according to an individual and objective
truth. We have attempted to clarify this on pp. 10-11.
2. Embeddability
Section 2.6 (p10) offers an account of how superlative quantifiers interact with modals. I
do not think that the paper delivers here. In fact, I cannot be sure that the authors derive
the correct truth-conditions. Section 2.6 only discusses examples with "at least", but the
difficult cases are the "at most" ones. Consider (i) and its two readings:
(i) John's paper is allowed to be at most 10 pages long.
(i-Aut) the upper page limit = 10
(i-SpI) the speaker is insecure about the upper page limit, but knows it not to exceed 10
If we take a wide scope reading for the modified numeral, we get:
(ii) the maximal number such that John's paper is allowed to be (at least) so long =< 10
In parallel to (29), I suppose this is thought to be the speaker insecurity reading (but see
below). If this is correct, then the authoritative reading, which is by far the most salient
reading for (i), would have to be derived via narrow scope. But then we get (iii):
(iii) it is allowed that [ the number of pages in John's paper =< 10 ]
This is not the authoritative reading, for it is far too weak. In particular, it fails to
introduce an upper bound. If I am correct that this is indeed the authoritative reading the
authors derive, then I do not see an easy fix. (Note that Buering's analysis, which as the
authors acknowledge is very close to theirs, lacks an account of "at most" altogether).
There are more issues with embedded superlative quantifiers. Buering notices that lower
bound superlative quantifiers embedded under existential modals lack an authoritative
reading -- they merely have a speaker insecurity reading. For example:
(iv) You password is allowed to be at least 6 digits long.
cannot be used as an instruction concerning the minimum required number of digits in a
password. Would this follow from the current analysis?
Response: Very fair point. We have addressed these examples in much more detail in the
present version. See especially section 3.5. The non-inquisitive analysis does not deal
with the interaction with modals fully, but the inquisitive analysis gives us an explanation
for the missing readings puzzle. We address de re readings in the inquisitive version in
footnote 7.
Finally, it is not evident that the derived speaker insecurity readings is correct. Speaker
insecurity readings involve epistemic insecurity, authoritative readings do not. In other
words, speaker insecurity readings carry the ignorance implicature, whilst authoritative
readings are cases where this implicature has been obviated. This distinction does not
follow from (29) versus (30). Of course it couldn't anyway since at this stage in the paper,
no mechanism for ignorance has been introduced. This is only done in section 3, where
ignorance is connected to inquisitive sincerity. Unfortunately, on page 20 the authors
confess that "it would be worth considering whether the move to the inquisitive setting
has any impact on the interaction with modality in future research". This is very
disappointing, and I believe the paper misses an important target here. Modals do not just
interact with the scalar meaning of superlative quantifiers, they also interact with the
ignorance implicature in the sense that they have the possibility of obviating the
occurrence of such an inference. As far as I am concerned this is part of the core data any
theory of superlative quantifiers should account for, and it is here where the author's
analysis falls short.
Response: Thank you for pushing us to investigate the interaction between inquisitivity
and modality. It helped us realize that the inquisitive theory actually does explain the
missing readings puzzle. We think the paper is much stronger now, with section 3.5.
3. Minor comments:
p 1. and 2., discussion concerning (1) and (2): These examples illustrate the role rank
orders play, but they do not say anything about the need to postulate a question under
discussion. The usefulness of a QUD for semantics should be defended a bit more
carefully. [done]
p 5., exx (8)-(10): I thought some more illustration would be handy, for instance by
applying (10) to one of the propositions on page 4. [moot]
p 6, middle: The types d and p should be introduced. [check]
p 7, just below (18), also elsewhere: "CQ" Is this the same as QUD? It's never properly
introduced. [fixed]
p 7: The assumption on this page is that the ranking for numeral sentences is p2 [moot]
Reviewer C
As the As themselves point out, the paper is very close to Buering’s theory (and I should
note that their view is also close to Cumnins and Katsos’s paper, which they fail to cite).
The current paper can therefore be seen as a way to represent the notion that superlative
modifiers express disjunction directly in the semantics.
While Buering presumably must assume some sort of intermediate representation (which
triggers implicatures), the As represent disjunction at the level of interpretation, using
Inquisitive Semantics. That’s a worthwhile idea, and it certainly merits exploring.
Yet it suffers from problems. Buering derives the implicature of ignorance directly from
the properties of disjunction, since it is well established that disjunctions implicate
ignorance. In contrast, the As must use constraints specifically devised for Inquisitive
Semantics. They claim this is an advantage, but I fail to see why. Even if these
constraints are independently motivated, as the As claim, surely they are not as well
established as the implicatures of disjunction.
Response: In our theory, superlative modifiers do not actually express disjunctions,
although they are like disjunctions in that they are inquisitive. The maxim of inquisitive
sincerity applies to all inquisitive propositions, not just disjunctions, so it is therefore
more general. We have made an effort to make this much clearer.
Another problem, common to both Buering and the current paper, is the handling of
embedding. Both would predict that superlative modifiers are freely embeddable, which
is contrary to fact. Geurts & Nouwen try to account for the embedding facts by
representing superlative modifiers as epistemic modals, whose embeddability is restricted
in certain ways; Cohen & Krifka argue that superlative modifiers are speech acts, and
they are embedded in just those environments in when a proposition can be derived from
them (hence, contrary to the As’s claim, they do not require the embedding operators to
be illocutionary operators themselves). However, the As say nothing about this important
issue; strangely, this is the case although the paper has a section titled “Embedding”—but
it deals with a different issue.
Response: Thank you. We have added a discussion of this issue in the section on Cohen
and Krifka. It is true that we have not said anything to explain why superlative modifiers
should resist embedding under negation, and Cohen and Krifka do offer an explanation of
that. We have argued that the Cohen and Krifka account is overly restrictive in this
respect, and have added a speculation that the relevant factor may be whether or not the
prejacent is relevant enough to be explicitly mentioned.
In [the first] part [of the paper], the As argue that superlative modifiers are evaluated with
respect to the QUD. They claim that this is necessary in order to explain their use with
non-entailment scales, and their focus sensitivity; and that competing approaches cannot
do this. However, both claims are far from convincing.
Regarding focus, all competing theories require some mechanism for associating the
superlative modifiers with some element in the sentence, and this mechanism might very
well be focus.
Regarding non-entailment scales, all competing approaches to superlative modifiers I am
aware of use the notion of being higher or lower on a scale; there is nothing that requires
the scale to be an entailment scale. This claim is particularly strange given the fact that
the main example the As use for tnon-entailment scale is taken (as the As acknowledge)
from one of the very papers they critique for being unable to account for this
phenomenon.
It is quite plausible that superlative modifiers are evaluated with respect to the QUD (it
could be argued that almost all utterances are so evaluated), but, even if true, this fact
would not carry the explanatory burden that the As claim for it.
Response: Points taken. Nouwen (2010) is the only competing theory that doesn’t predict
focus-sensitivity. We have de-emphasized this as an advantage. Regarding nonentailment scales: Nouwen’s (2010) analysis works only for numbers, but none of the
scalar analyses are restricted to entailment scales, as you point out. However, Geurts and
Nouwen have to adjust their theory for non-entailment scales.