A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes from recent (...) proposals that analyze depiction in terms of geometrical projection. In this essay, I will argue that, for a central class of pictures, the projection-based theory of depiction provides the best explanation for how pictures express pictorial spaces, while rival perceptual and resemblance theories fall short. Since the composition of pictorial space is itself the basis for all other aspects of pictorial content, the proposal provides a natural foundation for further pictorial semantics. (shrink)

What is it for a picture to depict a scene? The most orthodox philosophical theory of pictorial representation holds that depiction is grounded in resemblance. A picture represents a scene in virtue of being similar to that scene in certain ways. This essay presents evidence against this claim: curvilinear perspective is one common style of depiction in which successful pictorial representation depends as much on a picture's systematic differences with the scene depicted as on the similarities; it cannot be analyzed (...) in terms of similarity alone. The same problem arises for many other kinds of depiction. The essay concludes that depiction in general is not grounded in resemblance but geometrical transformation. (shrink)

This paper examines the interplay of semantics and pragmatics within the domain of film. Films are made up of individual shots strung together in sequences over time. Though each shot is disconnected from the next, combinations of shots still convey coherent stories that take place in continuous space and time. How is this possible? The semantic view of film holds that film coherence is achieved in part through a kind of film language, a set of conventions which govern the relationships (...) between shots. In this paper, we develop and defend a new version of the semantic view. We articulate it for a pair of conventions that govern spatial relations between viewpoints. One such rule is already well-known; sometimes called the "180° Rule," we term it the X-Constraint; to this we add a previously unrecorded rule, the T-Constraint. As we show, both have the effect, in different ways, of limiting the way that viewpoint can shift through space from shot to shot over the course of a film sequence. Such constraints, we contend, are analogous to relations of discourse coherence that are widely recognized in the linguistic domain. If film is to have a language, it is a language made up of rules like these. (shrink)

In this book, Yael Greenberg discusses and clarifies a number of controversial issues and phenomena in the generic literature, including the existence of ...

Since Freud, clinicians have understood that disturbing memories contribute to psychopathology and that new emotional experiences contribute to therapeutic change. Yet, controversy remains about what is truly essential to bring about psychotherapeutic change. Mounting evidence from empirical studies suggests that emotional arousal is a key ingredient in therapeutic change in many modalities. In addition, memory seems to play an important role but there is a lack of consensus on the role of understanding what happened in the past in bringing about (...) therapeutic change. The core idea of this paper is that therapeutic change in a variety of modalities, including behavioral therapy, cognitive-behavioral therapy, emotion-focused therapy, and psychodynamic psychotherapy, results from the updating of prior emotional memories through a process of reconsolidation that incorporates new emotional experiences. We present an integrated memory model with three interactive components – autobiographical memories, semantic structures, and emotional responses – supported by emerging evidence from cognitive neuroscience on implicit and explicit emotion, implicit and explicit memory, emotion-memory interactions, memory reconsolidation, and the relationship between autobiographical and semantic memory. We propose that the essential ingredients of therapeutic change include: reactivating old memories; engaging in new emotional experiences that are incorporated into these reactivated memories via the process of reconsolidation; and reinforcing the integrated memory structure by practicing a new way of behaving and experiencing the world in a variety of contexts. The implications of this new, neurobiologically grounded synthesis for research, clinical practice, and teaching are discussed. (shrink)

Should I believe something if and only if it’s true? Many philosophers have objected to this kind of truth norm, on the grounds that it’s not the case that one ought to believe all the truths. For example, some truths are too complex to believe; others are too trivial to be worth believing. Philosophers who defend truth norms often respond to this problem by reformulating truth norms in ways that do not entail that one ought to believe all the truths. (...) Many of these attempts at reformulation, I’ll argue, have been missteps. A number of these different reformulations are incapable of carrying out a central role a truth norm is meant to play, that of explaining justification. The truth norm I’ll defend, however, avoids the implausible results of a prescription to believe all the truths, but doesn’t thereby fail to explain justification. This norm, introduced by Conor McHugh, states that if one has some doxastic attitude about p—i.e. if one believes, disbelieves, or suspends judgement about whether p—then one ought to believe that p if and only if p is true. (shrink)

