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Vagueness in Context
Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The main feature of Shapiro's account is that the extensions (and anti-extensions) of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.
The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.
Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of "determinacy" and "borderline" -- and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.
As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects.
The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.
Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of "determinacy" and "borderline" -- and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.
As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak. But vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects.
240 pages, Paperback
First published January 1, 2006
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March 29, 2024This review makes large reference to Matti Eklund’s 2006 review for NDPR, as this book is dense, and Eklund’s review gets to the heart of it.
Stewart Shapiro's “Vagueness in Context” defends his theory of vagueness, focusing on four key ideas: contextualism, the "principle of tolerance," response-dependent borderline sentences, and open texture. While rich in concepts, the book lacks in-depth exploration and attention to objections. It suits researchers and graduate students familiar with the topic but may be overwhelming for newcomers. The chapters cover the theory's basics, model theory, higher-order vagueness, and additional issues like abstraction principles and realism. Despite its depth, it falls short in providing a comprehensive introduction.
A significant portion of the book focuses on building a formal framework, but first is the motivation. Stewart Shapiro's main claim is contextualism about vagueness, suggesting that vague expressions depend on context for their meaning. Other proponents include Hans Kamp, Jamie Tappenden, Diana Raffman, Scott Soames, and Delia Graff. Skepticism arises because even with context sensitivity considered, issues like sharp boundaries and higher-order vagueness persist.
Shapiro's contextualism, though unique, relies on distinctions between 'external' context (determined by factors like comparison class) and the broader context influenced by speakers' decisions on borderline cases. This approach connects to Shapiro's notion of determinate truth: a sentence is true in a given context if its meaning and external factors determine its truth. Shapiro, following Raffman, emphasizes that his contextualist thesis pertains to the extensions rather than the meanings of vague predicates, although the distinction between these two remains somewhat unclear.
Shapiro's principle of tolerance states that if two objects in a category only differ slightly in a relevant aspect where the category is tolerant, then if one is judged to belong to that category, the other cannot be judged differently, without altering the context. Regarding the response-dependence of borderline sentences, Shapiro adopts Raffman's idea, which can be divided into two parts. It suggests that most vague predicates adhere to the principle that an item is categorized as such if competent judges would agree. For borderline cases, this dependence operates from right to left.
The principle of open texture asserts that language rules allow individuals to interpret borderline cases in either direction. This concept, originating from Friedrich Waismann, is further explored in an appendix. Crispin Wright also introduced the idea that speakers can legitimately interpret borderline cases in multiple ways. Shapiro suggests that Wright supports the open texture thesis he discusses, a connection to explore later. Despite the centrality of these four theses in Shapiro's book, there's surprisingly little direct argument for them or discussion of objections from the literature. Shapiro seems to rely on the theory's appeal rather than rigorous argumentation.
Combining the theses, we understand that vague expressions are context-sensitive, with some objects falling under a vague predicate in certain contexts but not others. Even with external context, the truth of sentences like "Fa" isn't always settled due to open texture, allowing speakers to interpret them differently. Response-dependence implies that judgments from competent speakers determine the truth of borderline sentences. This framework aligns with the principle of tolerance, as judging a borderline case differently shifts the context and thus the predicate's extension. There are some criticisms to consider. Starting with the principle of tolerance, while initially plausible, further scrutiny may be needed. It seems like a principle that various vagueness theorists could agree on, but its relation to Shapiro's other theses isn't clear. Just because everyone agrees on the principle doesn't mean everyone can effectively adhere to it. Shapiro doesn't argue that his contextualism is the only view that can respect the principle.
Moving on to the idea of open texture, Shapiro's discussion lacks emphasis on crucial distinctions. Borderline sentences can be seen as 'unsettled' or 'open,' with their truth values not definitively determined. They can express truth in one context and falsehood in another. Speakers can legitimately disagree about their truth values, even with all relevant information. While Waismann primarily focused on (i), Shapiro aims for something stronger like (ii), but (i) doesn't necessarily imply (ii). Akin to Wright's view, goes further, suggesting that disagreement is permissible even when speakers have all the facts. She might avoid embracing the extreme (iii), but it could mean denying the authenticity of apparent disagreements. Contrary to what Shapiro's mention of Wright as an ally might imply, Shapiro doesn't support (iii). For Shapiro, cases of seeming disagreement aren't genuine. When one says "Harry is bald" and another says "No, he's not bald," either the context changes in a way that both assertions are true, or the context remains unchanged, and the assertions don't disagree.
