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Upper-Bounded Scalars and Argumentation-in-Language Theory

Laura Devlesschouwer

Abstracts

Scalar implicatures, such as the ‘not all’-implicature attached to “some”, have been at the center of debates on the semantics-pragmatics interface ever since Horn (1972). The question is whether ‘not all’ is part of the semantics of “some” or rather pragmatically inferred in context. The latter theory, inspired by Grice’s (1975, 1989) work, is by far the more popular one. It analyzes scalars such as “some” as semantically lower-bounded, i.e. as meaning ‘at least some’. I will defend the view that “some” is both lower- and upper-bounded, i.e. on which “some” means ‘some, not all’. In order to do so, I will first propose a distinction between ‘upper bound’ and ‘scalar implicature’, following Ariel (2003, 2004, 2006, 2015). I will thereby defend the idea that scalars such as “some” are semantically upper-bounded, but not that scalar implicatures are semantic. Second, I will give an overview of the most cited arguments against ‘not all’-semantics for “some”: the entailment from “All…” to “Some…”, the non-redundancy of the expression “some, but not all”, the cancelability of scalar implicatures, and the non-paraphrasability of “some” as “some, but not all”. In the discussion of the non-redundancy argument, I will use Anscombre and Ducrot’s (1983) theory of ‘argumentation in language’, which has been largely ignored by pragmaticists working on scalar implicatures. This theory will also permit me to reanalyze some problematic examples presented by Ariel (2015) that have led her to conclude that scalar implicatures with “some” and “most” are rare.

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Author's notes

I would like to thank Philippe De Brabanter, Walter De Mulder, and Philippe Kreutz for fruitful discussions. I also thank two anonymous reviewers for their useful comments.

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Introduction

1 Ever since their introduction by Horn (1972), scalar implicatures (SIs) have received much scholarly attention, in recent years most notably in the field of experimental pragmatics (e.g. Bott & Noveck 2004, Breheny et al. 2006, Degen & Tanenhaus 2016, Van Tiel et al. 2019). They are of particular importance to researchers interested in the semantics-pragmatics interface, because they are elements of meaning which seem conventional, but are not conventional – at least, according to the orthodox, Gricean view.

  • 1 In the following, whenever I talk about “some”, I am talking about its partitive use, not its in (...)

2 It is generally accepted that sentences containing a partitive expression such as “some (of)” 1tend to imply ‘not all’. Consider the following examples:

(1) “I ate some of your cookies”
(2) “I ate three of your cookies”
(3) ‘I did not eat all of your cookies’

3Intuitively, (1) and (2) both seem to imply (3). But logically they do not: if I ate all of your cookies, e.g. four, it is also true that I ate three of them (and that I ate two, and that I ate one) – you cannot eat four without having eaten three. Therefore, the meaning of “three” could not be ‘three and not more than three’, because if “I ate three of your cookies” is true, “I ate four of your cookies” might be true. To reflect this truth-conditional property of “three”, the first neo-Griceans have characterized the literal, semantic meaning of “three” as ‘at least three’ (e.g. Horn 1972, 1989 and Levinson 2000). This is called the ‘lower-bounded’ meaning of “three”, because it only provides a lower bound (the quantity cannot be less than three) but not an upper bound (it may be four, five, ten, thousand, a million, etc.). The same can be said about “some”: if I ate all of the cookies, it is also true that I ate some – one cannot eat all without having eaten some. Therefore, the literal meaning of “some” is considered to be ‘at least some’ rather than ‘some and not all’. This is likewise called a ‘lower-bounded’ meaning, although there is an upper bound (the quantity cannot be more than “all”).

4The ‘not all’-inference, then, is what is called ‘scalar implicature’. On the neo-Gricean view (e.g. Geurts 2010), the inference is made if the utterance would not be informative enough without it, whereas on the post-Gricean view (e.g. Carston 1995, 1998), the inference goes through if the utterance would not be relevant enough without it. On the former view, the ‘not all’-inference is the result of an implicature (scalar implicature), whereas on the latter it is a ‘pragmatic enrichment’ of the logical form of the utterance. But what matters for the purposes of the present paper is that in both theories, it is a context-dependent pragmatic inference, and drawing the inference is equivalent to interpreting the scalar as being ‘upper-bounded’ in context, i.e. interpreting “some” as meaning ‘some, not all’. It is the latter assumption that I will challenge.

5 I will defend the view that it is useful to distinguish ‘upper bound’ from ‘scalar implicature’, following Ariel (2003, 2004, 2006, 2015). Pragmaticists usually use the two terms as synonyms (e.g. van Tiel et al. 2019). Part of Ariel’s proposal is the idea that upper bounds, contrary to scalar implicatures, are included in the lexical semantics of scalar terms. This idea was already implicit in Bultinck’s (2002/2005) work about the numeral “two”, in which he extensively criticized the Gricean ‘at least’-analysis. He mentioned in passing that his theory probably also applies to other scalars like “some” (Bultinck 2005: 99). Criticism of the ‘at least’-view of numerals can already be found in e.g. Löbner (1985) and Koenig (1991). Many pragmaticists nowadays treat numerals differently from other scalars: they view them as having ‘underspecified’ semantics (cf. Carston 1995, 1998) or as having ‘exactly’-semantics (e.g. Marty et al. 2013). These views are different from Ariel’s (2015) and Bultinck’s (2002) upper-bounded view, though.

6I will concentrate on one case (the case of “some”), because it is impossible to address all types of scalars in a single paper, since they all have their own specific semantic and pragmatic properties (cf. numerals, “or”, scalar adjectives like “warm”, etc.). I will leave it to future work to show how the upper-bounded analysis applies to other scalars, but I believe the hearer will be able to infer how it applies to other partitive expressions than “some (of)” (e.g. “most of”, “half of”, “part of”, “two of”, …).

7 The paper is structured as follows. In Section 1, I explain the distinction between a lower-bounded and an upper-bounded analysis of “some”, and how this relates to scalar implicature. In Section 2, I present Anscombre & Ducrot’s (1983) theory of ‘argumentation in language’, which is later used in Sections 3.2 and 4. In Section 3, I discuss the arguments against an upper-bounded semantics for scalars: the entailment from “All…” to “Some…” (3.1), the non-redundancy of the expression “some, but not all” (3.2), the cancelability of scalar implicatures (3.3), and the non-paraphrasability of “some” as “some, but not all” (3.4). Finally, in Section 4, I argue that the paraphrasability of “some” as “some, but not all” is not only a bad argument against a semantic upper bound (as established in 3.4) but also a bad criterion for identifying scalar implicatures, as is done by Degen (2015) and Ariel (2015). As a consequence, I also reject Ariel’s (2015) claim that scalar implicatures are rare. I conclude with directions for future research.

