Copredication, polysemy and context-sensitivity

ABSTRACT Copredication, as exhibited by sentences such as ‘That book is heavy but informative,’ is commonly seen as a phenomenon that is tied to sentences featuring polysemous expressions. David Liebesman and Ofra Magidor have recently attacked this view by arguing that ‘book’ has a single context-sensitive sense. The first aim of the present paper is to show that Liebesman and Magidor are wrong to claim that ‘book’ is univocal, but that they may nonetheless be right to question that copredication requires polysemy. Its second aim is to consider implications of this result for the debates on copredication and on semantic variability.


Introduction
This paper is concerned with the connection between copredication and semantic variability. Copredication is the phenomenon whereby a single, felicitous occurrence of an expression appears to take several conflicting interpretations. Here are three examples of copredication: (1) That book is heavy but informative.
(2) Lunch was delicious, but went on forever. (Asher 2011, 11) (3) The school that caught fire was celebrating 4th of July when the fire started. (Ortega-Andrés and Vicente 2019, 2) Uttered in the right circumstances, these sentences have readings on which they are felicitous and true. But each of these readings appears to require a single occurrence of an expression to take several conflicting interpretations. In (1), it seems, 'that book' has to designate an informational book as well as a physical book. In (2), 'lunch' has to designate food as well as the event of eating the food. And in (3), 'the school' has to designate a school building as well as members of a school. Copredication has been the subject of a lively debate in recent years. At the centre of the debate is the question which lessons should be drawn from the possibility of copredication. Some theorists argue that copredication shows that meaning does not determine truth-conditions (Chomsky 2000, 16-17;Pietroski 2005;Collins 2017). Others hold on to the view that meaning determines truth-conditions and respond by advancing novel views about the expressions that allow for copredication. Several theorists have argued that copredicating expressions are associated with so-called dot objects, which have both physical and abstract aspects or parts. On the one hand, Asher (2011) argues that 'book' has as its lexical entry a meaning that has a physical and an informational aspect, relative to which a referent is individuated. On the other, Arapinis and Vieu (2015) and Gotham (2017) hold that 'book' designates an object that has a physical and an informational part. Arguing against dot-objects, Magidor (2017, 2019) have instead responded to copredication cases by proposing a view on which ordinary objects can have properties not usually associated with them; for instance, they argue that physical books can be informative and informational books can be heavy. Finally, Ortega-Andrés and Vicente (2019) have used copredication cases to motivate the view that an expression can have more than one semantic value at a time.
The current paper looks at questions about copredication that have received less attention: Which kinds of expressions lead to copredication? And what is the connection between copredication and semantic variability? 1 Copredication has been described as a phenomenon that arises only with occurrences of polysemous expressions: Co-predication occurs when one polysemous nominal expression has simultaneous predications selecting for two different meanings or senses.
Ortega-Andrés and Vicente (2019, 2) Such a verdict is natural, given that central examples in the debate (including the examples introduced above) involve expressions that are standardly taken to be polysemous, with the conflicting interpretations matching several senses standardly ascribed to the expressions in 1 For helpful discussion of the latter question, see Collins (2017, 680 and 687-689). question. For example, 'book' is standardly thought to have a sense designating informational books and another one designating physical books (as well as other senses), so it is prima facie plausible that this polysemy facilitates the copredication in (1). Let us call the view that copredication arises only with occurrences of polysemous expressions the polysemy view of copredication.
The polysemy view has not received much discussion or argumentative support. In my view, it is most plausibly seen as a background assumption that has led many theorists to focus on examples of copredication involving expressions standardly taken to be polysemous. 2 Recently, however, the polysemy view has come under attack. David Liebesman and Ofra Magidor (henceforth L&M) have argued that expressions such as 'book' are context-sensitive, rather than polysemous, and that copredication can arise even in the absence of polysemous expressions: Our view is that previous discussions of copredication are driven by two false views: one linguistic and the other metaphysical. The false linguistic view is that nouns like 'book' are ambiguous (or at least polysemous). Against this, we'll argue that 'book' has a single sense and it designates both informational and physical books […]. The false metaphysical view is that there are categorical constraints on property instantiation that ensure that, e.g. informational books can't be on shelves and physical books can't be informative. L&M (2017, 132) The focus of this paper is on what L&M call the 'the false linguistic view'. There are several reasons why L&M's arguments against this view are significant. If successful, they would, firstly, require a re-evaluation of the phenomenon of copredication and of the proposals that have been put forward in response. In particular, the polysemy view of copredication would have to be amended or abandoned. Secondly, they would force us the rethink the standard construal of polysemy and context-sensitivity as forms of semantic variability. After all, 'book' is not only prominent in central examples of copredication, it is itself a central example of (regular) polysemy; if L&M's arguments did show that 'book' is not polysemous, one might well expect the same result for other nouns, including 'school' and 'lunch'. 3 The paper is thus intended as a contribution to two debates: the debate on copredication and the debate on semantic variability.
