Indexical Color Predicates: Truth Conditional Semantics vs. Truth Conditional Pragmatics

Indexical Color Predicates: Truth Conditional Semantics vs. TruthConditional Pragmatics

Lenny Clapp

Canadian Journal of Philosophy, Volume 42, Number 2, June 2012,pp. 71-100 (Article)

Published by Canadian Journal of PhilosophyDOI: 10.1353/cjp.2012.0009

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CANADIAN JOURNAL OF PHILOSOPHY 71Volume 42, Number 2, June 2012, pp. 71-100

Indexical Color Predicates: Truth Conditional Semantics vs. Truth Conditional Pragmatics

LENNY CLAPPNorthern Illinois UniversityZulauf Hall 918Dekalb, IL 60115USA

I Introduction

Truth conditional semantics is the project of ‘determining a way of assigning truth conditions to sentences based on A) the extension of their constituents and B) their syntactic mode of combination’ (Roths-child and Segal, 2009). This research program has been subject to objec-tions that take the form of underdetermination arguments, an infl uential instance of which is presented by Travis:

… consider the words ‘The leaf is green,’ speaking of a given leaf, and its condition at a given time, used so as to mean what they do mean in English. How many dis-tinct things might be said in words with all that true of them? Many.… Suppose a Japanese maple leaf, turned brown, was painted green for a decoration. In sorting leaves by colour, one might truly call this one green. In describing leaves to help identify their species, it might, for all the paint, be false to call it that. So words may have all the stipulated features while saying something true, but while also saying something false. (Travis, 1994, 171-2)

Travis describes two contexts, one in which we are sorting leaves by color and the other in which we are sorting leaves by species. In the two contexts factors A) and B) at least seem to be the same. Yet the use of ‘The leaf is green’ in the color-sorting context says something true,

72 Lenny Clapp

but the use of it in the species-sorting context says something false. So, contrary to what is assumed by truth conditional semantics, factors A) and B) underdetermine the truth conditions of utterances of ‘The leaf is green.’

Such underdetermination arguments are invoked by theorists who reject truth conditional semantics in favor of truth conditional pragmat-ics, the central idea of which is that information available in the context that is not semantically encoded by an uttered sentence is relevant for determining the truth conditions of, or what is said by, the utterance.1 But defenders of truth conditional semantics do not accept such argu-ments, and there are two principal strategies of response.

First, the response of semantic minimalism is to reject the presumption that intuitive judgments concerning the truth conditions of assertions bear directly on the truth conditions of the sentences uttered.2 Minimal-ism responds to underdetermination arguments by maintaining that the truth-value of the sentence uttered in two contexts does not vary, rather what varies is only the truth-values of the speech acts performed. Thus according to minimalism, underdetermination arguments con-fuse semantic sentence-content and pragmatic speaker-content. And second, the response of indexicalism is to analyze some constituent expression of the sentence uttered in the two contexts as being an index-ical, i.e. a lexical item that as a matter of conventional meaning has dif-ferent semantic-contents in different utterance-contexts.3 So, under an indexicalist response, the fact that utterances of ‘The leaf is green’ can have different truth-values in different contexts is no more troubling for truth conditional semantics than is the fact that two utterances of ‘Today is Tuesday’ can have different truth-values on different days. Indexicalism thus differs from both truth conditional pragmatics and minimalism in that indexicalism rejects the claim that the judgments of truth conditions elicited in underdetermination arguments must be explained pragmatically. Rather, by extending the class of indexical

1 A wide variety of approaches, including semantic relativism (MacFarlane, 2007) and relevance theory (Sperber and Wilson, 1986), thus fall under the general rubric of truth conditional pragmatics. Paradigmatic defenders of truth conditional prag-matics include Travis (1997), Bezuidenhout (2002), and Recanati (2004).

2 Paradigmatic defenders of minimalism include Cappelen and Lepore (2005), and Borg (2004).

3 Note that under this usage of the technical term ‘indexical,’ any analysis of an expression e that posits hidden (aphonic) variables associated with e in order account for context-sensitivity qualifi es as an indexical analysis of e. This usage may involve an extension of the way the term is typically used, but it accurately refl ects the Kaplan-inspired motivation of indexicalist proposals.

Indexical Color Predicates: Truth Conditional Semantics vs. Truth Conditional Pragmatics 73

expressions the indexicalist hopes to increase the explanatory range of truth conditional semantics so that it encompasses such judgments of truth conditions.4

My purpose here is to criticize several indexicalist proposals that analyze color adjectives, e.g. ‘green,’ appearing in color predicates, e.g. ‘is green,’ as being, or otherwise involving, some sort of indexi-cal expression, and to present some empirical evidence suggesting that color adjectives are not indexicals. In the fi rst section I clarify the theoretical issue that divides truth conditional semantics and truth conditional pragmatics, and explain the indexicalist strategy relative to this fundamental disagreement. In the second section I consider two versions of hidden-variable indexicalism: I begin by explicating the rela-tively straightforward analysis of color adjectives proposed by Szabó (2001), and I demonstrate that this version of indexicalism is too con-strained and thus does not provide an adequate explanation of all the relevant judgments made manifest in underdetermination arguments involving color predicates. I then consider Hansen’s (2011) more open-ended hidden-variable analysis, which is specifi cally designed to over-come the limitations inherent in Szabó’s account. I then show, however, that Hansen’s more open-ended proposal runs afoul of the sorts of problems that MacFarlane (2007) and others have has raised for indexi-cal analyses of other sorts of expression, predicates of personal taste in particular. Such challenges for hidden-variable indexical analyses of color adjectives motivate the defender of truth conditional semantics to formulate an alternative sort of indexical analysis, and thus in third section I consider Rothschild and Segal’s (2009) metaphysically sophis-ticated overt-indexical proposal. I argue, however, that this alternative approach fails because under it so-called ‘indexical predicates’ are not really indexical expressions, and thus the metaphysically complex pro-posal does not succeed in saving truth conditional semantics from refu-tation by underdetermination arguments involving color predicates. Finally, in the fourth section I present empirical evidence suggesting that color adjectives are not indexicals.

II Truth conditional Semantics, Truth conditional Pragmatics and Indexicalism

Semantics concerns knowledge of the meanings of lexical items and how the meanings of grammatical combinations of lexical items, including

4 Paradigmatic indexicalist responses are presented in Szabó (2001), Stanley (2000), and Glanzberg (2008).

74 Lenny Clapp

sentences, depend upon the meanings of their constituents and their structure. Semantics thus concerns knowledge of expression types that competent speakers bring to particular contexts of language use. In contrast, pragmatics concerns application of such semantic knowledge in a particular context in the process of linguistic communication. Thus pragmatics involves a combination of semantic knowledge together with other sorts of knowledge and abilities, including perception, ‘mind-reading,’ general encyclopedic knowledge, and whatever else competent speakers utilize to interpret one another. This much, per-haps only in virtue of its imprecision, is common-ground between truth conditional semantics and truth conditional pragmatics. What divides them is the question of where the notion of truth, or truth conditions, belongs.

The fundamental idea of truth conditional semantics is that seman-tic knowledge suffi ces for the determination of the truth conditions of sentences. According to truth conditional semantics then, a competent interpreter’s ability to grasp the truth conditions expressed by a declar-ative utterance is explained solely by her knowledge of the meanings of words in the sentence, and how such meanings are combined, in accor-dance with the syntactic structure of the sentence. This fundamental idea of truth conditional semantics is encapsulated in what Larson and Segal (1995) call ‘hypothesis T.’ Where (T) is the familiar Tarski-schema,

(T) S is true if and only if p.

Larson and Segal propose

The T hypothesis A speaker’s knowledge of meaning for a language L is knowledge of a deductive system (i.e. a system of axioms and production rules) proving theo-rems of the form of (T) that are interpretive for sentences of L. (1995, 33).