1. Lower-Bounded vs. Upper-Bounded Semantics

  • 2 Note that by “upper-bounded” I mean ‘lower- and upper-bounded’, and by “lower-bounded” I mean ‘l (...)

8 Interpreting “some (of the) Xs” as upper-bounded means interpreting it as referring to a (relatively small) proper subset of all of the Xs, whereas lower-bounded “some (of the) Xs” refers to an improper subset.2 The difference between upper-bounded and lower-bounded semantics is illustrated in the following figures:

9

Figure 1. Upper-Bounded “Some (of the) Xs” (‘Some, Not All’)

Figure 1. Upper-Bounded “Some (of the) Xs” (‘Some, Not All’)

10

Figure 2. Lower-Bounded “Some (of the) Xs” (‘At Least Some’)

Figure 2. Lower-Bounded “Some (of the) Xs” (‘At Least Some’)

11In both figures, the outer circle delimits the set of all Xs, and the dots represent Xs. The latter are white in the black area and black in the white/grey areas but this is for reasons of visibility only. The other circles are other subsets of the total set of Xs. The latter contains only six members, for simplification. The black area is what is certainly referred to in the case at hand, the grey area is what is possibly referred to, and the white area is what is not referred to. The black area is the proper subset referred to by upper-bounded “some”. For the sake of convenience, this subset contains only two elements. It could have contained more elements (three, four, or even five), because what language users regard as “relatively small” is subjective, but this is not relevant for the present purposes (viz. analyzing “some” as lexically upper-bounded). Note that upper-bounded “some” is (necessarily) part of lower-bounded “some”, as can be seen in Figure 2: the black area is within the outer circle.

12Now, take the sentence “I ate some of the cookies”. Is the sentence true on a lower-bounded reading of “some” if I ate all of the cookies? When we look at Figure 2, we see that the answer is “yes”: if it is true that I ate all the cookies in the total set (i.e. all the elements in the largest circle), it is true that I ate both what was certainly referred to (the black area) and what was possibly referred to (the grey area). What about upper-bounded “some”? The answer is also “yes”: if I ate all the cookies in the total set, it is true that I ate all the cookies in the proper subset (the black area). Indeed, even in Figure 1, the black area is within the outer circle. In other words, the proper subset ‘some, not all’ is a part of ‘all’.

13An initial drawback to viewing “some” as semantically upper-bounded is that “some” cannot be paraphrased with “some, not all” (“I ate some, not all, of the cookies”), because in that case “I ate some of the cookies” would entail that I did not eat all of the cookies, which contradicts the truth-conditions given above. But in fact, this is not a problem: ‘some, not all’ is merely a paraphrase of the meaning of “some”, not of the word “some”. Saying that “some” means ‘some, not all’ does not mean that “some” can always be substituted with the linguistic expression “some, not all”.

14To better understand the difference between lower-bounded and upper-bounded “some”, it is useful to introduce two terms: ‘reference set’ and ‘complement set’ (cf. Ariel 2015). Their meanings are pretty straightforward: the reference set is the set being referred to by upper-bounded “some (of the) Xs” (the black area), and the complement set is the complement of the reference set, i.e. the ‘rest’ (the white/grey area). The reference set and complement set together form the total set of Xs. On an upper-bounded reading of “I ate some of the cookies”, the sentence says something about the reference set of cookies, namely that I ate them, and says nothing about the complement set. However, the complement set is conceptualized (see below). On a lower-bounded reading, the sentence also says about the reference set of cookies that I ate them, and in addition says something about the complement set of cookies, namely that it is possible that I ate them.

15The difference between the upper-bounded reading of “some” and a scalar implicature is this. Whereas upper-bounded “some” says nothing about the complement set, a scalar implicature does: it denies that what is true of the reference set is true of the complement set. So, in “I ate some of the cookies”, a scalar implicature conveys something about the rest of the cookies, namely that I did not eat them. Now, even though “some (of)” says nothing about the complement set, it does evoke the idea of a complement set. It also necessarily evokes the idea of a total set. After all, how could you know what “some of the cookies” means if you do not know what “all of the cookies” means? So-called ‘positive’ quantifiers like “some” put the reference set in the foreground, and the complement set in the background (cf. Just & Carpenter 1971 and Carpenter & Just 1972). Negative quantifiers like “not all” and “only some” do the opposite. This principle of foregrounding and backgrounding is called ‘profiling’ in Cognitive Grammar (cf. Langacker 1987, cited by Ariel 2015: 599). As we will see in Section 2, Anscombre & Ducrot (1983) take this idea of positive and negative quantifiers further by linking it to argumentation.

16Despite first appearances, the upper-bounded view can be perfectly incorporated into a Gricean theory of scalar implicatures. First, consider the derivation of scalar implicatures on the lower-bounded view:
1. The speaker has said that she ate some of the cookies
2. She could have been more informative by saying that she ate all of the cookies, but she didn’t
3. If the speaker had eaten all of the cookies, she would have said so, because she is cooperative and thus willing to provide me with all the relevant information
4. The reason she did not tell me that she ate all of the cookies is probably that this is not the case
(after Levinson 1983: 135, simplified)

17 Step 1 is in fact not fully explicit. It should be: “The speaker has said that she ate some of the cookies, which means that she ate at least some of the cookies”. Only if the hearer is aware that “some” means ‘at least some’ can he realize that it is less informative than “all”. This detail is often omitted by authors (an exception is Horn 1989: 214). The derivation of scalar implicatures based on upper-bounded scalars, on the other hand, could look like this:
1. The speaker has said something about some of the cookies, namely that she ate them, but she has said nothing about the rest of the cookies.
2. I am interested in knowing whether or not she ate the rest of the cookies, and the speaker knows that I am.
3. If the speaker had eaten the rest of the cookies, she would have said so, because she is cooperative and thus willing to provide me with all the relevant information
4. The reason she did not tell me that she ate all of the cookies is probably that this is not the case.

18On this account, the speaker is ‘ostentatiously’ silent about the complement set, in order to implicate that what she said about the reference set does not apply to the complement set. This contrasts with the lower-bounded view, where the speaker says that she possibly ate all of the cookies but implicates that she did not.

19One advantage of the upper bound/ scalar implicature distinction is that it permits one to give a smooth analysis of utterances like (4):

(4) I ate some of your cookies and also the rest.