In what follows, I will try to show that L&M's arguments against the polysemy of 'book' should be resisted. I will briefly introduce important aspects of polysemy and context-sensitivity and point to criteria that can be used to tell them apart (Section 2). I will then turn to L&M's arguments and, drawing on the criteria, make the case in favour of the polysemy of 'book' (Section 3). In Section 4, I will consider the implications of this result. While L&M's arguments do not give us a reason to overturn the standard view of polysemy and context-sensitivity, I will argue, they do provide insights into semantic variability. Furthermore, I will indicate that, even though there are good reasons to count 'book' as polysemous, there are other examples that suggest that L&M may well be right to question the polysemy view of copredication.

Semantic variability: polysemy and context-sensitivity
Polysemy and context-sensitivity have in common that they are forms of semantic variability, permitting an expression to have different semantic values on different uses. 4 They differ with respect to how the semantic variability is facilitated. A natural way of capturing this difference appeals to different layers of meaning. 5 Polysemous expressions have multiple related senses, whereas context-sensitive expressions have at least one sense that determines different semantic values in different contexts of utterance. Given this way of construing polysemy and context-sensitivity, a single expression can be both polysemous and context-sensitive. This is the case if an expression has multiple related senses, at least one of which determines different semantic values in different contexts of utterance. Semantic variability involving polysemy, context-sensitivity or both phenomena can thus take one of the three forms shown in Figure 1.
What are examples of expressions in each of these three categories? That is a matter of debate, but it might be helpful to mention some (fairly) uncontroversial cases. Mere polysemy is exemplified by 'since', which has a causal and a temporal sense, neither of which appears to be context-sensitive. Polysemy cum context-sensitivity is found with quote above). And it does seem to be the case that L&M's arguments could be given in a similar form for other expressions standardly taken to be polysemous, including 'school' and 'lunch'. 4 Throughout this paper, I will use expression to stand for a meaningful string of letters. 5 For a more detailed introduction to polysemy and context-sensitivity along these lines, see Viebahn and Vetter (2016, Section 2). many gradable adjectives: 'long', for instance, has a temporal and a spatial sense, and each of these senses is context-sensitive. Further examples in this category include 'healthy', 'smart' and 'light'. It is difficult to find clear examples in the third category, which is not surprising given the common assumption that most words are polysemous (cf. Vicente and Falkum 2017). But fairly good candidates here are pronouns and demonstratives, such as 'I' and 'that', which are clearly context-sensitive, but do not appear to be polysemous. 6 Much more would have to be said for a full characterisation of polysemy and context-sensitivity. For instance, one would have to say how the senses of polysemous expressions are related. 7 But for current purposes, the above shall suffice. Even this brief outline can support criteria that help to establish whether an expression is polysemous, context-sensitive or both. Furthermore, adopting a fairly minimal basis has the advantage of not having to rely on too many controversial claims in the discussion to follow.