Though truth conditional semantics is strictly a view about what knowledge suffi ces for understanding the truth conditions expressed by utterances of declarative sentences, its defenders often take it to imply a view concerning the cognitive architecture of competent language users. So, for example, Borg maintains that determination of truth con-ditions is ‘the result of processing in some distinct, compartmentalized language faculty, governed by computational processes and appeal-ing to something less than the full range of information possessed by the agent’ (2004, 8). Similarly, Larson and Segal (1995) maintain that knowledge suffi cient for understanding the truth conditions expressed by declarative utterances is encapsulated in a ‘semantic module’ which ‘contains specifi cations of meanings for the simplest expressions of the language and rules for deducing the meanings of complex expressions


on the basis of the meanings of their parts and the structural confi gura-tion in which they occur’ (1995, 22).

In contrast to truth conditional semantics, truth conditional pragmat-ics maintains that ‘it is not sentences but assertions that are true or false. That is, speakers say what is true or false by using sentences in some conversational context’ (Bezuidenhout, 2002, 105). Thus, according to truth conditional pragmatics, it is particular speech acts performed by using declarative sentences for particular purposes that express truth conditions. Because truth conditional pragmatics denies that it is sen-tences that are true or false, it rejects the central claim of truth con-ditional semantics that knowledge of only linguistic meanings and syntactic structure suffi ces for the grasping of the truth conditions of declarative utterances. This semantic underdetermination of truth con-ditions, or of what is said, is what Travis takes to be the general lesson of the previously cited argument:

… grasping what it is that is said in given words requires, over and above knowing what they mean, and what they refer to, an adequate appreciation of the effects … which their surrounding had.… That now emerges as an extra capacity, beyond knowledge of meaning and referents — beyond e.g. knowing what green is, and which leaf is in question — on which understanding what is said inescapably depends. (1994, 176-7)

Note that while nothing in the above citation suggests that knowl-edge of meaning is not encapsulated in a cognitive module, Travis clearly maintains that what is required for the grasping of truth condi-tional ‘what is said’ content is a capacity ‘over and above’ knowledge of meaning. The issue that divides truth conditional semantics and truth conditional pragmatics is thus not whether a competent language user’s semantic competence, her knowledge of meaning, can be encapsulated in a cognitive module. We may take that much as agreed upon. Rather, the issue that divides them is whether or not all of the knowledge required for the grasping of the truth conditional content of declarative utterances is of the sort that could be encapsulated in a semantic module.

Matters are complicated by the fact that grasping the truth conditional content expressed by some declarative utterances obviously requires extra-semantic, pragmatically provided, information that is not con-tained in a semantic module; in terms of Larson and Segal’s statement of the fundamental motivation of truth conditional semantics, the ‘T hypothesis’ is obviously false. This is because natural languages include obvious indexical expressions — ‘I,’ ‘that,’ tensed verbs, etc. — and thus it is obviously false that linguistic meaning together with a mode of com-bination supplied by syntax determines the truth conditions of every sentence. What does the proponent of truth conditional semantics do about this ‘very large fl y in the ointment’ (Davidson, 1967, 318)?

76 Lenny Clapp

The fundamental idea, sketched by Davidson (1967) and further developed by Kaplan (1989), involves two concessive steps. The fi rst step is to maintain, what is surely correct, that it is an aspect of the meanings, the semantic features, of such indexical expressions that they have ‘variable references’ and thus ‘can pick out a certain object on one occasion of use and certain other object on another occasion’ (Larson and Segal, 1995, 198). Since it is part of the meanings of indexicals that they have ‘variable reference,’ the fact that the semantic features of a sentence such as ‘I am here’ are not themselves suffi cient for the deriva-tion of an interpretive T-theorem, though it may violate the letter of the T hypothesis, does not violate the spirit of truth conditional semantics. That is, defenders of truth conditional semantics concede that the exis-tence of indexical expressions strictly speaking undermines the claim that knowledge of meaning and syntactic mode-of-combination alone determine truth conditions, but they still defend the weaker claim that semantic knowledge, together with additional pragmatically provided information that semantic knowledge specifi es as necessary, is suffi cient to determine truth conditions. As Larson and Segal (1995) put it, even sentences containing indexical expressions have ‘fully determinate semantic features’ that ‘constitute a sort of recipe that allows us to cal-culate the truth conditions of a propitious utterance once we know the relevant details of the context’ (1995, 219). Following Kaplan (1989), I will refer to such ‘recipes’ as characters, and following Recanati (2004, 7) I will say that words whose conventional meanings are characters require contextual saturation.

The second concessive step consists of a technique for incorporat-ing characters into truth-theoretic semantic theory. There are various ways this can be done, but the essential idea is that ‘the presence of variable-reference terms shows that we cannot assign values to expres-sions simpliciter; rather, we must assign them with respect to a context of use or a context of utterance’ (Larson and Segal, 1995, 199). The technique implemented by Larson and Segal (1995) and endorsed in Rothschild and Segal (2009) involves conditionalized T-theorems:

The basic idea is that the context-independent semantics provides the means to prove a T-theorem, given information about the extensions of expressions in spe-cifi c contexts. Very roughly, the idea for, say, ‘that is remarkable’ is that the context-independent semantics allows for one to derive a conditional along the lines of D:

(D) If u is an utterance ‘that is remarkable’ and the speaker uses ‘that’ in u to refer to x, u is true iff x satisfi es ‘is remarkable’ (2009, 471).

Semantic knowledge of the character of ‘that’ provides knowledge of conditionals such as (D). In virtue of having purely semantic knowl-edge of (D), an interpreter knows that determining the truth conditions


of an utterance of ‘that is remarkable’ requires having non-semantic knowledge concerning what the speaker is referring to by using ‘that.’ And once the semantically required yet pragmatically provided infor-mation is gathered from the context, the character can be saturated and the antecedent of (D) can be detached; what is expressed by the con-sequent has the form of a traditional T-theorem, expressing the truth conditions of the utterance.

So, it is conceded that the semantic module alone is insuffi cient to derive truth conditions; rather it is only this semantic knowledge ‘given information about the extensions of expressions in specifi c contexts’ (2009, 471) that determines truth conditions. This concession, however, is not a repudiation of truth conditional semantics because the knowl-edge that such non-semantic information is required to determine truth conditions is itself semantic knowledge, deriving from knowledge of the characters of indexicals. Thus Larson and Segal state explicitly that on their view it is ‘knowledge about pronouns and demonstratives [that] gives speakers the ability to take an utterance even in which various objects are demonstrated and referred to and to infer from it the truth conditions of that utterance’ (1995, 207).

The issue dividing truth conditional semantics and truth conditional pragmatics, as well as the indexicalist response to underdetermination arguments, can now be stated more precisely. Truth conditional seman-tics maintains that all truth conditional variability of sentences is a result of the presence of indexical expressions in those sentences. Thus, though mere semantic knowledge alone is not suffi cient to determine the truth conditions of utterances of such sentences, pure semantic knowledge together with pragmatically provided information that is specifi ed as required by the characters of such expressions does suffi ce to determine truth conditions. And hence the indexicalist response to underdetermination arguments is to maintain that the truth conditional variability manifested in such arguments is explained by the presence of some indexical expression in the sentence, an expression whose con-ventional meaning specifi es what information must be pragmatically provided to determine extension, and thus truth conditions. In contrast, truth conditional pragmatics maintains that the truth conditional vari-ability of some sentences is not explained by the presence of some such indexical expression, but instead requires appeal to ‘an extra capacity, beyond knowledge of meaning and referents’ (Travis, 1994, 177).