I offer a new argument against the legal positivist view that non-normative social facts can themselves determine the content of the law. I argue that the nature of the determination relation in law is rational determination: the contribution of law-determining practices to the content of the law must be based on reasons. That is why it must be possible in principle to explain what makes the law have the content that it does. It follows, I argue, that non-normative facts about (...) statutes, judicial decisions, and other practices cannot themselves determine the content of the law. A full account must appeal to considerations independent of the practices that determine the relevance of the practices to the content of the law. Normative facts are the best candidates. (shrink)

Because humans cannot know one another’s minds directly, every form of communication is a solution to the same basic problem: how can privately held information be made publicly accessible through manipulations of the physical environment? Language is by far the best studied response to this challenge. But there are a diversity of non-linguistic strategies for representation with external signs as well, from facial expressions and fog horns to chronological graphs and architectural renderings. The general thesis of this dissertation is that (...) there is an impressively wide spectrum of conventional systems of representation, corresponding to the many ways that the problem of communication can be solved, and that these systems can be described and explained using the tools of contemporary mathematical semantics. As a partial corrective to the countervailing norm, this work concentrates on the class of systems arguably most different from language— those governing the interpretation of pictorial images. Such representations dominate practical communication: witness the proliferation of maps, road signs, newspaper photographs, scientific illustrations, television shows, engineering drawings, and even the fleeting imagery of manual gesture. I argue that systems of depiction and languages embody a parallel technologies of communication. Both are based on semantics: systematic and conventional mappings from signs to representational content. But I also provide evidence that these semantics are profoundly divergent. Whereas the semantics of languages are based on arbitrary associations of signs and denotations, the semantics of systems of depiction are based on rules of geometrical transformation. Drawing on recent research in computer graphics and computational vision, I go on to develop a precise theory of pictorial semantics. This in turn facilitates a detailed comparison of iconic, image-based representation, and symbolic, language-based representation. A consequence of these conclusions is that the traditional, language-centric conception of semantics must be overhauled to allow for a more general semantic theory, one which countenances the wide variety of interpretive mechanisms actually at work in human communication. (shrink)

This essay argues for a model of pictorial representation which aims to explain the relationship between pictorial content and pictorial accuracy. Focusing on cases where pictures are intended to convey accurate information, the model distinguishes between two fundamental representational relations: on one hand, a picture expresses a content; on the other, it aims at a target scene. Such a picture is accurate when the content it expresses fits the target scene it aims at. In addition, the model follows the traditional (...) division of content into two aspects: singular content specifies the particular individuals which a picture is of, and attributive content specifies the properties and relations which the picture ascribes to those individuals. For a picture to be accurate, both aspects must be matched in the target. I call this the Three-Part Model because it distinguishes between the triad of factors, singular content, attributive content, and target, which together determine pictorial accuracy. Though previous work on depiction has not recognized the distinctive role played by target, I will argue that it is essential in order to make sense of accuracy judgements across a range of central cases. (shrink)

This introduction aims to familiarize readers with basic dimensions of variation among pictorial and diagrammatic representations, as we understand them, in order to serve as a backdrop to the articles in this volume. Instead of trying to canvas the vast range of representational kinds, we focus on a few important axes of difference, and a small handful of illustrative examples. We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that (...) of the properties of usage associated with signs. In Section 2 we illustrate these ideas with a case study of diagrammatic representation: the evolution from Euler diagrams to Venn diagrams. Section 3 is correspondingly devoted to pictorial representation, illustrated by the comparison between parallel and linear perspective drawing. We conclude with open questions, and then briefly summarize the articles to follow. (shrink)