How, then, can we decide which kind(s) of semantic variability an expression exhibits? Barbara Vetter and I have suggested the following three criteria, which I will rely on in what follows: 8 (1) Linguistic intuitions: To begin with, we can ask whether or not a semantically variable expression intuitively has several senses. Of course, this Figure 1. Semantic variability: polysemy and context-sensitivity. The middle category is a simplification, as it only shows the case in which an expression has several senses, all of which are context-sensitive. This is not to rule out that an expression with several senses, only one of which is context-sensitive, should be placed in the middle category. (Diagram adapted from Viebahn and Vetter 2016, 7.) criterion can only carry a limited amount of weight, and intuitions will not always be clear. But even the small class of examples considered above provides some clear cases: there is the clear intuition that 'since', 'long', 'healthy', 'smart' and 'light' have several senses, and in conjunction with other criteria this intuition can serve as one reason to count the expressions as polysemous; by contrast, a (fairly) clear intuition of only one sense, as in the case of 'I' or 'that', is a reason to count a semantically variable expression as merely context-sensitive. (2) Numbers of candidate semantic values: A semantically variable expression has several candidate semantic values, i.e. semantic values the expression could have on a certain use. While this holds for all kinds of semantic variability, the amount of candidate semantic values differs. In particular, context-sensitive expressions have many more candidate semantic values than merely polysemous ones. For instance, 'since' has at most a handful of candidate semantic values, while 'I' has as many candidate semantic values as there are language users. Comparatively few candidate semantic values thus indicate mere polysemy, while many candidate semantic values are a sign of context-sensitivity. 9 (3) Clusters of candidate semantic values: If an expression has many candidate semantic values, we should expect these candidate semantic values to come in clusters if the expression is polysemous (as well as context-sensitive), and we should expect no such clustering in the case of mere context-sensitivity. The thought here is that in the case of polysemy cum context-sensitivity, there will be a cluster of candidate semantic values for each sense of the expression. For instance, 'long' has a cluster of temporal candidate semantic values, and a cluster of spatial semantic values. No such clustering is obvious in the candidate semantic values of 'I'.
If the verdicts of all three criteria align, that can be strong evidence to place a semantically variable expression in one of the three categories. The criteria can thus be helpful in assessing the semantic variability of 'book' and in evaluating L&M's arguments against its polysemy.
3. The variability of 'book': polysemy vs. context-sensitivity As mentioned above, 'book' is commonly considered to be a prime example of polysemy. At least at first sight, the three criteria confirm this view. We have seen that 'book' intuitively has several senses: one for informational books, and another for physical books. The first criterion thus speaks in favour of polysemy (while leaving open whether the expression is also context-sensitive). The OED points to a few further senses of 'book', e.g. one for a subdivision of a larger written work, but still the overall number of candidate semantic values appears to be limited. If this is right, the second criterion indicates mere polysemy, and the third criterion does not apply. Initial impressions thus support the polysemy of 'book', so why do L&M take the expression to be univocal and merely context-sensitive?
L&M put forward three arguments against the polysemy of 'book'. 10 Their first argument concerns the number of candidate semantic values 'book' has: in their view, the initial impression of few candidate semantic values is mistaken. To support this claim, L&M (2017, 136) introduce sentences (4)-(6), uttered in a situation in which we are facing a bookshelf containing three physical books: two copies of the French translation of Naming and Necessity and one copy of the Hebrew translation.
(4) One book is on the shelf. (5) Two books are on the shelf. (6) Three books are on the shelf.
According to L&M, each of these sentences has a true reading in the situation described, which is evinced by the following extended versions of the sentences: (4.1) One book is on the shelf: Naming and Necessity. (5.1) Two books are on the shelf: the Hebrew translation of Naming and Necessity and the French translation of Naming and Necessity. (6.1) Three books are on the shelf: the one on the left, the one in the middle, and the one on the right. 11 10 L&M also argue that merely pointing to several readings of counting-sentences involving a semantically variable expression is not a good reason to treat the expression as polysemous (cf. L&M 2017, 133-134). I agree with them on this point.

11
To me, (5) and (5.1) sound slightly less natural than the other sentences; I think it would be fine to respond to (5) or (5.1) with 'No, it's just one book in different translations'. This may be due to the The idea is that, in the right circumstances, at least three different readings of 'book' can be brought out: one for physical books, one for informational books differentiating between different translations of a work, and one for informational books without such a differentiation. Through similar considerations, L&M argue, we could arrive at large number of possible readings (and thus candidate semantic values) for 'book', and we would have to posit a large number of senses if this variability were to be construed as polysemy: Reflection on similar issues concerning the individuation conditions for books (Do two editions of the same book count as the same book? Does a second physical copy with one word misprinted count as the same book as the original?) suggests that, on an ambiguity view, 'book' would have to have a large number of senses. L&M (2017, 136) L&M take this to be evidence in favour of their univocal view, on which 'book' has a single context-sensitive sense, which can designate both physical and informational books, but can also be contextually restricted to designate e.g. only physical books (cf. L&M 2017, 133). In response, I would like to make two points: Firstly, it is not clear that we could arrive at a large number of candidate semantic values along the route sketched. And secondly, even if we accept that 'book' has a large number of candidate semantic values, that does not speak against it being polysemous; rather, it fits well with a view on which 'book' is polysemous as well as context-sensitive.