20This utterance is definitely odd. First of all, it violates the maxim of Manner, because there is a simpler, shorter way of saying the same thing, namely: “I ate all of your cookies”. Second, the first part of the sentence (“I ate some of your cookies”) triggers the default implicature that the speaker did not eat all of the hearer’s cookies, but this implicature subsequently gets canceled when the speaker adds “and also the rest”. At the literal level, however, the sentence makes sense: the speaker first states that she ate a proper subset of the cookies, and then that she ate the complement set as well. Compare this with the lower-bounded view on which there is no distinction between ‘upper bound’ and ‘scalar implicature’. At the semantic level, the sentence would not be interpretable: the speaker first states that she ate an improper subset of cookies, i.e. either a proper subset (two, three, four or five cookies) or the total set (six cookies), and then that she ate “the rest”. But what does “the rest” refer to? There is no ‘rest’ of an improper subset, since the latter can refer to the total set. Indeed, in their experiments, Breheny et al. (2006: 14) assume that the phrase “the rest” triggers an obligatory scalar implicature in the preceding sentence containing a scalar term. The problem in (4) is that “the rest” forces and cancels the scalar implicature at the same time! So what will the final interpretation look like? Since scalar implicatures are cancelable and supposed to be canceled when information to the contrary is encountered, the implicature should be canceled in this case. But in that case the speaker communicates just the literal meaning of the sentence, which, as I argued, is uninterpretable. The only way out for Griceans would be to claim that, for some reason, the implicature is not canceled, and that the speakers conveys contradictory information (namely that she did not eat all of the cookies, but that she did), and that this would explain the oddity of the utterance. But this would still not solve the problem that the sentence does not make sense on the literal level. So why would Griceans prefer this explanation, when there is a simpler one which is, as illustrated above, perfectly compatible with Gricean theory?

21 In sum, lower-bounded and upper-bounded “some” both make the same truth-conditional contribution to sentences containing them. So, if we define semantics purely in terms of truth conditions, they have the same semantics. But I believe it is useful not to restrict semantics to truth conditions only. Whereas on both the lower-bounded and the upper-bounded analysis a “some”-sentence does not exclude the possibility that what applies to some of the Xs in fact applies to all of the Xs, only the lower-bounded view explicitly includes this possibility (cf. Bultinck 2005: 177). Indeed, if ‘possibly all’ is part of the semantics of “some”, a speaker using “some” is actually conveying that ‘all’ is possibly the case. From the hearer’s point of view, the lower-bounded and upper-bounded view also make different predictions: on the lower-bounded view, the hearer considers/conceptualizes the possibility that ‘all’ is the case, whereas on the upper-bounded view, he does not (see Figures 1 and 2).

2. Anscombre & Ducrot’s (1983) ‘Argumentation in Language’

22 Arguing, in Anscombre and Ducrot’s (henceforth: AD) sense, means orienting your hearer towards certain conclusions. Thus, every utterance has an argumentative orientation, which is an integral part of its meaning (1983: 87). For example, if I say: “Peter was almost late”, I could be orienting the hearer towards all kinds of negative conclusions concerning Peter, e.g. Peter is negligent, Peter does not care about our meetings, etc. Or, if I say: “Peter was almost late because of the bus”, I could be orienting the hearer towards certain conclusions concerning the bus or public transport in general, e.g. the bus is not a reliable means of transportation. I could not use these sentences to favor positive conclusions such as “Peter is lucky” or “The bus is reliable”. This is in fact surprising, because if Peter was almost late, this means he was not late, i.e. that he arrived on time. So why conclude he is negligent when in fact he was on time? The conclusions sentences are oriented to (henceforth: argumentative conclusions) are not always reasonable conclusions. Argumentative conclusions are not inferred conclusions, they are not based on the informational content of the sentence (AD 1983: 30). Rather, speakers merely present their utterances as allowing certain conclusions and disallowing others, by exploiting certain linguistic devices (ibid.). For example, “almost x” permits the speaker to orient the hearer towards conclusions that could be reasonably drawn if “x” was said instead of “almost x”. In other words, “almost late” is argumentatively treated as “late”. It is reasonable to draw negative conclusions concerning Peter if he was late, therefore “almost late” orients the hearer precisely towards such conclusions. “Barely x” has the opposite effect (cf. Ducrot 1980: 22). Although “Peter was barely late” presupposes that he was late, it orients the hearer towards conclusions that he would reasonably draw if Peter had not been late. Compare:

(5) “He was barely late, so give him a break.”
like “He was not late, so give him a break”
(6) ?? “He was almost late, so give him a break.”
like ?? “He was late, so give him a break”
(7) “He was almost late, so he should be more careful next time”
like “He was late, so he should be more careful next time”
(8) ?? “He was barely late, so he should be more careful next time”
like ??“He was not late, so he should be more careful next time”.

23 Similar observations can be made regarding “some” and “all”. Argumentatively, “some” behaves like “all”:

(9) “She did some of her chores, so she deserves a reward”
like “She did all of her chores, so she deserves a reward”
(10) ?? “She did some of her chores, so she should not be rewarded”
like ?? “She did all of her chores, so she should not be rewarded”.

24“Many” and “most” behave in the same way:

(11) “She did many/most of her chores, so she deserves a reward”
(12) ??“She did many/most of her chores, so she should not be rewarded”.

25 For Anscombre & Ducrot (1983), “some” – “many” – “most” – “all” and “almost x” – “x” form argumentative scales. On argumentative scales, the elements higher on the scale form stronger arguments than elements lower on the scale. All elements on a scale form arguments in favor of the same conclusions. For example, “All participants were satisfied” is a stronger argument than “Many participants were satisfied” for the conclusion “The conference was a success”.

Figure 3: Argumentative Scales

Figure 3: Argumentative Scales
  • 3 AD do not use the terms ‘positive/negative scale’ or ‘positive/negative orientation’, but I thin (...)

26 For every ‘positive’3 scale, there is a corresponding negative one. This follows from AD’s ‘Law of Negation’ which states that, if p is an argument for q, non-p is an argument for non-q (1983: 40). Additionally, there is a ‘Law of Inversion’ which states that, if A is a stronger argument than B in favor of the conclusion C, non-B is a stronger argument than non-A is in favor of non-C (AD 1983: 104). For example, while “All students passed” is a stronger argument than “Many of the students passed” for the conclusion “The exam was easy”, “Not many of the students passed” is a stronger argument than “Not all the students passed” in favor of the conclusion “The exam was not easy”. Words that carry implicit negation are also found on negative scales, for instance “few” (in contrast with positive “a few”) and “only + [quantifier]” (see Figure 4).

  • 4 “Only many” and “only most” are impossible in many cases (e.g. ?“I ate only many/most of the cook (...)

Figure 4: Negative Argumentative Scales4

Figure 4: Negative Argumentative Scales4

27 A test to identify argumentative scales is to see if the two arguments can be connected with “et même” (AD 1983: 32) – “and even” in English. AD give the example “Pierre est aussi grand que Jean et même plus grand” (ibid.): “Peter is as tall as John and even taller”. It seems to me that the similar expressions “ou même” (“or even”), “peut-être même” (“perhaps even”), and “voire” (“if not”) are more natural in such cases. In English, “indeed” can also be used. The argument that comes after the connecting expression is always stronger than the first:

  • 5 Real-life example from http://www.europarl.europa.eu/doceo/document/CRE-8-2018-04-18-INT-3-7739- (...)
  • 6 Real-life example from https://www.sacsplash.org/post/field-owls-clover, last consulted on 14/11 (...)
  • 7 Real-life example from https://www.babergh.gov.uk/planning/heritage/living-in-a-conservation-are (...)