Tarot use has become increasingly popular in contemporary society. However, unlike the position afforded divination in some cultures, it is not culturally consecrated as a legitimate way of knowing in the so‐called Modern West—in large part, due to the attempted disenchantment of the world by the colonial project of modernity. This paper posits that engagement with tarot divination can be a decolonizing methodology. I explore how divination's dependence on chance, the imagination, and engagement with spirits can heal the Cartesian mental (...) models that underly modernity's hold on our society. Academic writing on divination has, until recently, largely been authored by people who are not also practitioners of divination themselves. Writing as both a scholar and practitioner of tarot, I use the cards as a form of “imaginal research” to directly assist in the creation of this paper—allowing the tarot itself to speak (as much as me speak about it). (shrink)

This paper presents an analysis of face emoji (disc-shaped pictograms with stylized facial expressions) that accompany written text. We propose that there is a use of face emoji in which they comment on a target proposition expressed by the accompanying text, as opposed to making an independent contribution to discourse. Focusing on positively valenced and negatively valenced emoji (which we gloss as _happy_ and _unhappy_, respectively), we argue that the emoji comment on how the target proposition bears on a contextually (...) provided discourse value endorsed by the author. Discourse values embody what an author desires, aspires to, wishes for, or hopes for. Our analysis derives a range of non-trivial generalizations, including (i) ordering restrictions with regards to the placement of emoji and text, (ii) cases of apparent mixed emotions, and (iii) cases where the lexical content of the accompanying text influences the acceptability of a face emoji. (shrink)

In this paper, I argue that there is a picture of how law works that most legal theorists are implicitly committed to and take to be common ground. This Standard Picture (SP, for short) is generally unacknowledged and unargued for. SP leads to a characteristic set of concerns and problems and yields a distinctive way of thinking about how law is supposed to operate. I suggest that the issue of whether SP is correct is a fundamental one for the philosophy (...) of law, more basic, for example, than the issue that divides legal positivists and anti-positivists, at least as the latter issue is ordinarily understood. The goals of the paper are fourfold: 1) to identify and articulate in some detail the Standard Picture; 2) to show that SP is widely held and has important consequences for other debates in the philosophy of law; 3) to show that SP leads to a serious theoretical problem; 4) to sketch an alternative picture that promises to avoid this problem. I emphasize the modesty of these goals in one respect. I make no claim to refute SP or to fully develop and defend an alternative picture. (shrink)

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...) to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (shrink)

It has been suggested that a reporting channel administered by a third-party may represent a stronger procedural safeguard of anonymity and avoids the appearance of impropriety. This study examines whistleblowing intentions among lower-tier employees, specifically examines whether an externally-administered reporting channel increases whistleblowing intentions compared to an internally-administered one. In contrast to the findings of an earlier study by Kaplan et al. :273–288, 2009), our results suggest that whistle-blowing intentions are higher when the reporting channel is administered externally than when (...) it is administered internally. We also find that an externally-administered reporting channel mitigates the negative effect of bystanders on whistleblowing intentions. Implications are discussed. (shrink)