78 Lenny Clapp

III Hidden-Variable Color Predicates

Szabó’s (2001) hidden-variable analysis of color predicates is based upon two related principles: fi rst, ‘contextual incompleteness in adjec-tives has different dimensions’ (2001, 136), and second that ‘different dimensions of incompleteness correspond to different sorts of variables in the logical form’ (2001, 136). So, to provide an analysis of, e.g., ‘green’ the fi rst task is to identify the dimensions of ‘contextual incomplete-ness,’ and the second is to posit variables corresponding to these dimen-sions in the logical forms of sentences containing ‘green.’ Thus Szabó identifi es two dimensions of contextual incompleteness: fi rst, ‘“green” is … a scalar adjective’ (2001, 137), and thus its extension relative to some context depends upon which comparison class is contextually salient. And second, Szabó maintains that ‘an object is green if some contextually specifi able (and presumably suffi ciently large) part of it is green’ (2001, 138). And then Szabó posits two hidden variables, one for the ‘comparison class’ dimension, and the other for the ‘contextually specifi able … part’ dimension. Szabó thus concludes that ‘the logical form of ‘‘green’’ is ‘‘(green(C,P))(x)’’ where ‘‘C’’ is a [variable] standing for a comparison class and ‘‘P’’ is a variable standing for a certain part of the object’ (2001, 138). Finally, Szabó applies this indexical analysis to Travis’s underdetermination argument: ‘the context-dependency that appears in Travis’s example is a relatively easily characterizable kind: it is a matter of different contextually specifi ed values for the variable ‘‘P’’’ (2001, 138). Thus, the truth conditional variability manifested in Travis’s argument is to be explained by the (aphonic) indexical ‘P’ being contextually saturated by different parts of the leaf in the two contexts.

Szabó’s proposal clearly falls within the indexicalist paradigm. Though Szabó does not explicitly specify characters for color adjec-tives, that he thinks color adjectives have such ‘recipes’ as conventional meanings is implicit in the way he formulates his theory. Szabó uses the aphonic variable ‘P’ (as opposed to, say, ‘X’) to represent that it is an aspect of the conventional meaning of, e.g., ‘green’ that some part must be provided by the context of utterance in order to determine truth conditional content; thus, any competent speaker must know, perhaps only implicitly, that an occurrence of the color adjective ‘green’ requires contextual saturation by a particular part that is an aspect of the context. (And similar remarks apply to the comparison class variable ‘C.’) The problem with Szabó’s analysis is that the implicit characters it assigns to color adjectives are too constrained: underdetermination argu-ments reveal that there are far more than two dimensions of ‘contex-tual incompleteness’ associated with color adjectives. Szabó claims that Travis’s argument can be undermined by appeal to variation along the part-dimension that is semantically encoded in the (aphonic) reference-


variable expression ‘P.’ And he is surely correct to assume that other underdetermination arguments involving color predicates could be constructed where the intuitive ‘contextual incompleteness’ involved differing comparison classes; and thus (aphonic) reference-variable expression ‘C’ will also be required to defend truth conditional seman-tics. But these are not the only dimensions along which ‘contextual incompleteness’ can be found. Szabó considers, but then rejects, the proposal that ‘green’ is an ‘evaluative adjective’ whose extension might vary relative to different contextually provided judges: ‘it is incorrect to say that a leaf is green for me’ (2001, 137). But this does not accord with pre-theoretic intuition; in appropriate contexts we have no trou-ble understanding such perceiver-relative ascriptions of color. It is a trivial exercise to construct an underdetermination argument wherein the intuitive ‘contextual incompleteness’ depends upon a variation in judges.

Suppose we are scientists studying color-blindness, and each week is devoted to studying a particular subject. During the fi rst week we are studying subject #1. He is shown various swatches, and when one looks green to him he responds affi rmatively. During this fi rst week, we adopt our use of ‘green’ to match subject #1’s perceptual judgments; so, during the fi rst week, a swatch counts as green if and only if it is green for subject #1. The following week we are studying a different subject, subject #2, and during this second week we adopt our use of ‘green’ to match her perceptual judgments. And of course it might happen that a particular swatch, swatch 27 say, is green for subject #1, but not for subject #2. And thus uses of ‘Swatch 27 is green’ might count as true during the fi rst week, but not during the second week, and the intui-tive dimension of ‘contextual incompleteness’ concerns the judge. So, Szabó’s second principle compels us to add another hidden variable. And thus the proposed logical form is now ‘(green(C, P, J))(x),’ where ‘J’ is a variable standing for a judge.

But of course one can imagine situations in which other dimensions give rise to intuitive contextual incompleteness: Suppose there is a variety of fl ower that is green until the humidity drops below a cer-tain point, at which point it turns blue. So, whether or not this species of fl ower counts as green might vary depending upon what level of humidity is taken to be relevant, and thus we apparently need to posit a hidden humidity variable as well. (And note that just as he relevant judge need not be the speaker, so the relevant level of humidity need not be the humidity in the context of utterance.) Or perhaps there is a kind of fl uid that changes color depending the temperature, or time of day, or distance from the equator, etc. Such gruesome cases illustrate that there are far more than the two dimensions of semantic incom-pleteness recognized in Szabo’s analysis.

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Hansen (2011) provides a more sophisticated hidden-variable analy-sis that is specifi cally designed to go beyond Szabo’s hidden-variable analysis (and also beyond Kennedy and McNally’s 2010 ambiguity view5) in order ‘to accommodate the full variety of context sensitiv-ity displayed by color adjectives’ (2011, 203). First, Hansen, following Kennedy and McNally (2010), incorporates Szabo’s ‘part’ and ‘compar-ison class’ dimensions by positing an ambiguity between a quality and a quantity reading of (gradeable) color adjectives; the quantity reading roughly corresponds to Szabó’s ‘part’ dimension, and the quality read-ing roughly corresponds to Szabó’s ‘comparison class’ dimension.6 But Hansen rightly claims that the sorts of gruesome cases we have con-sidered will require more context-sensitivity than can be provided by positing this ambiguity. So, second, Hansen introduces three aphonic variables into the ‘core meaning that is shared by both adjective and noun meanings’ (2011, 215).7 Again following Kennedy and McNally (2010), Hansen proposes that the meanings of color adjectives derive from the more basic noun-form of color-words, but — inspired by Cohen’s (2004) relational metaphysics of colors — Hansen claims that these ‘core meanings’ are ‘pervasively’ (2011, 219) context-sensitive:

To mark the relational nature of color properties like green, I will add three relata, frame of reference (f), observation conditions (c), and observer (o) to the core denotation of green:

5 Kennedy and McNally (2010) argue that color-adjectives are ambiguous between (i) a non-gradeable classifi catory reading, (ii) a gradeable quality reading, and (iii) a gradeable quantity reading. I believe that the data Kenney and McNally invoke to justify the alleged gradeable/non-gradeable ambiguity is better explained by dis-tinguishing between different sorts of speech acts, but I cannot address these issues here.

6 It is actually a combination of the quantity/quality ambiguity together with Ken-nedy and McNally’s analysis of the aphonic degree-modifi er ‘pos’ that supplants Szabó’s ‘part’ and ‘comparison class’ dimensions. An occurrence of ‘is pos green-quan’ is satisfi ed by an object just in case a suffi cient number of the object’s relevant parts are green, where the suffi cient number is the contextually determined seman-tic value of the occurrence of ‘pos.’ Similarly, an occurrence of ‘is pos greenqual’ is satisfi ed by an object just in case it is suffi ciently close-in-color to a paradigmatic instance, or class of instances, of the color green, where again the suffi cient close-ness-in-color is the contextually-determined value of the modifi er pos. (See Ken-nedy and McNally, 2010, 94-5.)

7 Hansen suggests that ‘there is reason to pursue’ (2011, 206) an approach that eschews the quantity/quality ambiguity and instead posits a fourth variable ‘’ whose contextually supplied semantic values would be ‘dimensions.’ Hansen’s formal analyses, however, follows Kennedy and McNally in positing this ambigu-ity.


(a) [green]e = green f, c, o

This modifi ed core denotation of green would then contribute context sensitivity to the gradable adjective meaning ….