(13) “some, if not all”,
(14) “five, if not six”
(15) “there is a very
important, indeed vital, issue”5
(16) “Some years there will be very
few plants or even none, while other years there might be millions”6
(17) “The variety or special unity of the buildings, of which
only some, or even none are listed”7

  • 8 A ‘local’ scalar implicature is an implicature that is not based on a full-fledged utterance but (...)

28“If not” and “or even” are examples of what Horn (1972: 49) calls ‘suspension phrases’: expressions that ‘suspend’ scalar implicatures. Suspension means that the scalar implicature may or may not go through: if I say “Some, if not all the students are female”, it may be the case that some but not all the students are female (scalar implicature) or it may be the case that all students are female (no scalar implicature). This as opposed to cancelations where the implicature definitely does not go through, e.g. “Some, indeed all, of the students are female” (see 3.3.1). Horn (1972) views these suspension phrases as indicators of entailment scales: two scalar terms can be connected with such a phrase because they have ‘at least’-semantics. But in fact, it makes more sense to view the scalars as upper-bounded here, or even as carrying a ‘local’ scalar implicature8: “some or (even) all” means that the predicate is true either of ‘some’ and not of ‘all’, or of ‘all’. Saying that it means that either ‘at least some’ is the case or ‘all’, does not make much sense, because if ‘all’ is the case, ‘at least some’ is the case as well! Indeed, there is a rule known as ‘Hurford’s constraint’ which states that “or” cannot connect two terms if one term entails the other (cf. Chierchia et al. 2012: 2309): the utterance “She owns a pet or (even) a cat” is infelicitous, unless the word “pet” pragmatically receives a stricter meaning which excludes cats from its extension. Second, “if not” and “or even” can connect terms that are not on an entailment scale, as in (17): “none” does not entail “only some”, since “only some” presupposes “some”. Another example is the following scale of military ranks, from low to high:

(18) private – corporal – sergeant – lieutenant – colonel – general
(Huang 2017: 161, based on Hirschberg 1985: 98)

29The terms on this scale are mutually exclusive: if you are a colonel, you are not a general, and vice-versa. Yet it is possible to say things like:

(19) “Harry can become a corporal, or even a sergeant.”

30In addition to Horn’s (1972) ‘suspension phrases’, a bare “even” can signal the presence of an argumentative scale (cf. AD 1983: 58):

(20) “We don’t have ten submissions. In fact, we don’t even have five”.

31It does not only work for argumentative scales based on lexical items, as with the examples given so far, but also for scales that are context-dependent. Indeed, many argumentative scales are pragmatic: they are ad hoc, i.e. created on the spot. For example, if the likelihood of Mary going to the party is higher than that of Peter going to the party and that the latter is higher than that of Sally going to the party, we have an argumentative scale on which “Sally came to the party” is on top and “Mary came to the party” is at the bottom (example inspired from AD 1983: 47). This makes it possible to say things like:

(21) “Did Peter come to the party?”
– “Yes, (and) even Sally came”
(22) “Did Peter come to the party?”
– “No, (in fact) not even Mary came”.

32 In sum, the expressions “or even”, “if not”, and “even” signal the presence of argumentative scales, not necessarily of entailment scales. Scales that are usually considered entailment scales are generally also argumentative scales, but the opposite is not true: not every argumentative scale is an entailment scale.

3. Arguments Against ‘Some, Not All’-Semantics

3.1. Entailment

33 As explained in the Introduction, the fact that “I ate all of the cookies” entails “I ate some of the cookies” is used as an argument for viewing “some” as meaning ‘at least some’. Because indeed, if it is true that I ate all of them, it is true that I ate at least some of them. Everything that is (truthfully) said about all of the cookies, is true of at least some of the cookies. But this also holds for upper-bounded “some”: everything that is truthfully said about all of the cookies, is also true of a proper subset (i.e. ‘some, not all’) of the cookies. Indeed, as shown in Figure 1, ‘some, not all’ is a part of ‘all’. If all the cookies are tasty, every proper subset of cookies is also tasty. If I ate all the cookies, I ate every proper subset of the cookies.

3.2. Non-Redundancy

34 The fact that it is possible to say “some, but not all” without redundancy has been repeatedly used as an argument for the pragmatic nature of the ‘not all’-meaning (e.g. Sadock 1978: 294, Levinson 2000: 17, Degen 2013: 12). Now, it would be easy to say that on my upper-bounded view, the addition of “but not all” is not redundant because it makes the scalar implicature explicit, rather than just making the semantic upper bound explicit. However, I do not believe that the function of “but not all” is merely to make the scalar implicature explicit. After all, contra the implicit assumption made by the authors above, implicatures are not always statable without redundancy. Consider the following piece of discourse:

(23) “I saw some of your children. By that I mean that I did not see all of them.”

35Adding the second utterance is odd, because the hearer most likely already derived the scalar implicature when processing the first utterance. Plausibly, implicatures are only made explicit if the utterance that was supposed to carry the implicature did not unambiguously convey this implicature (i.e. if there was a risk of misunderstanding).

36There is also a second false assumption in the non-redundancy argument, namely that semantic redundancy is unacceptable. As Horn (1991) has pointed out, even entailments and semantic presuppositions can be stated without redundancy under the right conversational conditions. Consider the following examples:

(24) It’s odd that dogs eat cheese, but they do.
(25) Only Hercules can lift this rock, but he can.
(26) I don’t know why I love you, but I do.
(27) He regrets that he said it, but he did say it.
(28) The milk train doesn’t stop here anymore, but it used to.
(Horn 1991: 322).

37In each of these sentences, a presupposition of the first clause is non-redundantly stated in the second clause. According to Horn, who refers to AD’s theory, this is possible because of the argumentative distinctiveness of both clauses (1991: 326). For example, someone who wants to convince someone to give cheese to their dog will not say “It’s odd that dogs eat cheese”, because that invites the hearer to question the information, but rather “Dogs eat cheese”, cf. the “they do” in (24). An example with entailment is the following:

(29) “It’s a dog, not a cat!” (to a person giving cat food to a dog)

38If an animal is a dog, it is by definition not a cat, but specifying “It is not a cat” can be done to give an argument in favor of the conclusion “You should not give it cat food”. Note that it is possible to support the same conclusion by saying “It’s a dog” (“Don’t give it cat food, it’s a dog!”), because the opposition between “cat” and “dog” is sufficiently salient here. Adding “not a cat” makes the argument slightly more explicit, and therefore possibly stronger. The link between explicitness and argumentation-in-language is an interesting topic for future research.