On the first point: Could we use L&M's method to generate many more candidate semantic values for 'book'? That is not obvious. The questions whether two editions of the same book count as the same book or whether one misprinted word leads to a new book can indeed be answered differently. But arguably the reason for this is that 'book' is vague, just as most other natural language expressions. Vagueness is distinct from context-sensitivity and polysemy: though there are many expressions that are vague as well as context-sensitive and/or polysemous, there is no strict link between vagueness on the one hand, and contextsensitivity or polysemy on the other (as is noted e.g. by Williamson 1994, 214 andÅkerman 2012). The considerations offered by L&M thus do not seem to support a view of many candidate semantic values for 'book'. 12 Perhaps stronger considerations could be given along the lines vagueness of 'book' and the unclarity concerning the relation between different translations of a book. I will shortly touch on the issue of vagueness.
of Stanley and Szabó (2000), but I will not dwell on the matter here, as the case for univocity is weak even in the face of many candidate semantic values.
On the second point: Let us, for the sake of argument, assume that 'book' does have a large number of candidate semantic values. Given that assumption, should we hold that 'book' is univocal and not polysemous? The criteria introduced above suggest that we should not. Of course, there is still the intuition that 'book' has several senses. But what matters here is the assumption of many candidate semantic values. According to the second criterion, this is evidence against mere polysemy. Importantly, however, it is not evidence against an expression being polysemous, as polysemy and context-sensitivity are not exclusive. What is more, if 'book' does have many candidate semantic values, then clearly these will come in clusters: there will be a cluster of candidate semantic values for physical books, one for informational books, and possibly yet other clusters. So even given a large number of candidate semantic values, the criteria provide a clear verdict in favour of the polysemy of 'book', and in particular in favour of polysemy cum context-sensitivity.
L&M provide two further arguments against the polysemy of 'book', which I will take in reverse order. Their third argument is based on the apparent absence of true readings of certain negated sentences, such as: (7) [Pointing at a copy of War and Peace:] This isn't a book! (L&M 2017, 136) L&M hold that true readings of (7) should be available if 'book' is polysemous: one, on which 'this' picks out a physical book and 'book' designates informational books, and another, on which things are reversed. According to L&M, however, (7) does not have a true reading. I am not entirely convinced by this verdict. For instance, (7) does appear to have a true reading if it is uttered while pointing at a physical book that contains the first half of War and Peace, possibly followed up with: 'It's only half of a book.' Still, intuitions about this case diverge, so let us proceed on the assumption that (7) does not have a true reading. 13

12
The term candidate semantic value does come up in the debate on vagueness, and thus one might think that there is a sense in which 'book' has many candidate semantic valuesone for each precisification; here, however, we are interested in whether semantic variability leads to 'book' having many candidate semantic values. The considerations on offer do not seem to provide reasons to answer this question in the positive. 13 Here is some evidence that intuitions indeed diverge: of the three anonymous reviewers who read this paper, two agreed that (7) does have true readings, while one disagreed.
While it is an interesting question why it is difficult or even impossible to access a true reading of (7) in the situation given, the sentence does not provide a reason against treating 'book' as polysemous. For one thing, there are other sentences featuring clearly polysemous expressions that likewise lack certain true readings (in similar settings). For instance, it is certainly difficult to access a true reading of (8) on which 'this' picks out a queue (which does not have a temporal duration), while 'long' designates a temporal duration, although one may expect such a reading to be possible given the polysemy of 'long':

(8) [Pointing at a queue at a bus stop:] This isn't long! 14
Secondly, it is not clear why the potential readings for (7) given above (on which 'this' picks out a physical book and 'book' informational books, or vice versa) should be ruled out on a view that takes 'book' to be univocal and context-sensitive. In that case, however, the polysemy view and the context-sensitivity view are on the same footing with respect to sentences such as (7).