(b) [greenqual]<e,d> = x . qual(green f, c, o )(x)

(c) [greenquant]<e,d> = x . quant(green f, c, o )(x) (2011, 214-215)

Though much more can be said concerning the potential values of three posited variables ‘f,’ ‘c,’ and ‘o,’ suffi ce it to say that the charac-ters implicit in analyses such as (b) and (c) will enable the defender of truth conditional semantics to capture an open-ended range of intuitive dimensions of semantic incompleteness. Even setting aside the some-what problematic frame reference variable ‘f’8,’ Hansen’s analyses of color-predications will be able to account for all of the gruesome cases considered above, and more besides: the vision-scientist case is easily accounted for by variation of semantic values of the observer variable, and the cases involving fl owers and liquids that change colors relative to different levels of humidity, etc., can be accounted for by variation of semantic values of the observation conditions variable. The problem for Hansen’s open-ended hidden-variable analysis comes from the other direction: it predicts that there is more variation in the semantic values of color adjectives than is in fact observed.9

The general form of the problem is familiar from the recent debates between indexicalism and semantic relativism, particularly with regard to predicates of personal taste. MacFarlane (2007, 3) objects to an indexi-calist analysis of ‘delicious’ on the grounds that such an analysis results in ‘lost disagreement.’ Consider the following exchanges:

(1a) John: My name is John.

(1b) Mary: No, my name is not John. (??)

(2a) John: Apples are delicious.

(2b) Mary: No, they are not delicious.

8 Hansen seems to think there are only two potential values for ‘f’: object and stimulus. That there are only two potential values suggests that if something must be pos-ited in the semantics of color-adjectives to explain the alleged contextual variation with regard to frames of reference, it would be more plausible to posit an object/stimulus ambiguity.

9 As an anonymous referee pointed out, Szabó’s account also suffers from this over-generation of context-sensitivity.

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Exchange (1) involves two uses of the obvious indexical ‘my.’ Because this expression is an indexical whose character specifi es that a use of it refers to its speaker, the two uses in (1) have different referents. And thus Mary cannot, by uttering (1b), express disagreement with John; because ‘my’ is an indexical whose semantic value is the speaker, the truth conditional content she expresses with (1b) is compatible with the truth conditional content John expresses with (1a). Suppose ‘delicious’ is associated with an aphonic experiencer variable which is always assigned the speaker as semantic value. This simplistic speaker-indexical-ism would render the exchange in (2) as unacceptable as the exchange in (1). But the exchange in (2) is perfectly acceptable — disagreement is not lost — which implies that ‘delicious’ is not this sort of speaker-indexical. Similarly, if ‘green’ is associated with hidden observer and observation condition variables, and the values of these variables are always taken to be the speaker and the observation conditions that he or she occupies, then, for the same reasons, Mary’s utterance of (3b) would not express disagreement with the attitude displayed by John’s utterance of (3a):

(3a) John: The leaves are green.

(3b) Mary: No, they are not green.

The obvious response on behalf of the indexical analysis of both predicates of personal taste and color predicates is to deny that these predicates are speaker-relating indexicals like ‘my,’ but rather are more like discretionary indexicals such as ‘that.’ In this way the indexicalist can allow that the values of the hidden-variables need not be, nor even include10, the speaker and/or the observation conditions of the speaker, but rather can be some objective standard or type to which both John and Mary (tacitly) refer. Thus, the indexicalist can claim the disagreement intuitively expressed by exchange (3) is analogous to the disagreement intuitively expressed by exchanges such as

(4a) John: That is an elephant.

(4b) Mary: No, that is not an elephant.

10 It is not clear whether or not Hansen endorses a version of what Egan, Hawthorne and Weatherson (2005, 135) call ‘the speaker-inclusion constraint’ for the values of ‘o,’ though it is relatively clear that he does not endorse this constraint for the values of ‘c.’ For example, he seems to allow that the value of ‘c’ for some utter-ances is ‘a certain type of daylight’ (2011, 215) without assuming that the speaker is speaking in that type of daylight.


Exchange (4) can be interpreted in such a way that Mary is express-ing disagreement with John, so long as both occurrences of the indexi-cal ‘that’ are assigned the same semantic value. Similarly, so long as in exchange (3) John and Mary are using the hidden variables ‘o’ and ‘c’ to refer to the same type of observer and type of observation condi-tion, where typically these types would include both John and Mary and their observation conditions, it would follow that they are expressing incompatible truth conditional content, and disagreement would then not be lost. And it seems that Hansen has something like this in mind, for when he applies his theory to particular utterances, the potential semantic values for the observer and observation conditions variables are not particular people and circumstances, but rather types of observers and observation conditions.11

But the appeal to such types of observers and observation conditions faces a complementary diffi culty. The problem is that (4) is readily inter-preted such that the two occurrences of ‘that’ refer to different things, in which case no genuine disagreement is expressed. In contrast, (3) can-not but be interpreted as an expression of disagreement between John and Mary. To make the same point more explicit, consider the comple-ment to lost disagreement, the phenomenon of found agreement. The prob-lem is that whereas

(5a) John: That is an elephant.

(5b) Mary: Yeah, and that is not an elephant.

can readily be interpreted in such a way that both speakers speak truly, the same does not hold for

(6a) John: The leaves are green.

(6b) Mary: Yeah, and they are not green. (??)

(‘The leaves’ and ‘they’ are to be taken as having the same semantic value.) Hansen must explain not only why exchanges such as (3) are, except in very special circumstances, felicitous expressions of disagree-ment, he must also explain why, except in very special circumstances, exchanges such as (6) are infelicitous expressions of agreement. If ‘green’ really is associated with (aphonic) variables that must be contextually saturated by different observers (or observer-types) and observation-

11 Hansen makes reference to ‘different observer types’ (2011, 217), and he also invokes ‘different standard observation conditions’ (2011, 216).

84 Lenny Clapp

conditions, then why can, e.g., ‘The leaves are green’ not be readily used in the same conversation to express clearly distinct truth conditions, in the same way that ‘That is an elephant’ can be readily used within one conversation to express distinct truth conditions?

The general problem for hidden-variable indexicalism that is mani-festing itself here is that the sort of context-sensitivity that is evidenced through underdetermination arguments does not seem to be the sort of context-sensitivity that is explained by the presence of hidden vari-ables. Underdetermination arguments involving color adjectives dem-onstrate that in different conversational settings utterances of, e.g., ‘The leaves are green’ intuitively express different truth conditions, and, as we have seen, there is a seemingly limitless number of dimensions of semantic incompleteness. The disagreement and agreement data considered above, however, suggest that within the same conversational setting utterances of this sentence cannot, or at least under ordinary circumstances do not, express different truth conditions. This latter observation runs counter to the claim that the context-sensitivity made manifest in underdetermination arguments involving color adjectives is explained by the presence of hidden variables in need of saturation by character-specifi ed aspects of the context of utterance. If, e.g., ‘green’ were such an indexical expression, then competent speakers would readily exploit salient aspects of utterance-contexts in order to use it to express different contents within the same conversation, in the same way that they exploit salient aspects of utterance-contexts in order to use ‘that’ to express different contents within the same conversation. The fact that color adjectives are not readily used in this way strongly suggests that the context-sensitivity made manifest in underdetermi-nation arguments involving color adjectives is not explained by the presence of hidden variables in need of specifi c sorts of contextual satu-ration.

A digression: Hansen (2011), following Sundell (2011), suggests that data concerning intuitions of faultless disagreement can be made com-patible with his hidden-variable indexicalism by appealing to a meta-linguistic notion of ‘context disagreement.’12 Sundell (2011) proposes that the disagreement manifested in exchanges such as (2) involving predicates of personal taste does not concern whether or not the truth conditional content of (2a) in the context is true or false, but rather con-cerns what the truth conditional content of (2a) in the context is. Sundell

12 Neither Hansen nor Sundell uses the phrase ‘faultless disagreement’ but I believe this phrase is now standardly used to refer to the phenomenon they are concerned with, viz. ‘disagreements in which both parties speak truly’ (Sundell, 2011, 267). To my knowledge the phrase is fi rst used in Kölbel (2002).


cites with approval Barker’s (2002) example of a metalinguistic use of the allegedly indexical predicates ‘is tall’:

Feynman stands before us a short distance away … the exact degree to which Feynman is tall is common knowledge. You ask me what counts as tall in my coun-try. ‘Well,’ I say, ‘around here …’ and I continue by uttering [‘Feynman is tall’]. This is not a descriptive use in the usual sense. I have not provided any new infor-mation about the world, or at least no new information about Feynman’s height.… All I have done is given you guidance concerning what the prevailing relevant standard for tallness happens to be in our community; in particular, that standard must be no greater than Feynman’s maximal degree of height.… My purpose in uttering [‘Feynman is tall’] under such circumstances would be nothing more than to communicate something about how to use a certain word appropriately — it would be a metalinguistic use. (Barker, 2002, 1)13

Sundell correctly points out that such metalinguistic uses can be fol-lowed by denials, and such exchanges clearly manifest disagreement. In such a metalinguistic dispute involving ‘Feynman is tall,’ what the disputants ‘disagree about is what context they are in. In particular, they disagree about what level of height is the salient standard for tall-ness’ (2011, 279). Sundell’s proposal is thus ‘to extend the metalinguis-tic analysis of tall disputes to disputes about taste’ (Sundell, 2011, 282).

