In natural language we rarely use relation-words with more than three argument places. This paper studies one systematic device, rooted in natural language, by which relations of greater adicity can be expressed. It is based on a higher-order relation between 1-place, 2-place, and 4-place relations (and so on) of which the relation between the positive and comparative degrees of a predicate is a special case. Two formal languages are presented in this connection, one of which represents the language of communication (...) and the other the contextual information against which the first language is interpreted. A semantical theory is described, which treats the two languages in an interdependent way. Logical consequence is non-compact. Connections with issues about vagueness are made. (shrink)

This paper investigates the way that linguistic expressions influence vagueness, focusing on the interpretation of the positive (unmarked) form of gradable adjectives. I begin by developing a semantic analysis of the positive form of ‘relative’ gradable adjectives, expanding on previous proposals by further motivating a semantic basis for vagueness and by precisely identifying and characterizing the division of labor between the compositional and contextual aspects of its interpretation. I then introduce a challenge to the analysis from the class of ‘absolute’ (...) gradable adjectives: adjectives that are demonstrably gradable, but which have positive forms that relate objects to maximal or minimal degrees, and do not give rise to vagueness. I argue that the truth conditional difference between relative and absolute adjectives in the positive form stems from the interaction of lexical semantic properties of gradable adjectives—the structure of the scales they use—and a general constraint on interpretive economy that requires truth conditions to be computed on the basis of conventional meaning to the extent possible, allowing for context dependent truth conditions only as a last resort. (shrink)

Given the significant exculpatory power that ignorance has when it comes to moral, legal, and epistemic transgressions, it is important to have an accurate understanding of the concept of ignorance. According to the Standard View of factual ignorance, a person is ignorant that p whenever they do not know that p, while on the New View, a person is ignorant that p whenever they do not truly believe that p. On their own though, neither of these accounts explains how ignorance (...) can often be a degreed notion—how we can sometimes be slightly ignorant, quite ignorant, or completely ignorant that p. In this paper, I will argue that there is a route for advocates of the Standard View and the New View to accommodate the gradability of ignorance. On the view I defend, ‘ignorant’ picks out everyone that is ignorant to some degree, making it possible that ignorance can be both degreed and characterized as a lack of knowledge or true belief. Even though we can be ignorant to a greater or lesser extent, the only way to avoid being ignorant that p is to know or truly believe. (shrink)

Formal epistemologists often claim that our credences should be representable by a probability function. Complete probabilistic coherence, however, is only possible for ideal agents, raising the question of how this requirement relates to our everyday judgments concerning rationality. One possible answer is that being rational is a contextual matter, that the standards for rationality change along with the situation. Just like who counts as tall changes depending on whether we are considering toddlers or basketball players, perhaps what counts as rational (...) shifts according to whether we are considering ideal agents or creatures more like ourselves. Even though a number of formal epistemologists have endorsed this type of solution, I will argue that there is no way to spell out this contextual account that can make sense of our everyday judgments about rationality. Those who defend probabilistic coherence requirements will need an alternative account of the relationship between real and ideal rationality. (shrink)

A number of authors have defended permissivism by appealing to rational supererogation, the thought that some doxastic states might be rationally permissible even though there are other, more rational beliefs available. If this is correct, then there are situations that allow for multiple rational doxastic responses, even if some of those responses are rationally suboptimal. In this paper, I will argue that this is the wrong approach to defending permissivism—there are no doxastic states that are rationally supererogatory. By the lights (...) of contemporary linguistics, ‘rational’ is an absolute gradable adjective, and as such, can only be applied to things that satisfy the top of the scale of rationality. For this reason, it is not possible to believe what is rational while also failing to believe what is rationally optimal. (shrink)

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (shrink)

The Stoic understanding of virtue is often taken to be a non-starter. Many of the Stoic claims about virtue – that a virtue requires moral perfection and that all who are not fully virtuous are vicious – are thought to be completely out of step with our commonsense notion of virtue, making the Stoic account more of an historical oddity than a seriously defended view. Despite many voices to the contrary, I will argue that there is a way of making (...) sense of these Stoic claims. Recent work in linguistics has shown that there is a distinction between relative and absolute gradable adjectives, with the absolute variety only applying to perfect exemplars. I will argue that taking virtue terms to be absolute gradable adjectives – and thus that they apply only to those who are fully virtuous – is one way to make sense of the Stoic view. I will also show how interpreting virtue theoretic adjectives as absolute gradable adjectives makes it possible to defend Stoicism against its most common objections, demonstrating how the Stoic account of virtue might once again be a player in the contemporary landscape of virtue theorizing. (shrink)