39 Another variant of the non-redundancy argument is given by Horn (1989: 215), who argues that “only some” should be redundant if “some” were semantically upper-bounded. This is based on the false assumption that the only function of “only” is to provide an upper bound. As illustrated in Section 2, one of the functions of “only” is to invert the argumentative orientation of the following scalar (in fact, AD would say that this is the main function of “only” and that all other functions are derived from this). Another function of “only x” is, according to some, to suggest that there was an expectation for more than x (cf. Zeevat 2009).

3.3. Cancelability

  • 9 Generalized Conversational Implicatures (GCIs), of which scalar implicatures are the most famous (...)

40Grice (1975: 39) introduced cancelability as one of the distinguishing features of implicatures. Levinson (2000: 49) even views cancelability as the “core phenomenon” of Generalized Conversational Implicatures.9 Cancelability is often used as an argument for regarding a certain aspect of meaning as pragmatic rather than semantic/conventional. The reasoning that “It cannot be semantic/conventional, because it is cancelable” is found for instance in Geurts (2010: 20, 82, 83, 107), Horn (2006: 24, 38), and Levinson (2000: 68).

41 There are two types of cancelability: explicit and implicit. An implicature is explicitly cancelable if it is possible to add a clause that makes explicit that the implicature is not intended (cf. Grice 1975: 39, Grice 1989: 44). Grice himself did not give any examples of explicit cancelation with “some”, but the most cited ones in the literature are those with “indeed” and “in fact”:

(30) “Some, in fact/indeed all of them, came” (Levinson 2000: 81)
(31) “John ate some of the cookies. In fact, he ate all of them” (Levinson 2000: 42)

42Implicit or contextual cancelability means that an implicature which normally seems to arise by uttering a certain form of words does not necessarily arise when the same words are uttered in a different context (cf. Grice 1975: 39, Grice 1989: 44). For example, whereas “Some of the students did well on the test” generally implicates that not all students did well on the test, the sentence “If some of the students did well on the test, then Mary won’t be fired” generally means that Mary won’t be fired if at least some of the students did well on the test (Breheny 2008: 95).

43 In the following, I will first discuss explicit cancelability (3.3.1), then contextual cancelability (3.3.2).

3.3.1. Explicit Cancelability

44 According to Griceans, the reason it is possible to say things like “Some, in fact all of them, came” is that the part after the “in fact” entails the part before it: “All of them came” entails “Some of them came”. What comes after the “in fact” is more informative than the part before it. But, as argued under 3.1, this is not a valid argument in favor of ‘at least’-semantics. On the upper-bounded view, “All of them came” also entails “Some of them came” and is more informative: if I know that it is true of a proper subset of people (“some of them”) that they came, I do not know anything about the rest of the people, whereas if I know that all people came, I know what some of them did and what the rest did.

45A special variety of “in fact”-cancelations are those where it is not the same speaker, but a different one, who cancels the implicature, e.g.:

(32) A: “Are many of your friends linguists?”
B: “Yes, in fact all of them”
(Horn 1992: 175).

46Griceans seem to assume that the reason speaker B says “Yes, in fact all” rather than “No, all” is that she is aware that “all” logically entails “many”. However, this needn’t be the case. Consider the following dialogue from Anscombre and Ducrot (1983: 80, my translation):

(33) A: “Is dinner ready?”
B: “Yes, almost” (rather than: “No, almost”)

47By saying “yes”, speaker B is not answering logically. Rather, she is following the orientation of A’s question. A parallel example is:

(34) A: “Is dinner almost ready?”
B: “Yes, in fact it is ready” (rather than: “No. It’s ready.”).

48Speaker B uses “yes”, not because it is a logically correct answer, but rather because she is respecting the argumentative orientation of A’s question.

3.3.2. Contextual Cancelability

49 There are contexts in which scalars seem to receive an ‘at least’-interpretation. The Gricean analysis of these cases is that the scalar implicature is canceled and that the scalar conveys its literal ‘at least’-reading. But what if scalars are semantically upper-bounded? In that case, the ‘at least’-reading should be analyzed as pragmatic. This is perfectly feasible. First, note that the linguistic expression “at least some” (as used in an actual utterance) is not contradictory on the upper-bounded analysis, as some would claim (e.g. Horn 1989: 215). Indeed, assuming that “at least x” means ‘x or more’, “at least some” would mean ‘a proper subset or more’ on the upper-bounded analysis, which is unproblematic. For the same reason, it is unproblematic to claim that an implicit (pragmatic) ‘at least’ can be added to the meaning of “some”. On the lower-bounded analysis of “some”, on the other hand, the expression “at least some” would be problematic (cf. Koenig 1991: 141 on numerals). Indeed, “at least some” would mean ‘an improper subset or more’, which is hard to make sense of, since what does it mean to have ‘more’ than an improper subset? There is nothing ‘more’ than an improper subset, since the latter can refer to the total set, which is the upper limit (see also Section 1 about “the rest” and Section 2 about “some or all”).

50There are at least two types of contextual cancelations with “some”. The first are cases in which the speaker only possesses partial information. In the literature, this is analyzed as the absence of the so-called Competence Assumption, an assumption necessary to the generation of scalar implicatures (cf. Breheny et al. 2013). For example, a student has seen the first five exams from a pile of corrected exams and they were graded A, B, B, C, and C (all of which are passing grades). She then says: “Some of us passed”, which seems to mean something like ‘all I know is that at least some of us passed’. So, in my view, there is not only an implicit ‘at least’, but also an implicit ‘all I know is that…’. This type of cancelation is, I believe, rather rare, so I will leave the verification of my hypotheses to future research. The other type of cancelation is when “some” is embedded in an intensional context, e.g. when it is in the scope of “hope” or a conditional “if”-clause. This is the type of cancelation I will turn my attention to.

51First, consider the following example of “some” in the scope of a conditional “if”-clause:

(35) If you eat some of your vegetables, you will get dessert.

52 This is a case where “some” seems to be interpreted as ‘at least some’, or, as defenders of the lower-bounded view would say: where “some” only expresses its literal meaning. But the reason why we interpret “some” as ‘at least some’ in (35) is most likely pragmatic (cf. Geurts 2006: 372 on numerals). We would find it odd if a parent were to reward a child for eating some of the vegetables but not for eating all of the vegetables, but this is an inference based purely on world knowledge (ibid.). This hypothesis is strengthened by the fact that, when pragmatic assumptions are different, the scalar can receive a different interpretation:

(36) If some of the leaves fell, autumn is starting.

53Here, the hearer does not necessarily infer that if all of the leaves fell, autumn is starting. On the contrary, he may infer that if all of the leaves fell, autumn is already past its initial stage. But note that the latter inference is pragmatic as well. So, what is the literal meaning of (35) on an upper-bounded analysis? It is just this: ‘in the case that you eat some but not all of your vegetables, you will get dessert’. Nothing is said about the case in which you eat more than just some of your vegetables. Mutatis mutandis for (36).