In this paper, I propose a new way of understanding the space of possibilities in the field of mental content. The resulting map assigns separate locations to theories of content that have generally been lumped together on the more traditional map. Conversely, it clusters together some theories of content that have typically been regarded as occupying opposite poles. I make my points concrete by developing a taxonomy of theories of mental content, but the main points of the paper concern not (...) merely how to classify, but how to understand, the theories. Also, though the paper takes theories of mental content as a case study, much of the discussion is applicable to theories of other phenomena. To a first approximation, the difference between the traditional and the proposed taxonomies turns on whether we classify theories of content by, on the one hand, their implications for a non-redundant supervenience base for content facts (i.e., for facts about what contents thoughts have) or, on the other, by their constitutive accounts of content. By a "constitutive account," I mean the kind of elucidation of the nature of a phenomenon that theorists have tried to give for, for example, knowledge, justice, personal identity, consciousness, convention, heat, and limit. The tendency to taxonomize by supervenience base is encouraged, I suggest, by a failure to keep clearly in view a distinction between constitutive and modal determination. Many philosophers would accept that a constitutive account cannot be captured in purely modal terms. Giving a constitutive account is not the same as specifying modally necessary and sufficient conditions. Nevertheless, philosophers often try to cash constitutive claims in modal terms. A case in point is that theories of content tend to be conceptualized in terms of the theories' implications for a supervenience base for content facts. My thesis goes beyond the by-now somewhat familiar proposition that not all modal determinants of a phenomenon are constitutive determinants. One who has taken that point on board might nevertheless conceive of a philosophical account as an attempt to specify constitutive determinants of the target phenomenon that make up a non-redundant supervenience base for the phenomenon. Shoehorning a philosophical account into this form leaves out elements that are modally redundant, but may be explanatorily or ontologically significant. For example, when a constitutive account has multiple levels, the different levels will typically be modally redundant. Formulating the account as a specification of a supervenience base of constitutive determinants will therefore flatten the account into a single level. Many of my arguments can be illustrated by considering the place of normativity in the theory of content. The new taxonomy gives a distinct niche to normative theories of content - theories that explain a thought's having a certain content at least in part in terms of the obtaining of normative facts. By contrast, on a traditional map, normative theories are invisible as such because normative facts supervene on non-normative ones. (shrink)

This paper deals with the exceptions-tolerance property of generic sentences with indefinite singular and bare plural subjects (IS and BP generics, respectively) and with the way this property is connected to some well-known observations about felicity differences between the two types of generics (e.g. Lawler's 1973, Madrigals are popular vs. #A madrigal is popular). I show that whereas both IS and BP generics tolerate exceptional and contextually irrelevant individuals and situations in a strikingly similar way, which indicates the existence of (...) a basically equivalent tolerance mechanism, there is also a difference between them, unnoticed so far, which concerns the degree to which the properties of the legitimate exceptions can be characterized in advance. Following claims in Greenberg (2003), I argue that both this newly observed difference as well as the traditional felicity differences result from an underlying contrast in the type of ‘non-accidentalness’ expressed by the two types of generic sentences, and more formally, in the accessibility relations that their generic quantifier (Gen) is compatible with. To capture the new difference in tolerance of exceptions, I develop an improved version of the exceptions-tolerance mechanism for generic sentences suggested in Kadmon & Landman (1993), namely, a restriction on the set of individuals and situations quantified by Gen, which is partially vague to two different degrees using supervaluationist methods. The different degrees of vagueness in this restriction are shown to be systematically dependent on the two types of accessibility relations that IS and BP generics are compatible with, which are redefined as precise and vague restrictions on the generic quantification over worlds. (shrink)

Music can reduce stress and anxiety, enhance positive mood, and facilitate social bonding. However, little is known about the role of music and related personal or cultural variables in maintaining wellbeing during times of stress and social isolation as imposed by the COVID-19 crisis. In an online questionnaire, administered in 11 countries, participants rated the relevance of wellbeing goals during the pandemic, and the effectiveness of different activities in obtaining these goals. Music was found to be the most effective activity (...) for three out of five wellbeing goals: enjoyment, venting negative emotions, and self-connection. For diversion, music was equally good as entertainment, while it was second best to create a sense of togetherness, after socialization. This result was evident across different countries and gender, with minor effects of age on specific goals, and a clear effect of the importance of music in people's lives. Cultural effects were generally small and surfaced mainly in the use of music to obtain a sense of togetherness. Interestingly, culture moderated the use of negatively valenced and nostalgic music for those higher in distress. (shrink)