It is clear that beliefs can be assessed both as to their justification and their rationality. What is not as clear, however, is how the rationality and justification of belief relate to one another. Stewart Cohen has stumped for the popular proposal that rationality and justification come to the same thing, that rational beliefs just are justified beliefs, supporting his view by arguing that ‘justified belief’ and ‘rational belief’ are synonymous. In this paper, I will give reason to think that (...) Cohen’s argument is spurious. I will show that ‘rational’ and ‘justified’ occupy two distinct semantic categories – ‘rational’ is an absolute gradable adjective and ‘justified’ is a relative gradable adjective – telling against the thought that ‘rational belief’ and ‘justified belief’ are synonymous. I will then argue that the burden of proof is on those who would equate rationality and justification, making the case that those who hold this prominent position face the difficulty of explaining how rationality and justification come to the same thing even though ‘rational’ and ‘justified’ are not synonymous. (shrink)

Breheny et al. argue against the structural approach to alternatives. The empirical force of their argument comes mostly from challenges raised against Trinh and Haida. This paper aims to respond to these challenges, showing how they can be met by a natural refinement of Trinh and Haida’s proposal which turns out to capture additional facts previously not accounted for. Another aim of this paper is to recount the debate with enough precision and explicitness in order to enhance understanding and facilitate (...) future discussions. (shrink)

The pluralist about material constitution maintains that a lump of clay is not identical with the statue it constitutes. Although pluralism strikes many as extravagant by requiring distinct things to coincide, it can be defended with a simple argument. The monist is less well off. Typically, she has to argue indirectly for her view by finding problems with the pluralist's extravagance. This paper offers a direct argument for monism that illustrates how monism about material constitution is rooted in commonsense as (...) reflected in linguistic practice. In particular, I argue that everyday judgements that are contrastive like "The statue is beautiful for a lump of clay" entail the identity of the statue and the clay. (shrink)

The goal of this short paper is to show that esthetic adjectives—exemplified by “beautiful” and “elegant”—do not pattern stably on a range of linguistic diagnostics that have been used to taxonomize the gradability properties of adjectives. We argue that a plausible explanation for this puzzling data involves distinguishing two properties of gradable adjectives that have been frequently conflated: whether an adjective’s applicability is sensitive to a comparison class, and whether an adjective’s applicability is context-dependent.

In a thoughtful paper, Peter Martin Jaworski has written, “The debate over originals, authenticity, fakes, duplicates, and forgery got its start in the mid-60s and then continued until the ‘80s.”Peter Martin Jaworski. “In Defense of Fakes and Artistic Treason: Why Visually-Indistinguishable Duplicates Are as Good as the Originals.” Journal of Value Inquiry (2013), pp. 391–405. Quotation at p. 392. The debate, at least insofar as I participated in it, questioned whether original paintings and forgeries were sufficiently alike – sufficiently the (...) same kinds of things – that as a general rule the same qualities could be predicated of them. I and others argued they were not. To know the qualities of a painting, to make sense of the many often conflicting interpretations critics may offer of the same canvass, one must as a first step know what kind of painting it is. The relevant qualities of a painting, call them “artistic” or “aesthetic” or “stylistic” or whatever, are predicated of them i .. (shrink)

In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...) semantics avoid the entailment problems that result from Kratzer’s semantics. Our discussion focuses on methodological issues concerning the choice between different semantics. (shrink)

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...) The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

Benjamin Bagley ('Properly Proleptic Blame', Ethics 127, July 2017) sets out a dilemma for addressed blame, that is, blame addressed to its targets as an implicit demand for recognition. The dilemma arises when we ask whether offenders would actually appreciate this demand, via a sound deliberative route from their existing motivations. If they would, their offense reflects a deliberative mistake. If they wouldn't, addressing them is futile, and blame's emotional engagement seems unwarranted. Bagley wants to resolve the dilemma in such (...) a way that addressed blame's distinctive elements of hostility and emotional engagement can be accounted for. I argue that Bagley's focus on the proleptic character of addressed blame helps to avoid the dilemma, but that Bagley has difficulties accounting for the element of hostility in addressed blame. I suggest that an alternative account of addressed blame makes better sense of Bagley's paradigm example, avoids Bagley's dilemma in the way Bagley's original solution does, because it preserves addressed blame's proleptic character, and can account for addressed blame's elements of emotional engagement and hostility. (shrink)