54 A similar analysis can be given to scalars in the scope of “hope”, although it requires a little bit more elaboration:

(37) I hope that some of my relatives will remember my birthday.

55Intuitively, we interpret (37) as meaning that the speaker hopes that at least some of her relatives will remember her birthday. That is because we would find it odd if a person were to be happy when some of her relatives remember her birthday, but not when all of them do. But this is, again, a pragmatic assumption. For consider (38), as uttered by an academic who is about to give a speech mainly aimed at women older than forty:

(38) I hope that some of the participants will be younger than forty.

56It would be reasonable to assume that the speaker hopes that some but not all participants will be younger than forty. This interpretation is pragmatic as well. So, what is the literal meaning of (37) on an upper-bounded analysis? It would be something like: ‘the object of the speaker’s hope is a situation in which a proper subset of her relatives remembers her birthday’. From this we can infer that the speaker will be satisfied in the case that some, but not all, of her relatives remember her birthday (since people ought to be satisfied when their hope is fulfilled). This does not exclude the possibility that the speaker will be satisfied in the case that more than just some of her relatives remember her birthday, but it does not explicitly include this possibility either (see Section 1).

  • 10 On the assumption that there are no other elements in the sentence that need pragmatic enrichmen (...)

57 The above analyses may have given the impression that “some” always receives an ‘at least’- or ‘not all’-enrichment, as on Carston’s (1998) underspecification-analysis of numerals, but this is not the case. On the underspecification view, sentences containing a scalar are not interpretable without pragmatics; they do not have full-fledged truth conditions without pragmatics. On the upper-bounded view, however, sentences with scalars can receive a purely literal10 interpretation. This can happen in conditionals, if the hearer does not consider any other situations apart from the one described in the antecedent. It can also happen in non-embedded contexts, but for partitive expressions, this is rare. The hearer would have to interpret the sentence purely ‘logically’, as in example (4). An exception could be cases where the hearer knows that the speaker only possesses partial information, as in the case described in the second paragraph of this section.

3.4. Upper Bound and Paraphrasability

58 Geurts (2010: Chapter 7) criticizes the so-called ‘conventionalist’ view of scalar implicatures, on which “some” means ‘some, not all’. Since Geurts (2010) makes no distinction between scalar implicature and upper bound, his arguments could be misinterpreted as arguments against the upper-bounded view. Therefore, I will reanalyze the examples he uses in his argumentation. They all involve scalars embedded in intensional contexts.

59Geurts (2010: 135) notes that the meanings of the following A-sentences cannot always be paraphrased as the following B-sentences:

(39) A. “Tony hopes that Cleo had some of the figs”
B. ‘Tony hopes that Cleo had some but not all of the figs’
(40) A. “Tony regrets that Cleo had some of the figs”
B. ‘Tony regrets that Cleo had some but not all of the figs’

60 He does not explain why, but his analysis of later examples permits one to infer why he thinks the above examples are problematic: (39A) is not necessarily paraphrasable as (39B) because (39A) could mean that Tony hopes that Cleo had at least some of the figs (see previous section), and (40A) is not necessarily paraphrasable by (40B) because the latter implies that Tony regrets that Cleo did not have all of the figs, i.e. he wanted Cleo to eat all of the figs, but this clearly does not follow from “Tony regrets that Cleo had some of the figs” (he most likely wanted her to eat no figs at all). This is indeed a problem for the lexicalist view of scalar implicatures (the view that scalar implicatures are part of the lexical semantics of scalar words), and prima facie also for the post-Gricean ‘enrichment’ view (cf. Carston 1995, 1998). On this view, the word “some” gets pragmatically enriched with ‘and not all’ rather than that a whole negative proposition is implicated, as on Geurts’s (2010) view. On Geurts’s (2010) view, it is the whole alternative proposition with ‘all’ that is negated, which makes the correct predictions:

61(39) C. ‘it is not the case that Tony hopes that Cleo ate all of the figs’
(40) C ‘it is not the case that Tony regrets that Cleo ate all of the figs’

62The examples are not problematic for the upper-bounded view, though. On this view, the literal meanings of (39A) and (40A) are, respectively:

(39) D. ‘Tony hopes that Cleo ate a relatively small proper subset of the figs’
(40) D. ‘Tony regrets that Cleo ate a relatively small proper subset of the figs’

63 As explained in Section 1, what is stated about a proper subset of Xs can be true of the total set of Xs (this possibility is just not conveyed, contrary to what the lower-bounded view implies). Hence, (39D) is literally true even if Tony hopes that Cleo ate all of the figs and (40D) is true even if Tony regrets that Cleo ate all of the figs. This in turn implies, for (39D), that Tony may be happy even if Cleo ate all of the figs, i.e. he does not necessarily hope that she will not eat all of the figs.

64 Geurts also gives examples of modals such as “can”:

(41) A. “You can have some of the dates”
B. ‘you can [have some and not all of the dates]’

65He notes that if (41A) is analyzed as (41B), as conventionalists would (have to) do, this implies that the speaker is permitting the addressee not to have all the dates, rather than forbidding him to eat some of them (Geurts 2010: 145-6). First of all, I do not understand why Geurts uses “rather”: according to the analysis in (41B), the speaker seems to be both permitting the hearer to eat some of the dates and permitting him not to eat all of the dates (“some and not all”). But this is taking the paraphrase at face value, as if the “and” in the paraphrase were an actual distributive conjunction, as it can be when used in an utterance. According to the upper-bounded view, the more accurate paraphrase would be (41D) or (41E):

(41) D. ‘[some but not all of the dates] is one of the things you can have’
E. ‘you can have a relatively small proper subset of the dates’

66 Finally, Geurts (2010: 154-5) claims that (42A) implies (43C), probably because he presumes that (42A) should be analyzed as (42B) on the conventionalist view:

(42) A. “You have to read some of these papers”
B. ‘you have to [read some and not all of these papers]’
C. ‘you are not allowed to read all of them’

67Indeed, if you have to read ‘not all’ of the papers, this means you must make it the case that you do not read all the papers, i.e. you are not allowed to read all the papers. The upper-bounded analysis does not make this prediction: (42A) would be analyzed as:

(42) D. ‘reading some and not all of these papers is one of the things you have to do’

68 Note that the upper-bounded view makes the same predictions as the lower-bounded view with respect to scalar implicatures (see also Section 1). The (simplified) interpretation process of (42A) would look like this:
1. The speaker said that I have to read a proper subset of the papers.
2. She did not tell me whether I have to read the remaining papers.
3. The reason she did not tell me is probably that I do not have to read the remaining papers.