Given the complexity of teams involved in creating AI-based systems, how can we understand who should be held accountable when they fail? This paper reports findings about accountable AI from 26 interviews conducted with stakeholders in AI drawn from the fields of AI research, law, and policy. Participants described the challenges presented by the distributed nature of how AI systems are designed, developed, deployed, and regulated. This distribution of agency, alongside existing mechanisms of accountability, responsibility, and liability, creates barriers for (...) effective accountable design. As agency is distributed across the socio-technical landscape of an AI system, users without deep knowledge of the operation of these systems become disempowered, unable to challenge or contest when it impacts their lives. In this context, accountability becomes a matter of building systems that can be challenged, interrogated, and, most importantly, adjusted in use to accommodate counter-intuitive results and unpredictable impacts. Thus, accountable system design can work to reconfigure socio-technical landscapes to protect the users of AI and to prevent unjust apportionment of risk. (shrink)

Ethical dilemmas in critical care may cause healthcare practitioners to experience moral distress: incoherence between what one believes to be best and what occurs. Given that paediatric decision-making typically involves parents, we propose that parents can also experience moral distress when faced with making value-laden decisions in the neonatal intensive care unit. We propose a new concept—that parents may experience “moral schism”—a genuine uncertainty regarding a value-based decision that is accompanied by emotional distress. Schism, unlike moral distress, is not caused (...) by barriers to making and executing a decision that is deemed to be best by the decision-makers but rather an encounter of significant internal struggle. We explore factors that appear to contribute to both moral distress and “moral schism” for parents: the degree of available support, a sense of coherence of the situation, and a sense of responsibility. We propose that moral schism is an underappreciated concept that needs to be explicated and may be more prevalent than moral distress when exploring decision-making experiences for parents. We also suggest actions of healthcare providers that may help minimize parental “moral schism” and moral distress. (shrink)

There are norms on action and norms on assertion. That is, there are things we should and shouldn't do, and things we should and shouldn't say. How do these two kinds of norm relate? Are norms on assertion reducible to norms on action? Many philosophers think they are not. These philosophers claim there is a sui generis norm specific to assertion, a norm which is also often claimed to be constitutive of assertion. Both claims, I argue, should be rejected. The (...) phenomenon claimed to support them – the intuitive wrongness of certain assertions – does not in fact support them. Because assertion is an action, the wrongness of assertions can be explained purely by norms on action. And the specifically epistemic wrongness an assertion norm is typically supposed to explain can be explained by an uncontroversial norm on action: one shouldn't act on epistemically faulty beliefs. No additional sui generis norm on assertion is needed. (shrink)

The prevailing interpretation of Kant’s _First Critique _in Anglo-American philosophy views his theory of a priori knowledge as basically a theory about the possibility of empirical knowledge, or the a priori conditions for that possibility. Instead, Robert Greenberg argues that Kant is more fundamentally concerned with the possibility of a priori knowledge—the very possibility of the possibility of empirical knowledge in the first place. Greenberg advances four central theses: the _Critique_ is primarily concerned about the possibility, or relation to objects, (...) of a priori_,_ not empirical knowledge, and Kant’s theory of that possibility is defensible; Kant’s transcendental ontology must be distinct from the conditions of the possibility of a priori knowledge; the functions of judgment, in Kant’s discussion of the Table of Judgments, should be seen according to his transcendental logic as having content, not as being just logical forms of judgment making; Kant’s distinction between and connection of ordering relations and reference relations have to be kept in mind to avoid misunderstanding the _Critique_. At every step of the way Greenberg contrasts his view with the major interpretations of Kant by commentators like Henry Allison, Jonathan Bennett, Paul Guyer, and Peter Strawson. Not only does this new approach to Kant present a strong challenge to these dominant interpretations, but by being more true to Kant’s own intent it holds promise for making better sense out of what have been seen as the _First Critique_’s discordant themes. (shrink)