That leaves L&M's second argument against the polysemy view, which takes as its starting point a sentence in which 'book' is used in a general sense so as to designate both physical and informational books. The sentence is adapted from a real-life sentence in the syllabus of a history of the book course: (9) Each week, you will be assigned a single book, on which you will be required to submit a report: on odd weeks, your book will be a theoretical book on the history of bookmaking, while on even weeks, our special collections librarian will assign you a volume from our historical collection to examine. (L&M 2017, 136) Here, the first occurrence of 'book' appears to be used in a general way, without a restriction to physical or informational books. This fits well with L&M's univocal, context-sensitive analysis, and it seems to fit less well with the polysemy view.
This does appear to be a challenge for a view on which 'book' is polysemous. But given the evidence in favour of such a view and (as I have tried to argue) the absence of other evidence against it, it should rather be seen as evidence in favour of general uses of polysemous expressions, 14 One anonymous reviewer was able to access a true reading of (8), though noted that it is hard to access. and not as a reason to reject the polysemy of 'book'. How, then, could a polysemy view account for such general uses? I want to briefly sketch two routes that I take to be promising.
One option is to posit a general sense among the senses of 'book', one that covers both physical and informational books. So, on this view, 'book' has at least three senses: a physical sense, an informational sense and a general sense that applies both to physical and to informational books. As far as I can see, this approach is compatible with different theories of polysemy representation. 15 On the one hand, there are sense enumeration lexicons, which entail that the different senses of a polysemous expression are represented separately in the lexicon. Such theories have to add a separately represented general sense to the lexicon. On the other hand, onerepresentation approaches associate polysemous expressions either with a core-meaning or with an overspecified meaning, and from this coremeaning or overspecified meaning the relevant senses are derived or selected in context. Within this tradition, it might be possible to identify the general sense with the core meaning, or to specify it as one of the senses that can be derived from the core meaning or selected from the overspecified meaning. 16 Another option is to allow that several senses of 'book' can be operative at the same time. This second approach thus associates a plurality of semantic values with a single expression (on a single use). Such a pluralist approach has recently been proposed in several debates concerning semantic variability: von Fintel and Gillies (2011) have put forward a pluralist view of 'might' to account for cases in which speaker and addressee are in different epistemic positions; King (2014) and Viebahn (2020) have argued that gradable adjectives can have several semantic values if they are accompanied by unspecific or conflicting intentions; and, most relevantly, Ortega-Andrés and Vicente (2019) hold that copredication requires polysemous expressions to take several semantic values (on a single use).

15
See Vicente and Falkum (2017, Section 5) for an helpful overview of such theories. 16 This approach is in the same boat as L&M's univocal view of 'book' with respect to the following question: Why can the general sense of 'book' not be used to count all the things it designates at once? For example, given a general sense of 'book', one might expect 'Four books are on the shelf' to have a true reading in a situation in which three copies of Naming and Necessity are on the shelfafter all, the general sense designates each copy as well as the informational book. But the sentence clearly does not have a true reading in this situation. The same problem applies to L&M's univocal view, as one might expect the unrestricted reading of 'book' to lead to a true reading in the situation given. In response, L&M (2017, 134-135) argue that the relevant reading is ruled out 'due to some restriction on double counting'. It seems that adherents of the general-sense polysemy view can explain the lack of a true reading in the same fashion. This approach, too, seems to be compatible with both sense enumeration lexicons as well as one-representation approaches.
I acknowledge that both options require further motivation and spelling out. For example, with respect to the first option one might ask why we should add a further general sense that is only accessed in certain very specific contexts. And the pluralist approach faces the challenge of explaining under which circumstances polysemous expressions can have several semantic values. Still, I cannot see any principled reasons why the approaches cannot be successful, and thus I think that sentences such as L&M's (9) should be taken as an incentive to investigate the phenomenon of polysemy further, and not as a reason to move 'book' out of the class of polysemous expressions and in to that of merely context-sensitive ones.