Shapiro's distinction between external and internal context complicates matters. He suggests that two speakers can be in the same external context yet differ in their assertions regarding borderline sentences. While this stance isn't as radical as Wright's, Shapiro's formulations sometimes blur the line between using a term and mentioning it. While this isn't always problematic, it could lead to confusion. In discussions about the open texture thesis, clearer formulations would have been preferable. For instance, instead of saying a speaker is free to assert "Pa" and "¬Pa," it would be clearer to say a speaker is free to assertively utter both "Pa" and "¬Pa," emphasizing that Shapiro doesn't support (iii).
Let's consider the contextualist thesis. There's reason to doubt the usefulness of appealing to context. Contextualists have an appealing explanation for sorites paradoxes, especially the forced march type. They argue that the lack of a clear boundary between "F" and "non-F" items is because it's never in our focus; whenever we examine a segment of a sorites series, the boundary, if it exists, isn't there. Despite this explanation, several puzzles about vagueness persist even within contextualism, and they seem just as serious as before. While it might make sense for long sorites series, denying the ability to judge "F-ness" for each item in short, easily surveyed series seems arbitrary (think of a series for "natural number much smaller than 10"). Although a speaker's focus may never align with a potential sharp boundary, semanticists studying the speaker's language still question the extension of the predicate "F" in a given context. It remains implausible that there's a clear boundary for what "F" applies to and what it doesn't. The contextualist may argue that there's no sharp boundary, leading to issues of higher-order vagueness. Where exactly is the boundary in the sorites series between objects where "F" clearly applies and those where it's indeterminate? Isn't this issue just as serious as the original issue with sharp boundaries, indicating no real progress?
Shapiro addresses the issue of higher-order vagueness in a chapter, but he doesn't seem to grasp its urgency. It's not merely another issue to tick off the list; it suggests that we haven't made real progress. His solution is to suggest that the vagueness in determining who counts as a competent user of a predicate "F" makes "borderline F" vague. But how does this address the issue at hand? Considering the vagueness in determining who is competent yields a more complex division of cases, but this process can be repeated indefinitely. No multi-part division seems better than the original two-part one. Shapiro acknowledges these issues but appears surprisingly casual about them. He suggests that as we get into increasingly complex questions about who is a competent user of "F," the questions become too difficult to evaluate. This dismissal raises two concerns.
(a) Even if the experiment breaks down in practice, one might question whether the competence-performance distinction should prevent us from concluding definitively at the fourth or fifth level.
(b) Even if Shapiro is correct in predicting the breakdown of the experiment and its significance, one may wonder: how does this aid our understanding? The best explanation seems to suggest that although the relevant counterfactuals become indeterminate, this indeterminacy differs from vagueness. It may not pose an issue for a theory of vagueness if it fails to address indeterminacy. Let's discuss response-dependence. Shapiro draws inspiration from Raffman's work on how speakers react to borderline cases and sorites series. They both note that the same speaker may judge a borderline case differently in different contexts, which supports contextualism. This motivation opens the view to criticism: just because speakers make different judgments doesn't mean they're correct. Sorensen raises this issue against Raffman, and Shapiro acknowledges it affects his theory too. This discrepancy between judgments and genuine context-sensitivity is addressed through response-dependence. Although neither Raffman nor Shapiro provides arguments for response-dependence, they postulate it as a solution.
(Shapiro's book lacks explicit arguments because he believes the theory's attractiveness speaks for itself.) However, there are reasons to doubt this. Let's consider an important distinction. When we say (1) "Speaker judgments help determine that 'F' is true of a," it seems plausible regardless of the predicate. Claims like (2) "Speaker judgments help determine that a is F" may seem implausible for certain predicates (like 'square'). With this in mind, let's revisit borderline cases of vague predicates. Take Harry, a borderline case of 'bald' where external context doesn't settle his baldness. Shapiro argues that a subject can still judge "Harry is bald" and appeals to response-dependence. But let's compare: (3) Speaker judgments determine that 'bald' is true of Harry in a context C. (4) [In context C,] speaker judgments determine that Harry is bald. For response-dependence to apply, (4) must be true. (3) seems more plausible. (4) seems equally implausible regardless of Harry's borderline status. Speaker judgments determine Harry's baldness as much as they do for a clearly bald Yul or a clearly hairy Tom. Response-dependence doesn't address Sorensen's concern. It's not entirely clear what response-dependence entails. Shapiro initially claims it applies only to borderline sentences not settled by external context. In other parts of the discussion, Shapiro suggests a stronger view that vagueness arises from response-dependence.