69In sum, Geurts’s (2010) arguments may be valid against a conventionalist view of scalar implicatures, but not against a conventionalist view of upper bounds.

4. Scalar Implicatures and Paraphrasability

70 In the typical examples of utterances with “some” that convey a scalar implicature, “some” seems to be paraphrasable as “some but not all”:

(43) A. “I saw some of your friends”
B. “I saw some, but not all, of your friends”
(44) A. “Some people like dogs”
B. “Some, but not all, people like dogs”

71So, it seems that when “some” can be paraphrased as “some but not all”, a scalar implicature is present. But, I will argue, the opposite is not true: a scalar implicature may be present even when a “some but not all”-paraphrase is inappropriate.

72 Ariel (2003: 17) believes that scalar implicatures are rare, but that is because she implicitly gives a restrictive definition of the term ‘scalar implicature’. Consider the following example from Ariel (2004: 668):

(45) “Most UCSB students have 0 ... 1 ... 2 ... 3 or 4 drinks per week (4000 don't drink at all)”

73This sentence was found on a poster for an anti-drinking campaign on the UCSB campus. It is therefore safe to assume that the utterer’s goal was to convince students not to have more than four drinks per week. So, Ariel argues, the utterer would not want the addressee to infer that ‘not all UCSB students have 0, 1, 2, 3, or 4 drinks per week’ (i.e. ‘some students have more than 4 drinks per week’) because this would “defeat the speaker’s purpose” (ibid.); it would be “incompatible with the speaker’s goal” (Ariel 2004: 659). Relying on corpus data, she argues that this is the typical scenario when scalars such as “most” are used (ibid.). But is it really that improbable that speakers knowingly implicate things that they ideally would not want the hearer to infer? Sure, it would be more convenient for the utterer of (45) if the hearer interpreted “most” as ‘most or all’ or as ‘all’, but then why didn’t she say “most or all” or “all”? Because that would be misleading: in the latter case, she would be lying (violation of Grice’s first maxim of Quality) and in the former she would be underinformative (violation of Grice’s first maxim of Quantity). Ariel would perhaps agree with this, but somehow she does not acknowledge that Grice’s maxims do their usual job here and lead to a scalar inference (cf. her reaction to an early manuscript of Horn 2006 in Ariel 2004: 675). Whether the utterer of (45) finds it desirable or not, hearers do normally derive the scalar inference in an utterance such as (45), and they expect the utterer to be committed to having conveyed this piece of (pragmatic) meaning.

  • 11 For examples of PCIs, see Grice (1975: 50-56).

74In sum, Ariel assumes that an implicature must be a speaker’s main message. It is reasonable to assume that Particularized Conversational Implicatures (PCIs)11 have this property, but it is less evident for Generalized Conversational Implicatures (see fn. 9), the category that scalar implicatures belong to. This argument could be used against theories that do not distinguish between PCIs and GCIs, such as Geurts’s (2010). However, while Ariel has a potential argument for the claim that scalar inferences are rarely the main point of an utterance and hence are rarely ‘real’ implicatures, she has no argument against the pervasiveness of scalar inferences.

75 I have just argued why I believe that scalar inferences sometimes must be generated even if they defeat the speaker’s purposes, but I have not yet explained why this is not problematic. The answer is: argumentation in language. Speakers can convey anything they want that supports the opposite argumentative conclusion from the one they wish to defend, as long as it does not come off as the main point of their utterance. I will illustrate this by reanalyzing some of Ariel’s examples that involve paraphrasability issues. Ariel carried out tests in which she let participants choose between one out of two possible responses to a certain statement, whereby the two possible responses each contain a different paraphrase of “some”. The first puzzle she encounters is why participants preferred the B1-response in the case of (46) but the B2-response in case of (47):

(46) A: We’re looking for a good mediator.
B1: Stevens managed to resolve
some of the issues in our extremely difficult case, so we all think very highly of her.
B2: Stevens managed to resolve
some, not all of the issues in our extremely difficult case, so we all think very highly of her.

(47) A: Stevens managed to resolve some of the issues in our extremely difficult mediation case, so we all think very highly of her
B1: Congratulations to her for having resolved
some, and maybe all the issues
B2: Congratulations to her for having resolved
some, even if not all the issues.
(Ariel 2015: 577)

  • 12 Unless the utterer of the “so”-clause is a different person from the utterer of the preceding cl (...)

76 Ariel (ibid.) says it is clear why B1 was preferred in (46): bare “some” focuses on the reference set, i.e. the issues that Stevens resolved, which is something positive, hence it supports the positive conclusion “so we all think very highly of her”, contrary to “some, not all” which evokes the issues that Stevens did not manage to solve. Note that “some, but not all” would also be dispreferred. But, by the same logic, B1 should be preferred over B2 in (47) (ibid.). Indeed, “some, and maybe all” has the same argumentative orientation as bare “some”. Ariel’s (2015: 578) explanation is that the test in (47), as opposed to that in (46), tested the semantic meaning of “some” (since it asked to paraphrase a sentence containing “some”). And, since “some” is upper-bounded rather than only lower-bounded, “some, even if not all” is a more accurate paraphrase than “some, and maybe all”. However, this explanation is not quite right. In both (46) and (47), the interpretation of “some” (and of “some, not all”, “some, and maybe all”, and “some, even if not all”) is involved, not the just the semantics. Ariel does not explain why (47) would only test the semantic meaning of “some”, nor why (46) would test something more than its pure semantic meaning. Perhaps because she believes that only in (46) do the responses take argumentative orientation into account, since they make use of “so”-clauses (and “so”-clauses indeed introduce explicit argumentative conclusions of the preceding clause,12 see Section 1). But argumentation is involved in (47) as well. For imagine B2 in (47) contained the paraphrase “some, but not all”:

(47) B2*: ? Congratulations to her for having resolved some, but not all the issues.

77 It is unclear whether B2 (in the form of B2*) would still have been the preferred response, since it is argumentatively odd. Participants would then have to choose between an unfaithful representation of the speaker’s intended meaning (“some, and maybe all”) and an argumentatively odd utterance (B2*) – a test which would be pointless. So why is “some, even if not all” acceptable, but not “some, but not all”? The argumentative orientations are, despites first appearances, not the same (pace Ariel). “P even if q” indicates that q is a weaker argument than p. Or, more accurately: it says that the argument q will not change the conclusion drawn from p. When a speaker uses “p but q”, she presents q as the stronger argument (AD 1983: 109). To be sure, making two opposite arguments in the same utterance is not irrational: the speaker mentions a (potential) counterargument to her point and dismisses it with her own argument. In sum, the paraphrasability of “some” as “some, even if not all” in (47) is not attributable to the semantic upper bound only, as Ariel claimed, but to the scalar inference that (47A) induced. “Even if not all” suggests that Stevens did not solve all the issues. That is a stronger interpretation than the purely semantic, upper-bounded reading of “some” (which would predict the interpretation that some of the issues were solved by Stevens, without implying anything about whether or not she solved all of them). Conversely, the non-paraphrasability of “some” with “some but not all” in (47) is not a sign of the absence of a scalar inference, but rather a matter of argumentative orientation. In sum, testing the paraphrasability of “some” as “some but not all” is not an accurate test for detecting scalar inferences, as is done in e.g. Degen (2015).