I hope to have shown that L&M's arguments against the polysemy of 'book' are indecisive. In particular, these arguments seem to disregard the possibility of polysemy cum context-sensitivity. If 'book' is indeed context-sensitive, it should be classified as context-sensitive as well as polysemous, with polysemy accounting for the divide between physical and informational candidate semantic values, and context-sensitivity providing further distinctions among informational candidate semantic values (e.g. possibly between candidate semantic values on which two editions of a book count as the same book and others on which two editions of a book count as different books).

Implications
What are the implications of the foregoing? To begin with, there are implications for our understanding of polysemy and context-sensitivity as forms of semantic variability. L&M's arguments give us no strong reason to abandon the traditional view on which nouns like 'book' are polysemous, but they nonetheless provide insight into semantic variability. The result of their first argument may be taken as further evidence that many expressions are polysemous as well as context-sensitive. And the second argument calls for further work on general uses of polysemous expressions. Should such general uses be captured by positing a corresponding general sense (e.g. a sense that applies to all books for 'book')? Should we rather hold that in general uses several senses of a polysemous expression are operative at the same time? Or is there yet another way to account for general uses while holding on to the polysemy of 'book'?
Then, there are implications for the debate on copredication. The first of these is negative: L&M's arguments do not establish that central examples of copredication involve expressions that are univocal and context-sensitive. For these examples, the link between polysemy and copredication remains intact. This may well have an impact on proposals for capturing copredication. For example, L&M aim to account for copredication by pointing to the metaphysical view of property inheritance, according to which physical books can inherit properties from their corresponding informational books, and vice versa. This view allows physical books to be informative and informational books to be heavy. A key aspect of the view is that 'properties can be instantiated by different objects in different ways' (L&M 2017, 143). According to L&M, this aspect coheres especially well with the view that 'book' and other nouns are univocal: To hold fast to the ambiguity of 'book' while independently stressing the fact that there are many ways to instantiate ordinary properties and exemplify ordinary predicates would run the risk of arbitrariness. So, even if the combination of our metaphysical view with an ambiguity view of 'book' isn't incoherent, it is unmotivated. L&M (2017, 143) The results of this paper suggest that adherents of the property inheritance view might have to rethink how the polysemy of 'book' coheres with the claim that there are many ways to instantiate ordinary properties. At first view, it seems that the risk of arbitrariness is less severe for a view on which 'book' is both polysemous and context-sensitive than it is for a view on which the expression is merely polysemous. After all, with polysemy cum context-sensitivity one would expect there to be many candidate semantic values. The important question, then, is whether the ways of instantiating ordinary properties or the ways of exemplifying ordinary predicates form clusters. If they do, that would fit well with a view on which 'book' is polysemous and context-sensitive.
A second view that could be impacted is the polysemy account of copredication due to Ortega-Andrés and Vicente (2019). This account appeals to several senses of 'book' in order to explain why (1) (repeated below) can be felicitous and true: (1) That book is heavy but informative.
Ortega-Andrés and Vicente argue, firstly, that both the physical and the informational sense of 'book' are operative in (1) (leading to several semantic values), and secondly, that both of these senses (as well as others) are activated in addressees upon their encounter with the word 'book'. Polysemy thus plays a decisive role in this account, and it is unclear whether it could be made to fit with a view on which 'book' is univocal and context-sensitiveafter all, then there would be no senses to be jointly operative or to be co-activated. Now, it seems that adherents of the polysemy approach should welcome the results of this paper so far: if L&M's arguments against polysemy are inconclusive, a potential danger has been warded off.