Hansen (2011) proposes that the metalinguistic analysis of tall dis-putes also be applied to intuitively faultless disagreements about color. Hansen (2011, 217) considers an exchange between two observers who, as result of physiological differences,14 disagree as to the color of a cer-tain color sample:

(15a) Observer 1: That Munsell chip is perfectly green.

(15b) Observer 2: No, that Munsell chip is not perfectly green. It’s bluish green.

Hansen claims that this exchange displays ‘the same profi le as disagree-ments involving predicates of personal taste: they all involve pairs of utterances that seem on the one hand to both be capable of being true, and at the same time they seem like cases of disagreement’ (2011, 217). Thus Hansen proposes that just as the notion of metalinguisitic context disagreement can be invoked to show how indexical analyses of ‘deli-cious’ are compatible with intuitions of faultless disagreement with

13 Barker’s metalinguistic use is reminiscent of Austin’s (1952-3) distinctions between various sorts of assertions according to their direction of fi t.

14 Hansen (2011) cites Hardin (1988, 171) as claiming that ‘variations in macular pig-ment’ are capable of producing disagreements as to whether or a blue-green object is blue, or green.

86 Lenny Clapp

regard to exchange (2), so the same notion can be invoked to show how indexical analyses of ‘green’ are compatible with intuitions of faultless disagreement with regard to exchange (15).

Here is not the place to investigate the phenomenon of fault-less disagreement in detail, but two brief points are relevant. First, it is extremely plausible that at least part of what is going on in some cases of intuitive faultless disagreement is the sort of metalinguistic disagreement that Sundell describes. As Sundell (2011, 278) suggests, such ‘context-sharpening’ through the course of a conversation is nearly ubiquitous; it is one aspect of what Lewis (1979, 347) calls ‘the kinematics of conversational score.’ But precisely because of the near ubiquity of the phenomenon it would be an error to suppose that such processes of negotiation, and accommodation, concerning the standards governing uses of a term is specifi c to indexicals. As we stroll through the transportation museum, the extension of our uses of ‘airplane’ will be negotiated and accommodated, and thereby sharpened, but I trust that nobody maintains that ‘airplane’ is an indexical.

Second, and more importantly, exchanges such as (15) that give rise to intuitions of faultless disagreement are not relevant to the problem that I am raising for Hansen’s indexical analysis of color adjectives. The problem I am raising is not that if Hansen’s indexical analysis of color adjectives were correct, then intuitive faultless disagreements such as (15) would not arise. Indeed, since I think intuitions of faultless dis-agreement are at least partially explained by the processes of accom-modation and negotiation Lewis (1979) describes, I think it is likely that such intuitions will arise with regard to almost any term. Rather, the problem I am raising for Hansen’s indexical analysis is that the profi le of non-faultless disagreements and agreements involving color adjec-tives is not the same as the profi le of non-faultless disagreement and agreement for obvious indexicals (e.g. ‘my’ and ‘that’), which strongly suggests that the context-sensitivity made manifest by underdetermi-nation arguments involving color adjectives is not explained by the presence of hidden-variables in need of contextual saturation.

IV Overt-Indexical Color Predicates

Underdetermination arguments involving color predicates demon-strate that there is a sense in which they are context-sensitive. But the recently reviewed data concerning disagreement and agreement phe-nomena suggest that color adjectives are not associated with various kinds of hidden variables whose semantic values (in contexts) are cor-responding kinds of contextually provided entities. Thus the defender of truth conditional semantics has motivation to fi nd an alternative approach to the context sensitivity of color adjectives. This alterna-


tive approach should, fi rst, explain why color adjectives allow for the open-ended context sensitivity made manifest in underdetermination arguments, yet, second, explain why color adjectives — unlike obvious indexicals — cannot readily be used within the same conversational setting to refer to different semantic values.15 The overt indexical analy-sis proposed by Rothschild and Segal (2009) seems to be specifi cally designed to satisfy these desiderata.16

In contrast to Szabó’s and Hansen’s proposals, Rothschild and Segal (2009) do not claim that various kinds of hidden-variables are associ-ated with color adjectives.17 In contrast, they claim that their ‘analy-sis … treats ‘‘red’’ itself as a simple indexical, like ‘‘I’’ or ‘‘that.’’ There are no variables associated with ‘‘red.’’ It’s just a word that happens to change extension across contexts’ (2009, 470). Given this characteriza-tion of their analysis, one would expect the proposal for ‘red’ to be very similar to the proposal for, e.g., ‘that,’ the essence of which is expressed in the conditionalized T-theorem (D), cited above. That is, if ‘red’ is ‘a simple indexical’ like ‘that,’ and (D) provides an analysis of ‘that is remarkable,’ then one would expect the analyses of ‘Keble College is red’ to be analogous to (D). More specifi cally, one would expect the analysis of ‘Keble College is red’ to be something like,

(R) If u is an utterance of ‘Keble College is red’ and the speaker uses ‘red’ in u to designate extension E, u is true iff Keble Col-lege is an element of E.

15 Predelli (2005) presents an alternative response to Travis’s underdetermination argument, which he claims preserves the principles of truth conditional semantics. Predelli’s analysis, however, is a version of semantic relativism and thus it does not preserve the fundamental idea that the truth conditions of a declarative utterance are determined by only semantic knowledge together with knowledge of contex-tual features that are specifi ed by knowledge of (something like) characters.

16 That Rothschild and Segal’s motivation for their more complex analysis is the sort of consideration raised by exchanges (3) and (6) is suggested by the following remark: ‘If it is possible for someone truly to say of a given object ‘‘Well, it’s red, but it’s not red,’’ using ‘‘red’’ in different senses, then we would represent this by something like this: ‘‘Well, it is redj but not redk’’’ (2009, 471, n. 10). Their use of this conditional suggests that they take the possibility of such seemingly contra-dictory yet true utterances to be dubious.

17 Rothschild and Segal (2009) present a reverse binding argument against hidden-variable analyses. Whereas Stanley (2000) infl uentially argues that various bound interpretations require positing hidden-variables, Rothschild and Segal argue that postulating such hidden-variables over-generates bound interpretations. All of these binding arguments, however, depend upon questionable syntactic assump-tions.

88 Lenny Clapp

But, despite Rothchild and Segal’s characterization of their proposal, they do not endorse anything like (R), but instead endorse a novel and fundamentally different approach to the context-sensitivity of color adjectives.