Eklund references several books. These include Crispin’s “Truth and Objectivity” and “Saving the Differences”. He also references Soames’ “Understanding Truth” and Sorensen’s “Vagueness and Contradiction”.
https://open.substack.com/pub/coconif...
Stewart Shapiro's “Vagueness in Context” defends his theory of vagueness, focusing on four key ideas: contextualism, the "principle of tolerance," response-dependent borderline sentences, and open texture. While rich in concepts, the book lacks in-depth exploration and attention to objections. It suits researchers and graduate students familiar with the topic but may be overwhelming for newcomers. The chapters cover the theory's basics, model theory, higher-order vagueness, and additional issues like abstraction principles and realism. Despite its depth, it falls short in providing a comprehensive introduction.
A significant portion of the book focuses on building a formal framework, but first is the motivation. Stewart Shapiro's main claim is contextualism about vagueness, suggesting that vague expressions depend on context for their meaning. Other proponents include Hans Kamp, Jamie Tappenden, Diana Raffman, Scott Soames, and Delia Graff. Skepticism arises because even with context sensitivity considered, issues like sharp boundaries and higher-order vagueness persist.
Shapiro's contextualism, though unique, relies on distinctions between 'external' context (determined by factors like comparison class) and the broader context influenced by speakers' decisions on borderline cases. This approach connects to Shapiro's notion of determinate truth: a sentence is true in a given context if its meaning and external factors determine its truth. Shapiro, following Raffman, emphasizes that his contextualist thesis pertains to the extensions rather than the meanings of vague predicates, although the distinction between these two remains somewhat unclear.
Shapiro's principle of tolerance states that if two objects in a category only differ slightly in a relevant aspect where the category is tolerant, then if one is judged to belong to that category, the other cannot be judged differently, without altering the context. Regarding the response-dependence of borderline sentences, Shapiro adopts Raffman's idea, which can be divided into two parts. It suggests that most vague predicates adhere to the principle that an item is categorized as such if competent judges would agree. For borderline cases, this dependence operates from right to left.
The principle of open texture asserts that language rules allow individuals to interpret borderline cases in either direction. This concept, originating from Friedrich Waismann, is further explored in an appendix. Crispin Wright also introduced the idea that speakers can legitimately interpret borderline cases in multiple ways. Shapiro suggests that Wright supports the open texture thesis he discusses, a connection to explore later. Despite the centrality of these four theses in Shapiro's book, there's surprisingly little direct argument for them or discussion of objections from the literature. Shapiro seems to rely on the theory's appeal rather than rigorous argumentation.
Combining the theses, we understand that vague expressions are context-sensitive, with some objects falling under a vague predicate in certain contexts but not others. Even with external context, the truth of sentences like "Fa" isn't always settled due to open texture, allowing speakers to interpret them differently. Response-dependence implies that judgments from competent speakers determine the truth of borderline sentences. This framework aligns with the principle of tolerance, as judging a borderline case differently shifts the context and thus the predicate's extension. There are some criticisms to consider. Starting with the principle of tolerance, while initially plausible, further scrutiny may be needed. It seems like a principle that various vagueness theorists could agree on, but its relation to Shapiro's other theses isn't clear. Just because everyone agrees on the principle doesn't mean everyone can effectively adhere to it. Shapiro doesn't argue that his contextualism is the only view that can respect the principle.
Moving on to the idea of open texture, Shapiro's discussion lacks emphasis on crucial distinctions. Borderline sentences can be seen as 'unsettled' or 'open,' with their truth values not definitively determined. They can express truth in one context and falsehood in another. Speakers can legitimately disagree about their truth values, even with all relevant information. While Waismann primarily focused on (i), Shapiro aims for something stronger like (ii), but (i) doesn't necessarily imply (ii). Akin to Wright's view, goes further, suggesting that disagreement is permissible even when speakers have all the facts. She might avoid embracing the extreme (iii), but it could mean denying the authenticity of apparent disagreements. Contrary to what Shapiro's mention of Wright as an ally might imply, Shapiro doesn't support (iii). For Shapiro, cases of seeming disagreement aren't genuine. When one says "Harry is bald" and another says "No, he's not bald," either the context changes in a way that both assertions are true, or the context remains unchanged, and the assertions don't disagree.