The present article attempts to evaluate various tenets of moral philosophy by reviewing empirical data from the field of organizational justice bearing on: (a) people''s concerns about fairness in organizations, and (b) the consequences of following or not following rules of justice. With respect to concerns about fairness in organizations, utilitarian claims that people believe that fairness requires distributions of reward based on merit were assessed. Similarly, evidence was reviewed bearing on the claim of psychological egoists that judgments of fairness (...) reflect a self-interested bias. Finally, Kant''s view that people should never lie was evaluated in light of evidence describing people''s actual attitudes toward lying. In all three cases, the underlying philosophical premises were concluded to be overly simplistic in view of complexities about human nature revealed in empirical research. In addition, evidence was reviewed that shed light on the teleological claims of utilitarians regarding the purported benefits of following two common organizational practices — using merit-based pay, and punishing harmdoers. Here, too, the empirical evidence (findings that these techniques do not consistently yield the greatest good for the greatest number) suggests that the premise underlying utilitarian thought is based on unfounded, overly simplistic assumptions about the effects of following various allegedly moral ideas. It is concluded that our analyses provide a useful first step toward the desired goal of business ethicists of integrating prescriptive and descriptive approaches to justice. (shrink)

We seem to be responsible for our beliefs in a distinctively epistemic way. We often hold each other to account for the beliefs that we hold. We do this by criticising other believers as ‘gullible’ or ‘biased’, and by trying to persuade others to revise their beliefs. But responsibility for belief looks hard to understand because we seem to lack control over our beliefs. In this paper, I argue that we can make progress in our understanding of responsibility for belief (...) by thinking about it in parallel with another kind of responsibility: legal responsibility for criminal negligence. Specifically, I argue that that a popular account of responsibility for belief, which grounds it in belief’s reasons-responsiveness, faces a problem analogous to one faced by H.L.A. Hart’s influential capacity-based account of culpability. This points towards a more promising account of responsibility of belief, though, if we draw on accounts of negligence that improve on Hart’s. Broadly speaking, the account of negligence that improves on Hart’s account grounds culpability in a concern for others’ interests, whereas my account of epistemic responsibility grounds responsibility for belief in a concern for the truth. (shrink)

Tagging is the phenomenon in which regions of a picture, map, or diagram are annotated with words or other symbols, to provide descriptive information about a depicted object. The interpretive principles that govern tagged images are not well understood, due in part to the difficulty of integrating pictorial and linguistic semantic rules. Rather than directly combining these rules, I propose to use the framework of perspectival feature maps as an intermediary representation of content, in which the outputs of pictorial and (...) linguistic interpretation may be assimilated. The result is a simple and compositional semantics for tagged images. (shrink)

"Analytic philosophy has leveled many challenges to Kant's ascription of necessary properties and relations to objects in his Critique of Pure Reason. Some of these challenges can be answered, it is argued here, largely in terms of techniques belonging to analytic philosophy itself, in particular, to its philosophy of language. This Kantian response is the primary objective of this book. It takes the form of a compromise between the real existence of the objects that we can intuit and that get (...) our knowledge started - dubbed initiators - and the ideality of the necessary properties and relations that Kant ascribes to our sensible representations of initiators, which he entitles appearances. Whereas the real existence of initiators is independent of us and our senses, the necessity of these properties and relations of appearances is due to their origins in the mind."--BOOK JACKET. (shrink)

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

This paper concentrates on giving precise content to the general wisdom on the scalar presupposition of even, according to which the prejacent of even, p, is stronger than its relevant focus alternatives, q. To that end I first examine both familiar challenges for the popular ‘comparative likelihood’ view of the ‘stronger than’ relation, as well as novel challenges, having to do with the context dependency of even and with its sensitivity to standards of comparison. To overcome these challenges and to (...) account for the full range of data I develop a revised, ‘gradability-based’ scalar presupposition for even, which differs from the ‘comparative likelihood’ one in several respects: instead of directly comparing degrees to which propositions are more or less likely, we compare extents to which non-focus entities x in p and q exceed the salient standard on a scale associated with a contextually supplied gradable property G. To capture cases where information about contrastive topics is crucial for fixing two distinct standards on G, I follow theories which view even as a general, two-place alternative-sensitive operator, allowing it to associate with both focus and contrastive topics. Beyond the ability to account for a large range of intricate felicity variations and inferences found with even, a more general contribution of the paper lies in showing the linguistic relevance of tools originally developed in the literature on gradable predicates to the semantics of scalar alternative–sensitive particles. (shrink)