The essence of their fundamentally different approach is revealed in the following passage:

Our theory requires a rather complicated metaphysics of language. We group together all the tokens of an expression that occur within a given context: so, for example, if the customer says to the greengrocer, ‘Is that a red one?’ and the green grocer says, ‘Yes, it is a red one,’ we group together those two tokens of ‘red.’ We treat the tokens of an indexical predicate that occur within the same contexts as tokens of a single syntactic type. No token of that type can occur in another context. We indicate the syntactic type by indexing. Thus all tokens of ‘red’ that occur in a given context receive the same index, as in ‘redj.’ We will use numbers to keep these context-bound expressions in line: thus all the ‘redj’s occur in the j-th context. The context-bound expression types are subtypes of larger types, such as the one that includes all the ‘redj’s, ‘redk’s, etc. We can think of this larger type as context-independent and possessed of a context-independent semantics. Its semantics, intuitively speaking, is given by a function from contexts to extensions. The semantics for each context bound ‘redj’ is the extension it receives relative to its context. This extension is determined by the conversational standards of the context: an object satisfi es a token of ‘redj’ in a context, if it counts as red by the standards of that context. (2009, 471-2)

The proposal is then formalized in terms of a T-theory as follows (where ‘n’ ranges over numerals, and each numeral is mapped to a con-text, so that ‘cn’ can be read as ‘context n’):

(1) (x)(n) (x satisfi es ‘Keble College,’ cn iff x = Keble College)

(2) (x)(n) (x satisfi es ‘is red’^n, cn iff x is red@ by the standards of cn)

(3) (S)(NP)(VP) (If S = NP^VP, then

((n) (S is true, cn iff (x)(x satisfi es NP, cn and x satisfi es VP, cn))18

(4) (u)(n)(S) (if u is an utterance of S in cn, then (u is true iff S is true, cn))

Some remarks of clarifi cation concerning these axioms: (1)-(3) defi ne satisfaction and truth for expression types relative to contexts, whereas

18 For the sake of clarity I have slightly altered the formulation of axiom (2). I have also corrected what must be a typo in Rothschild and Segal’s formulation of axiom (3): where I have the existential quantifi er ‘(x)’ Rothschild and Segal have the universal quantifi er ‘(x)’.


(4) presents a non-relative defi nition of truth for utterances in terms of the relative notion of truth for sentence types. The crucial axiom is (2). Note, fi rst, that (2) defi nes satisfaction for a particular predicate type only relative to the unique context in which tokens of this type exist; so, for example, the satisfaction conditions of ‘is red6’ are defi ned only relative to context 6. This refl ects the complex metaphysics according to which ‘tokens of an indexical predicate that occur within the same contexts [are identifi ed] as tokens of a single syntactic type. No token of that type can occur in another context’ (2009, 471). Second, context @ is this context, the context in which the axioms are presented and interpreted; Rothschild and Segal refer to this context as the ‘academic’ and/or ‘general’ context. Thus it is ‘red@’ that we theorists use when we utter sentences such as ‘The watermelon is red by the standards of the greengrocer’s context.’ But of course the greengrocer is no philoso-pher, and thus he uses some other color adjective to describe the water-melon. (For example, if the greengrocer’s context is context 5, then he uses ‘red5.’) Finally, note that, as one would expect with a semantic analysis of indexicals, absent pragmatic knowledge concerning the con-text in which a particular utterance of ‘is red’ occurs, no truth condi-tions can be derived from the axioms. Let us evaluate an utterance u* of ‘Keble College is red’ that takes place in an arbitrary context j* about which we lack relevant pragmatic knowledge. The semantic axioms (1)-(4) enable us to derive

(Tj*) u* is true iff Keble College is red@ by the standards of cj*

but absent relevant pragmatic knowledge concerning context j*, we have no idea what the RHS amounts to — we know that the sentence is true relative to j* iff Keble College is red@ by some standard or other, but we have no idea what that standard is. This is analogous to having the semantic knowledge that an arbitrary utterance of ‘That is remark-able’ is true iff the referent of the sub-utterance of ‘that’ is remarkable, without having the pragmatic knowledge of what is referred to by this sub-utterance. Similar to the relationship (D) bears to utterances of ‘That is remarkable,’ axioms (1)-(4) enable one to derive statements of the truth conditions of utterances of ‘Keble College is red’ only if supplemented by pragmatic information concerning particular con-texts of utterance.19

19 There is an insignifi cant disanalogy between the conditional analysis of ‘that is remarkable’ presented by (D) and the analysis of ‘Keble College is red’ presented

90 Lenny Clapp

I grant that axioms (1)-(4) constitute a T-theory that, when supple-mented with suffi cient pragmatic information, enable one to derive interpretive T-theorems for utterances of ‘Keble College is red.’ My objection to Rothschild and Segal’s analysis is not that it will deliver intuitively incorrect truth conditions. Rather my objection is that the analysis is not an instance of indexicalism: the acknowledged truth con-ditional variability of, e.g., ‘Keble College is red’ cannot be a result of a character of ‘red’ that specifi es what pragmatically provided informa-tion is required to determine truth conditions. Thus Rothschild and Segal’s theory fails to show how the truth conditional variation mani-fested in underdetermination arguments involving color adjectives can be explained in terms of purely semantic knowledge together with pragmatically provided information that such knowledge itself speci-fi es. Consequently the theory fails to defend truth conditional seman-tics from such arguments.

A necessary condition for ‘red’ to have a character as its meaning is that its extension vary across different contexts of utterance; its exten-sion must vary systematically in some way with regard to relevant aspects of the contexts, where which aspects are relevant is specifi ed by the character. So, for example, the extension of the demonstrative ‘that’ varies across different contexts depending upon (roughly) the intentions of the speaker to refer to something, and the extension var-ies in this systematic way because the character of ‘that’ determines that its extension, relative to a context of utterance, is the object the speaker intends to refer to by using it. But axioms (1)-(4) do not even state satisfaction conditions for the type ‘red,’ at least if the type ‘red’ is construed as the ‘larger type’ of which all the context-bound adjectives — ‘red6,’ ‘red19’ etc. — are subtypes. So the satisfaction conditions of the supertype ‘red’ do not, under Rothschild and Segal’s analysis, vary systematically across contexts, for the simple reason that under Roth-schild and Segal’s analysis, this supertype is not assigned satisfaction conditions at all.

Axioms (1)-(4) do, however, assign satisfaction conditions to each subtype ‘redj,’ but the satisfaction conditions of these subtypes do not vary systematically across contexts. For, fi rst, Rothschild and Segal state that according to their metaphysics, ‘No token [of ‘‘redj’’] can occur in another context’ (2009, 471). So, for example, under axiom (2) ‘red9’ is not assigned satisfaction conditions relative to c10, because it is metaphysically impossible for an instance of ‘red9’ to occur in any context

by axioms (1)-(4). The disanalogy results from the fact that ‘is red’ is a predicate rather than a referring term.


other than c9. So, ‘red9’ cannot have different satisfaction conditions in different contexts, because it cannot even occur in different contexts. And second, Rothschild and Segal maintain that ‘the semantics of each context-bound ‘redj’ is the extension it receives relative to its context’ (2009, 472, my emphasis), and moreover that for each ‘redj’ the exten-sions of utterances of sentences containing this context-bound predi-cate are ‘simply inherited’ from the type. And therefore not only is it metaphysically impossible for a context-bound predicate type to occur outside of its proper context, but moreover each instance of a context-bound type in its proper context is assigned the very same satisfaction-conditions. So, Rothschild and Segal’s claim that their analysis treats ‘red’ as ‘just a word that happens to change extension across contexts’ (2009, 470) is false, for under axioms (1)-(4) nothing changes extension across contexts.

A defender of Rothschild and Segal’s analysis might respond by claiming that I have misunderstood the sort of context-sensitivity they are attributing to color adjectives. The context-sensitivity is not to be found in the variance of the extensions of the supertypes across con-texts, because they are not assigned satisfaction conditions at all. Nor is it to be found within each subtype, e.g., ‘red5,’ for though such sub-types are assigned extensions, they do not vary across contexts. Rather, the response continues, the context-sensitivity is to be located in the metaphysical subtype-supertype relation that obtains between, e.g., each ‘redj’ and the supertype ‘red.’ Thus what varies across contexts is not what extension is assigned to the supertype ‘red,’ but rather what subtype of the supertype ‘red’ is tokened; across different contexts cj different subtypes ‘redj’ are tokened. Indeed, the defense concludes, it is precisely by exploiting this new sort of metaphysical context-sensi-tivity that Rothschild and Segal are able to allow for enough context-sensitivity to account for underdetermination arguments involving color predicates, but not so much that their analysis treats color adjec-tives as straightforward indexical expressions such as ‘my’ and ‘that’ thereby running afoul of the disagreement and agreement phenomena reviewed above.