Shapiro's distinction between external and internal context complicates matters. He suggests that two speakers can be in the same external context yet differ in their assertions regarding borderline sentences. While this stance isn't as radical as Wright's, Shapiro's formulations sometimes blur the line between using a term and mentioning it. While this isn't always problematic, it could lead to confusion. In discussions about the open texture thesis, clearer formulations would have been preferable. For instance, instead of saying a speaker is free to assert "Pa" and "¬Pa," it would be clearer to say a speaker is free to assertively utter both "Pa" and "¬Pa," emphasizing that Shapiro doesn't support (iii).
Let's consider the contextualist thesis. There's reason to doubt the usefulness of appealing to context. Contextualists have an appealing explanation for sorites paradoxes, especially the forced march type. They argue that the lack of a clear boundary between "F" and "non-F" items is because it's never in our focus; whenever we examine a segment of a sorites series, the boundary, if it exists, isn't there. Despite this explanation, several puzzles about vagueness persist even within contextualism, and they seem just as serious as before. While it might make sense for long sorites series, denying the ability to judge "F-ness" for each item in short, easily surveyed series seems arbitrary (think of a series for "natural number much smaller than 10"). Although a speaker's focus may never align with a potential sharp boundary, semanticists studying the speaker's language still question the extension of the predicate "F" in a given context. It remains implausible that there's a clear boundary for what "F" applies to and what it doesn't. The contextualist may argue that there's no sharp boundary, leading to issues of higher-order vagueness. Where exactly is the boundary in the sorites series between objects where "F" clearly applies and those where it's indeterminate? Isn't this issue just as serious as the original issue with sharp boundaries, indicating no real progress?
Shapiro addresses the issue of higher-order vagueness in a chapter, but he doesn't seem to grasp its urgency. It's not merely another issue to tick off the list; it suggests that we haven't made real progress. His solution is to suggest that the vagueness in determining who counts as a competent user of a predicate "F" makes "borderline F" vague. But how does this address the issue at hand? Considering the vagueness in determining who is competent yields a more complex division of cases, but this process can be repeated indefinitely. No multi-part division seems better than the original two-part one. Shapiro acknowledges these issues but appears surprisingly casual about them. He suggests that as we get into increasingly complex questions about who is a competent user of "F," the questions become too difficult to evaluate. This dismissal raises two concerns.
(a) Even if the experiment breaks down in practice, one might question whether the competence-performance distinction should prevent us from concluding definitively at the fourth or fifth level.
(b) Even if Shapiro is correct in predicting the breakdown of the experiment and its significance, one may wonder: how does this aid our understanding? The best explanation seems to suggest that although the relevant counterfactuals become indeterminate, this indeterminacy differs from vagueness. It may not pose an issue for a theory of vagueness if it fails to address indeterminacy. Let's discuss response-dependence. Shapiro draws inspiration from Raffman's work on how speakers react to borderline cases and sorites series. They both note that the same speaker may judge a borderline case differently in different contexts, which supports contextualism. This motivation opens the view to criticism: just because speakers make different judgments doesn't mean they're correct. Sorensen raises this issue against Raffman, and Shapiro acknowledges it affects his theory too. This discrepancy between judgments and genuine context-sensitivity is addressed through response-dependence. Although neither Raffman nor Shapiro provides arguments for response-dependence, they postulate it as a solution.
(Shapiro's book lacks explicit arguments because he believes the theory's attractiveness speaks for itself.) However, there are reasons to doubt this. Let's consider an important distinction. When we say (1) "Speaker judgments help determine that 'F' is true of a," it seems plausible regardless of the predicate. Claims like (2) "Speaker judgments help determine that a is F" may seem implausible for certain predicates (like 'square'). With this in mind, let's revisit borderline cases of vague predicates. Take Harry, a borderline case of 'bald' where external context doesn't settle his baldness. Shapiro argues that a subject can still judge "Harry is bald" and appeals to response-dependence. But let's compare: (3) Speaker judgments determine that 'bald' is true of Harry in a context C. (4) [In context C,] speaker judgments determine that Harry is bald. For response-dependence to apply, (4) must be true. (3) seems more plausible. (4) seems equally implausible regardless of Harry's borderline status. Speaker judgments determine Harry's baldness as much as they do for a clearly bald Yul or a clearly hairy Tom. Response-dependence doesn't address Sorensen's concern. It's not entirely clear what response-dependence entails. Shapiro initially claims it applies only to borderline sentences not settled by external context. In other parts of the discussion, Shapiro suggests a stronger view that vagueness arises from response-dependence.
Eklund references several books. These include Crispin’s “Truth and Objectivity” and “Saving the Differences”. He also references Soames’ “Understanding Truth” and Sorensen’s “Vagueness and Contradiction”.
https://open.substack.com/pub/coconif...
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