Conclusion

78 In this paper, I have argued to make a distinction between ‘upper bound’ and ‘scalar implicature’ following Ariel (2015). This entailed giving a new definition to ‘upper bound’: upper-bounded “some (of the) Xs” refers to a proper subset of the total set of Xs, whereas lower-bounded “some (of the) Xs” refers to an improper subset (i.e. it possibly refers to all of the Xs). Like Ariel (2015), I have argued that upper bounds are semantic and lexical, contrary to scalar implicatures, which are pragmatic and context-dependent. I have looked at various arguments against upper-bounded semantics, that is, arguments against the view that “some” means ‘some, not all’. I have concluded that all these arguments were in fact arguments against lexicalizing scalar implicatures, not against lexicalizing upper bounds. I have argued that “some” can be seen as meaning ‘some, not all’ but that this does not imply, as is usually assumed, that “some” is paraphrasable as “some, not all”. One of the reasons why “some” is not paraphrasable as “some, not all” is that “some” and “not all” have opposite argumentative orientations (cf. Anscombre & Ducrot 1983). Anscombre and Ducrot’s (1983) theory of ‘argumentation in language’ has also proven useful for the analysis of some problematic examples presented by Ariel (2015), which had led her to conclude that scalar implicatures are rare. I have concluded that, while it may be the case that scalar inferences are rarely implicatures proper, scalar inferences do regularly go through. Hence, they could be viewed as ‘defaults’.

79The notion of default is problematic, however. Many experimental studies have found evidence against the view that scalar inferences are default (e.g. Bott & Noveck 2004, Breheny et al. 2006, Huang & Snedeker 2018). They all did so by showing that literal interpretations of utterances containing scalars entail less processing costs than when a scalar inference is derived. However, I believe that these studies are based on a misinterpretation of Levinson (2000). First, Levinson never suggested that canceling an implicature would entail more processing costs. On the contrary, he speaks of the “prevention” of scalar implicatures (cf. Levinson 2000: 50). Second, he suggested that GCIs (the category to which scalar implicatures belong) would be easier to process than PCIs, not that GCIs are accessed as easily as (let alone more easily than) semantic content. Finally, even if PCIs turn out to be processed as quickly as GCIs, the intuition that GCIs are ‘default’ in some other sense would remain. For example, defaultness could be a feature of contexts rather than of inferences (cf. Jaszczolt 2005: 5). The concept of ‘default contexts’ is still very much unexplored territory. Future research will determine in what ways the notion of default contexts can enrich our understanding of GCIs and PCIs.

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Notes

1 In the following, whenever I talk about “some”, I am talking about its partitive use, not its indefinite use (the reduced form [s’m] as in “Give me some cigarettes”, cf. Israel 2000: 170). Also note that I use double quotes for words and utterances, and single quotes for meanings and interpretations.

2 Note that by “upper-bounded” I mean ‘lower- and upper-bounded’, and by “lower-bounded” I mean ‘lower- and not upper-bounded’.

3 AD do not use the terms ‘positive/negative scale’ or ‘positive/negative orientation’, but I think it is intuitively clear what I mean by these terms, cf. ‘positive’ and ‘negative’ quantifiers (see Section 1).

4 “Only many” and “only most” are impossible in many cases (e.g. ?“I ate only many/most of the cookies”), because “only” seems to carry the extra suggestion that the quantity or proportion involved is low.

5 Real-life example from http://www.europarl.europa.eu/doceo/document/CRE-8-2018-04-18-INT-3-7739-0000_DA.html?redirect, last consulted on 14/11/2019. Found in the English Web 2015 (enTenTen15) corpus with Sketch Engine.

6 Real-life example from https://www.sacsplash.org/post/field-owls-clover, last consulted on 14/11/2019. Found in the English Web 2015 (enTenTen15) corpus with Sketch Engine.

7 Real-life example from https://www.babergh.gov.uk/planning/heritage/living-in-a-conservation-area/, last consulted on 14/11/2019. Found in the English Web 2015 (enTenTen15) corpus with Sketch Engine.

8 A ‘local’ scalar implicature is an implicature that is not based on a full-fledged utterance but arises before the utterance has been entirely processed. Not every pragmaticist believes in local implicatures (see e.g. Geurts 2010: Chapter 7). Those who do, usually use scalars that are embedded under an operator like “or” or the conditional “if” as examples.

9 Generalized Conversational Implicatures (GCIs), of which scalar implicatures are the most famous example, are those implicatures that seem to be tied to a particular form of words (cf. Grice 1975: 37).

10 On the assumption that there are no other elements in the sentence that need pragmatic enrichment.

11 For examples of PCIs, see Grice (1975: 50-56).

12 Unless the utterer of the “so”-clause is a different person from the utterer of the preceding clause. Consider:

A: “I did most of my homework.”

B: “So you didn’t do all of it.”

B’s conclusion is an inferred conclusion (see Section 2), not an argumentative one (although B’s utterance can be used as an argument to support a different conclusion).

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List of illustrations

Title Figure 1. Upper-Bounded “Some (of the) Xs” (‘Some, Not All’)
URL http://journals.openedition.org/anglophonia/docannexe/image/2580/img-1.png
File image/png, 45k
Title Figure 2. Lower-Bounded “Some (of the) Xs” (‘At Least Some’)
URL http://journals.openedition.org/anglophonia/docannexe/image/2580/img-2.png
File image/png, 63k
Title Figure 3: Argumentative Scales
URL http://journals.openedition.org/anglophonia/docannexe/image/2580/img-3.jpg
File image/jpeg, 120k
Title Figure 4: Negative Argumentative Scales4
URL http://journals.openedition.org/anglophonia/docannexe/image/2580/img-4.jpg
File image/jpeg, 117k
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References

Electronic reference

Laura Devlesschouwer, “Upper-Bounded Scalars and Argumentation-in-Language Theory”Anglophonia [Online], 28 | 2019, Online since 20 December 2019, connection on 11 April 2021. URL: http://journals.openedition.org/anglophonia/2580; DOI: https://doi.org/10.4000/anglophonia.2580

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About the author

Laura Devlesschouwer

University of Antwerp & Université Libre de Bruxelles
ldevless@live.be

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Copyright

Licence Creative Commons
Anglophonia – French Journal of English Linguistics est mis à disposition selon les termes de la licence Creative Commons Attribution - Pas d'Utilisation Commerciale - Pas de Modification 4.0 International.

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