The problem is that this new sort of context-sensitivity is not due to something like a character of the supertype ‘red’; i.e. the new sort of context-sensitivity is not due to our semantic knowledge of a ‘recipe that allows us to calculate the truth conditions of a propitious utterance once we know the relevant details of the context’ (1995, 219). For, fi rst, though Rothschild and Segal vaguely suggest that ‘intuitively speak-ing’ the semantics of the supertype ‘red’ ‘is given by a function from contexts to extensions’ (2009, 471-2), they never describe any sort of character, or ‘recipe,’ knowledge of which would enable an interpreter to compute such a function. And moreover, second, if they did provide

92 Lenny Clapp

such a recipe, then the ‘complicated metaphysics of language’ presup-posed by Rothschild and Segal would be rendered otiose. If the super-type ‘red’ is given a character which determines for each context cj a subtype ‘redj’ and the (fi xed) extension of that subtype, so that each ‘redj’ has the same extension as the larger type ‘red’ relative to context j, then there is no need to posit the subtypes ‘red3,’ ‘red6,’ etc. That is, if the supertype ‘red’ were assigned such a character, then Rothschild and Segal’s analysis would be reduced to something along the lines of the simple indexical analysis (R). But, as was explained above, it is the inadequacy of such a simple indexical analysis that (apparently) moti-vates Rothschild and Segal’s more complex analysis.

V Evidence that Color Adjectives are Not Indexicals

I have examined two hidden-variable analyses of color adjectives and an overt-indexical analysis of color adjectives, and I have argued that each of them fails to provide an adequate defense of truth conditional semantics from underdetermination arguments involving such expres-sions. But it does not follow from these limited results that no such indexical analysis could be provided. How might this more general conclusion be supported? In this section I will support this general con-clusion by reviewing some empirical evidence in favor of an analysis of the meanings of color adjectives according to which they are semanti-cally context-invariant.

It is important to appreciate that even if an indexical analysis of some adjectives is justifi ed it by no means follows that an indexical analy-sis of color adjectives is justifi ed. Kennedy and McNally (2005, 2007) and Syrett et al. (2010) argue that while relational gradeable adjectives, e.g. ‘small,’ ‘warm,’ ‘tall’ are (when used without a degree-modifi er) index-icals, other absolute gradeable adjectives, e.g. ‘full,’ ‘quiet,’ ‘wet,’ are (even when used without a degree-modifi er) semantically context-invariant.20 They argue that the primary factor determining which category adjec-tives fall into is ‘the structure of the scales they use’ (2007, 1). Absolute adjectives are associated with closed scales, scales with endpoints in one or both directions, whereas relational adjectives are associated with scales that are open in both directions. So, e.g., ‘full’ is associated with a scale that is closed in both directions: A container that is totally empty

20 In the discussion I will be concerned only with gradeable adjectives appearing with-out a degree-modifi er. Thus, for expository purposes, I will omit the qualifi ers and take it for granted the relevant adjectives are gradeable and occur without a degree-modifi er.


cannot be further along the amount-scale in the negative direction, and a container that is completely full cannot be further along this scale in the positive direction. In contrast, ‘small’ is associated with a scale that is open in both directions: No matter how small something is, it could be further along the size-scale in the negative direction, and no matter how big, it could be further along this scale in the positive direction. That is, no matter how small a thing is, it cannot be absolutely small, and no matter how big a thing is, it cannot be totally big. And some adjectives are associated with scales that are closed in one direction, but open in the other. For example, ‘loud’ is associated with a scale that is closed in the negative direction, but open in the positive direction; there is no degree on the noise-scale less than completely quiet, but no noisy thing can be completely loud.

Kennedy and McNally argue that many adjectives associated with closed scales are semantically related to an endpoint of their scale, and there are two ways they can be so related. ‘Maximum-standard’ abso-lute adjectives ‘require their arguments to possess a maximal degree of the property in question’ (2007, 22). So, for instance, ‘full’ is semanti-cally related to the positive endpoint on the amount scale, and thus a jar containing liquid can satisfy ‘is full’ if and only if the degree to which it contains liquid is the positive endpoint of the amount-scale. So, to satisfy ‘is full’ the jar must be maximally full. Similarly, ‘quiet’ is semantically related to the negative endpoint of the noise-scale. For a room to satisfy ‘is quiet’ the degree of noise it possesses must be the negative endpoint of the scale; the room must be maximally quiet. In contrast, ‘minimum-standard’ absolute adjectives ‘simply require their arguments to possess some minimal degree of the property they describe’ (2007, 21). A paradigmatic minimum-standard absolute adjec-tive is ‘open.’ This adjective is associated with a scale that is closed in both directions: a window could be completely open, or completely closed. But ‘open,’ in contrast to ‘full,’ does not require that its argument pos-sess the property of its associated scale to a maximum degree. Rather, to satisfy ‘is open’ a door need only be not closed; i.e. the degree to which the door possesses the relevant property need only exceed the nega-tive endpoint of the scale. Similarly, to satisfy ‘is bent’ a stick need only possess some degree of bend greater than zero; it need only be less than perfectly straight. Thus, the meanings of both maximum-standard and minimum-standard absolute adjectives relate arguments to the seman-tically fi xed endpoints of closed scales, though in different ways: predi-cates containing maximum-standard adjectives require their arguments to possess the relevant property to the degree of one of the endpoints, whereas predicates containing minimum-standard adjectives require only that their arguments have the property to a greater (or lesser) degree than an endpoint.

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Kennedy and McNally maintain that both predicates containing relative adjectives and those containing absolute adjectives require their arguments to possess the relevant property to a particular degree, where this degree is the ‘standard of comparison’ (2007, 16-17). But the two types of predicate differ as to how the relevant standard of com-parison is determined:

The endpoints of a totally or partially closed scale provide a fi xed value as a potential standard, which in turn makes it possible to assign context-independent truth conditions to the predicate (greater than a minimum, equal to a maximum). The alternative — and the only option available for adjectives with open scales — is to compute the standard based on some context-dependent property of degrees. (2005, 361)

So, for example, since the maximum endpoint is ‘inherent … to the meaning of a closed scale adjective’ (2007, 34), ‘full’ is semantically context-invariant — as a matter of meaning it invariantly designates the positive endpoint of the amount scale. As a consequence the cor-responding predicate is also semantically context-invariant: regardless of the context, a jar containing some amount of liquid is semantically determined to satisfy ‘is full’ if and only if the degree to which the jar contains liquid is the positive endpoint of the scale. Thus, meaning alone determines that the jar must be completely full to satisfy ‘is full.’ In contrast, ‘there is nothing about the meaning of an open scale adjec-tive alone that provides a basis for determining [a standard of compari-son]’ (2007, 35) and as consequence such adjectives have conventional meanings that require a kind of contextual saturation. For instance, the size-scale is open in both directions, and thus ‘small’ — though it is semantically related to the negative direction of the scale — cannot be semantically related to a particular degree. And as a result the corre-sponding predicate ‘is small’ is semantically in need of saturation: if ‘is small’ is predicated of a child, context must somehow supply the stan-dard — the degree on the size scale — that the child must fall under in order to satisfy the predicate.21

21 Though I agree with Kennedy and McNally that open-scale adjectives are indexi-cals — they are context-sensitive as a matter of conventional meanings — it would be a mistake to attribute this semantic context-sensitivity to the presence of free variables at the level of logical form. One reason to resist such a literal interpretation of hidden-variable analyses of open-scale adjectives is that, though they exhibit more context sensitivity than closed-scale adjectives, they do not exhibit as much context-sensitivity as obvious indexicals. (Of course one might use free variables in stating one’s indexical analysis, but we must keep distinct the formalism used to express an analysis, and the properties that the formalism is intended to describe.)