How demanding is the virtuous life? Can virtue exist alongside hints of vice? Is it possible to be virtuous within a vicious society? A line of thinking running through Diogenes and the Stoics is that even a hint of corruption is inimical to virtue, that participating in a vicious society makes it impossible for a person to be virtuous. One response to this difficulty is to claim that virtue is a threshold concept, that context sets a threshold for what is (...) considered virtuous. On this way of thinking, what counts as virtuous in one society may be more demanding than what passes for virtuous in another. This response seems plausible when considering that virtue-theoretic terms like `honest' are gradable adjectives. Many gradable adjectives, like `tall' and `expensive,' have contextual thresholds that shift depending on the situation, and so is tenable that virtue-theoretic adjectives might function with contextual thresholds as well. A major difficulty for this response, however, is that virtue terms are absolute gradable adjectives, a variety of gradable adjectives that do not require a contextual threshold. Absolute gradable adjectives instead draw their truth conditions from their maximal degree, suggesting that Diogenes and the Stoics were correct to think that virtue is incompatible with even a small degree of vice. (shrink)

AtCategories7, 6a36-7 Aristotle defines relatives, but at 8a13-28 worries that the definition may include some substances. Aristotle introduces a second account of relatives to solve the problem. Recent commentators have held that Aristotle intends to solve the extensional adequacy worry by restricting the extension of relatives. That is, R2 counts fewer items as relative than R1. However, this cannot explain Aristotle’s attitude to relatives, since he immediately returns to using R1. I propose a non-extensional reading. R1 and R2 do not (...) specify different sets of relatives, but rather different ways to understand each relative. (shrink)

This volume analyzes and studies how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else.

Color adjectives have played a central role in work on language typology and variation, but there has been relatively little investigation of their meanings by researchers in formal semantics. This is surprising given the fact that color terms have been at the center of debates in the philosophy of language over foundational questions, in particular whether the idea of a compositional, truth-conditional theory of natural language semantics is even coherent. The challenge presented by color terms is articulated in detail in (...) the work of Charles Travis. Travis argues that structurally isomorphic sentences containing color adjectives can shift truth value from context to context depending on how they are used and in the absence of effects of vagueness or ambiguity/polysemy, and concludes that a deterministic mapping from structures to truth conditions is impossible. The goal of this paper is to provide a linguistic perspective on this issue, which we believe defuses Travis’ challenge. We provide empirical arguments that color adjectives are in fact ambiguous between gradable and nongradable interpretations, and that this simple ambiguity, together with independently motivated options concerning scalar dimension within the gradable reading accounts for the Travis facts in a simpler, more constrained, and thus ultimately more successful fashion than recent contextualist analyses such as those in Szabó (Perspectives on semantics, pragmatics and discourse: A festschrift for Ferenc Kiefer, 2001) or Rothschild and Segal (Mind Lang, 2009). (shrink)

I have attempted to show that many attributive adjectives can be dealt with within the framework of first-order predicate calculus by the method suggested in this paper. I've also supplied independent reasons for the claim that attributive adjectives that are not responsive to this method require a formal treatment different from the one that the adjectives successfully dealt with by that method require. Thus, if the method I've argued for is sound, then the scope of first-order predicate calculus was shown (...) to be wider than assumed by several logicians. This I take to be of interest from a logical point of view. (shrink)

This paper explores the hypothesis that all comparative sentences— nominal, verbal, and adjectival—contain instances of a single morpheme that compositionally introduces degrees. This morpheme, sometimes pronounced much, semantically contributes a structure-preserving map from entities, events, or states, to their measures along various dimensions. A major goal of the paper is to argue that the differences in dimensionality observed across domains are a consequence of what is measured, as opposed to which expression introduces the measurement. The resulting theory has a number (...) of interesting properties. It characterizes the notion of ‘measurement’ uniformly across comparative constructions, in terms of non-trivial structure preservation. It unifies the distinctions between mass/count nouns and atelic/telic verb phrases with that between gradable and non-gradable adjectives. Finally, it affords a uniform characterization of semantically anomalous comparisons across categories. (shrink)

A property modifier is a function that takes a property to a property. For instance, the modifier short takes the property being a Dutchman to the property being a short Dutchman. Assume that being a round peg is a property obtained by means of modification, round being the modifier and being a peg the input property. Then how are we to infer that a round peg is a peg? By means of a rule of right subsectivity. How are we to (...) infer that a round peg is round? By means of a rule of left subsectivity. This paper puts forward two rules of left subsectivity. The rules fill a gap in the prevalent theory of property modification. The paper also explains why the rules are philosophically relevant. (shrink)

Is there a principled difference between entailments in natural language that are valid solely in virtue of their form or structure and those that are not? This paper advances an affirmative answer to this question, one that takes as its starting point Gareth Evans’s suggestion that semantic theory aims to carve reality at the joints by uncovering the semantic natural kinds of the language. I sketch an Evans-inspired account of semantic kinds and show how it supports a principled account of (...) structural entailment. I illustrate the account by application to a case study involving the entailment properties of adverbs; this involves developing a novel proposal about the semantics for adverbs like ‘quickly’ and ‘slowly’. In the course of the discussion I explore some implications of the account for the place of model-theoretic tools in natural language semantics. (shrink)