However, L&M may well be right to question the view that copredication must be due to polysemous expressions. Even if existing examples do involve polysemous expressions, it seems that examples of copredication can be given for which this is not the case. Here are some candidates: (10) [Pointing at a copy of a book:] That is heavy but informative. (11) [At the end of a very long lunch:] That was delicious, but went on forever. (12) [Pointing at a picture of a school:] It was celebrating 4th of July when the fire started. 17 In the situations given, these sentences have readings on which they are felicitous and true. Each of these readings appears to require a single occurrence of an expression to take several conflicting interpretations. But 'that' and 'it', the copredicating expressions, are standardly taken to be non-polysemous: they appear to be fairly clear examples of expressions that are context-sensitive and univocal. The examples thus suggest that the polysemy view, according to which copredication arises only with occurrences of polysemous expressions, is mistaken. However, this conclusion may not be unavoidable, as there are ways for adherents of the polysemy view (or of related views) to respond. I would like to end by briefly exploring two such responses. 18 For one thing, it might be argued that (10)-(12) do involve polysemous expressions after all. Indeed, the fact that 'that' and 'it' support copredication and that they can designate objects of very different kinds might be seen as 17 Collins (2017, 680) mentions a similar example of copredication without polysemous expressions. Following an utterance of 'That book [pointing at a concrete particular] you haven't read,' Collins remarks, a speaker might truly respond with: 'Oh, I read that on my kindle the other week.' According to Collins, this shows that 'even a demonstrative allows for copredication via simultaneously picking out a concrete particular and something more abstract such as a body of information'. However, the main focus of Collins's paper is not on the question whether copredication requires polysemy. 18 Many thanks to two anonymous reviewers for suggesting the responses I am about to discuss. evidence in favour of their polysemy. Moreover, this response seems to be supported by the second and third criteria introduced above. Clearly 'that' and 'it' have many candidate semantic values, and these candidate semantic values seem to come in clusters: clusters which correspond to the different kinds of things that can be picked out by the expressions. While these observations do seem to speak in favour of polysemy, one potential problem for this view is the fact that 'that' and 'it' are not in any clear sense intuitively associated with several senses. This intuitive lack of several senses for 'that' and 'it' and the contrast it creates with standard examples of polysemy (which intuitively do have several senses) calls for an explanation.
According to a second response, there can be an important connection between copredication and polysemy even if some examples of copredication do not involve polysemous expressions. Note that 'that' and 'it' in (10)-(12) designate objects or concepts that are commonly designated by polysemous expressions. One might hold that the concepts evoked by (10)-(12) are structured and offer different senses for interpretation. More generally, copredication might thus be said to require activation of a word meaning associated with a polysemous expression. In this way, a close connection between copredication and polysemy could be upheld without positing that copredication requires a sentence to feature at least one polysemous expression.
Both responses add new perspectives and questions to the debates on semantic variability and copredication. In order to evaluate the first response, we have to get clearer about how the criteria introduced above should be weighted. In particular, we have to decide which verdict should be given if the second and third criteria (concerning number and clusters of candidate semantic values) point towards polysemy cum context-sensitivity but the first criterion (concerning intuitions about senses) points in the opposite direction (or at least fails to support the verdict of the other criteria). It is also an open question under which circumstances candidate semantic values should count as clustered. These are important questions that can help to shed further light on the distinction between polysemy and context-sensitivity. Furthermore, if the first response can be successfully defended, the polysemy view (spelled out in terms of polysemous expressions) could remain intact, but standard views on semantic variability would have to be revised. On the one hand, the polysemy of expression such as 'that' and 'it' would show that there can be polysemy in the absence of intuitively distinct senses. On the other, there would be a further reason to accept the pervasiveness of polysemy: if even 'that' and 'it' are polysemous, very few, if any, examples of expressions remain that are context-sensitive but not polysemous.
The second response requires us to scrutinise the commitments of those theorists who see a close connection between copredication and polysemy. Are they committed to a connection at the level of expressions or merely at the level of interpretation? The view presented in Ortega-Andrés and Vicente (2019) does seem to be based on the polysemy view as outlined at the beginning of this paper. After all, Ortega-Andrés and Vicente hold that the co-activation of several senses which makes copredication possible is due to the interpreter's encounter with a polysemous word. It may well be possible to amend this view in a way that does not require activation by words, but rather by concepts. On this amended view, copredicating expressions (whether polysemous or not) first activate a certain structured concept, which then supplies the senses required for copredication. This does seem to offer an explanation of how hearers interpret cases of copredication. But it is unclear which lessons should be drawn with respect to the semantic values of copredicating expressions. Should we hold that the copredicating expressions in (10)-(12) have several semantic values? Or do we only find this multiplicity at the level of concepts?
Finally, regardless of the success of the responses, the examples do show that the phenomenon of copredication is more varied than has been hitherto assumed: contrary to what the currently discussed range of examples suggests, copredication sentences need not feature expressions standardly taken to be polysemous. It thus makes good sense not to focus entirely on such expressions in investigating the phenomenon of copredication.