What about color adjectives? They are gradeable, and thus are seman-tically associated with scales, degrees of possessing the relevant color. But are these color-scales open or closed? There is substantial empiri-cal evidence suggesting that color-scales are closed in both directions. For, taking the negative direction fi rst, just as a jar containing no liquid — and thus at the negative endpoint — cannot have a lesser amount, so paint swatches that are not red to any degree cannot become less red. (This is not to say that it is clear or even determinate where one is to draw the line between being red to some minimal degree, and not being red at all.) That color adjectives are associated with scales that are closed in the negative direction is further evidenced by the fact that they accept degree modifi ers that are appropriate only for adjectives with negative endpoints. So, while all of the degree modifi ers applied to ‘red’ and ‘open’ in (7a-b) are felicitous, the same modifi ers applied to ‘small’ in (7c) are infelicitous22:

(7a) That is barely/slightly/partially red.

(7b) That is barely/slightly/partially open.

(7c) That is barely/slightly/partially small. (??)

And, now taking the positive direction, just as jars containing the maxi-mum amount of liquid — and thus at the positive endpoint — cannot have a greater amount, so swatches that are perfectly red cannot get any redder.23 And again, that color adjectives are associated with scales that are closed in the positive direction is further evidenced by the fact that they accept degree modifi ers that are appropriate only for adjectives with positive endpoints:

(8a) That is totally/completely/perfectly red.24

(8b) That is totally/completely/perfectly full.

(8c) That is totally/completely/perfectly big. (??)

22 Kennedy (2007, 34) proposes the modifi ers ‘slightly’ and ‘partially’ as providing a test for an adjective’s being a minimal standard absolute adjective. I propose that ‘barely’ provides an even better test.

23 Byrne and Hilbert (2003, 13) report that red, green, yellow and blue have unique hues: ‘there is a shade of red (‘‘unique red’’) that is neither yellowish nor bluish.’

24 It may be that the modifi ers ‘totally’ and ‘completely’ require a quantity reading of ‘red,’ whereas the modifi er ‘perfectly’ requires a quality reading. If such an ambi-guity is accepted, then example (8a) provides evidence that both meanings of ‘red’ are associated with scales that are closed in the positive direction.

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Finally, as is suggested by the above evidence, color adjectives accept proportional modifi ers, which can be applied only to adjectives associated with scales that are closed in both directions:

(9a) That is 50%/mostly/two-thirds red.

(9b) That is 50%/mostly/two-thirds full.

(9c) That is 50%/mostly/two-thirds loud. (??)

More evidence that color adjectives are closed-scale absolute adjec-tives is (or could be) provided by differences with regard to the ability of competent interpreters to accommodate presuppositions of defi nite descriptions containing either absolute or relative adjectives. Syrett et al. (2010) report that competent speakers are easily able to accommo-date the uniqueness presuppositions of requests such as

(10a) Please give me the big one.

but are not easily able to accommodate the uniqueness presuppositions of requests such as

(10b) Please give me the full one.

(10c) Please give me the spotted one.

Experiments were performed in which competent adults and children were placed in a context with two salient objects, one larger than the other. When an experimenter used (10a) to request subjects to give him an object, subjects readily complied by handing over the larger of the two objects. In contrast, in a context with two spotted disks, though one with noticeably more spots than the other, speakers rejected a request made using (10c) as infelicitous. Kennedy (2007, 28-29) proposes that the data is explained by the fact that ‘big’ is an indexical requiring sat-uration by a contextually supplied standard, whereas ‘spotted’ is not such an indexical, and the relevant standard is inherent to its mean-ing. That is, interpreters can easily accommodate the presuppositions of (10a) by adjusting the context-dependent standard so that only the larger of the two objects satisfi es ‘is big.’ But because the minimal stan-dard is inherent in the meaning of ‘is spotted,’ the request made using (10c) cannot be accommodated; both disks are judged to exceed the semantically encoded minimum standard, and because this standard is semantically determined, it cannot be adjusted to accommodate the uniqueness presupposition. Kennedy concludes that the judged infe-licity of requests made using (10b) and (10c) ‘despite the pressure to


satisfy the requirements of the defi nite, shows that the standards for full and spotted are not sensitive to the context (in the same way as relative adjectives), but are instead fi xed to maximum and minimum values on the scale respectively’ (2007, 29).

Though Syrett et al. do not test subjects using color adjectives, intu-ition suggests that competent interpreters are unable to accommodate defi nite descriptions involving color adjectives just as they are unable to accommodate absolute adjectives such as ‘spotted.’ That is, in a con-text containing two red objects, though one noticeably more red than the other, competent interpreters would reject a request made using

(10d) Please hand me the red one.

as infelicitous. And the explanation would be essentially the same as the explanation of interpreters’ inability to accommodate requests made using (10c): because the relevant standard is inherent in the meaning of ‘is red,’ the request made using (10d) cannot be accommodated; both objects are judged to exceed the semantically encoded standard, which cannot be adjusted to accommodate the uniqueness presupposition.

Thus Kennedy and McNally provide evidence that absolute adjec-tives are unlike relative adjectives in that such absolute adjectives are not indexicals requiring contextual saturation by a standard. And the same sort of evidence supports the conclusion that color adjectives are absolute adjectives, and thus are not indexicals requiring such satu-ration.25 But then what ought Kennedy and McNally say in response to underdetermination arguments involving color adjectives? Indeed, what would they say about an underdetermination argument involv-ing the absolute minimum-standard adjective ‘open’?26 Though Ken-nedy and McNally do not directly address such underdetermination arguments, they do claim that ‘relative [adjectives] are context-sensi-tive relative to an aspect of their meaning (variability in the standard of comparison), while absolute [adjectives] are context-sensitive rela-tive to their use’ (Syrett et al., 2010, 9). That is, the context-sensitivity evidenced by underdetermination arguments involving absolute adjec-tives ‘involves layers of reasoning that go beyond the computation of

25 Though I will not pursue the issue further here, additional evidence supports the more precise categorization of color adjectives as minimum-standard absolute adjec-tives; color adjectives thus belong in the same category as ‘spotted’ and ‘open.’

26 For example, a door might count as open in a context in which there is shared concern of letting cold air into a home, but not count as open relative to a context where there is shared concern about whether or not it is permissible for a visitor to enter the home.

98 Lenny Clapp

semantic content, even semantic content that requires fi xing contextual parameters, and takes into account alternative denotations and judg-ments of communicative intent’ (Syrett et al., 2010, 30). This sort of pragmatic explanation of context-sensitivity is of course precisely what is proposed by truth conditional pragmatics.27

VI Conclusion

If the above arguments against indexicalism applied to color predicates are sound, then the truth conditional context-sensitivity made manifest by underdetermination arguments involving color predicates cannot be explained semantically, and thus must be explained pragmatically. This leaves it open as to which of the remaining strategies — minimalism or truth conditional pragmatics — is to be pursued in these cases. Recall that what distinguishes minimalism from truth conditional pragmatics is that the latter maintains that in many cases purely semantic knowl-edge does not determine truth conditional content of sentences (even relative to contexts), while the former maintains that purely semantic knowledge always determines truth conditional content of sentences (relative to contexts), with the caveat that this minimal purely semantic content is not discernable as such by ordinary speakers. Though I can-not address the issue here, at this point I am allied with indexicalism; that is, Rothschild and Segal are correct to maintain that this alleged indiscerability of semantic content ‘makes it very hard to understand what the data for a semantic theory are supposed to be’ (2009, 469-70). I conclude then that underdetermination arguments involving color predicates do undermine truth conditional semantics, and thus some version of truth conditional pragmatics must be pursued.28

Received: September 2011Revised: May 2012

27 There is thus a signifi cant tension between the analysis of absolute gradable adjec-tives provided by Kennedy and McNally (2005, 2007) and Syrett et al, (2010), and Kennedy and McNally’s (2010) proposal that color adjectives (both the gradable and non-gradable sense) are hidden-variable indexicals.

28 Early versions of this paper were presented at the Taller sobre la Percepción y el Len-guaje del Color, held May 20-21, 2010, in the Instituto de Investigaciones Filosófi cas, and at the III Encuentro sobre Lenguaje, Contexto y Cognición, held August 4-6 in Valparaíso, Chile. The paper has benefi ted from the helpful comments offered by the participants of those conferences, as well as from the substantial criticism and advice provided by two anonymous referees.


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Indexical Color Predicates: Truth Conditional Semantics vs. Truth Conditional Pragmatics

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