In this paper, I deploy an argument that I have developed in a number of recent papers in the service of three projects. First, I show that the most influential version of legal positivism – that associated with H.L.A. Hart – fails. The argument’s engine is a requirement that a constitutive account of legal facts must meet. According to this rational-relation requirement, it is not enough for a constitutive account of legal facts to specify non-legal facts that modally determine the (...) legal facts. The constitutive determinants of legal facts must provide reasons for the obtaining of the legal facts (in a sense of “reason” that I develop). I show that the Hartian account is unable to meet this requirement. That officials accept a rule of recognition does not by itself constitute a reason why the standards specified in that rule are part of the law of the community. I argue that it is false that understanding the explanatory significance of officials’ acceptance of a rule is part of our reflective understanding of the nature of law. The second project of the paper is to respond to a family of objections that challenge me to explain why normative facts and descriptive facts together are better placed to provide reasons for legal facts than descriptive facts alone. A unifying theme of the objections is that explanations have to stop somewhere; descriptive facts, it is suggested, are no worse a stopping place than normative facts. Third, the paper spells out a consequence of the rational-relation requirement: if an account of what, at the most basic level, determines legal facts is true in any possible legal system, it is true in all possible legal systems. For example, if a Hartian account of legal facts is true in any possible legal system, it is true in all possible legal systems. I use this all-or-nothing result in my critique of a Hartian account, but the result is of interest in its own right. (shrink)

We show that the class of strongly jump-traceable c.e. sets can be characterised as those which have sufficiently slow enumerations so they obey a class of well-behaved cost functions, called benign. This characterisation implies the containment of the class of strongly jump-traceable c.e. Turing degrees in a number of lowness classes, in particular the classes of the degrees which lie below incomplete random degrees, indeed all LR-hard random degrees, and all ω-c.e. random degrees. The last result implies recent results of (...) Diamondstone's and Ng's regarding cupping with superlow c.e. degrees and thus gives a use of algorithmic randomness in the study of the c.e. Turing degrees. (shrink)

This book, first published in 1991, offers an integrative approach to the study of formal models in the social and behavioural sciences. The theory presented here unifies both the representation of the social environment and the equilibrium concept. The theory requires that all alternatives that are available to the players be specified in an explicit and detailed manner, and this specification is defined as a social 'situation'. A situation, therefore, not only consists of the alternatives currently available to the players, (...) but also includes the set of opportunities that might be induced by the players from their current environment. The theory requires that all recommended alternatives be both internally and externally stable; the recommendation cannot be self-defeating and, at the same time, should account for alternatives that were not recommended. In addition to unifying the representation and the solution concept, the theory also extends the social environments accommodated by current game theory. (shrink)

We define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it distinguishes between whether the simplest Scott sentence is $\Sigma _{\alpha }$, $\Pi _{\alpha }$, or $\mathrm {d-}\Sigma _{\alpha }$. We give a complete classification of the possible Scott complexities, including an example of a structure whose simplest Scott sentence is $\Sigma _{\lambda + 1}$ for $\lambda $ a limit (...) ordinal. This answers a question left open by A. Miller.We also construct examples of computable structures of high Scott rank with Scott complexities $\Sigma _{\omega _1^{CK}+1}$ and $\mathrm {d-}\Sigma _{\omega _1^{CK}+1}$. There are three other possible Scott complexities for a computable structure of high Scott rank: $\Pi _{\omega _1^{CK}}$, $\Pi _{\omega _1^{CK}+1}$, $\Sigma _{\omega _1^{CK}+1}$. Examples of these were already known. Our examples are computable structures of Scott rank $\omega _1^{CK}+1$ which, after naming finitely many constants, have Scott rank $\omega _1^{CK}$. The existence of such structures was an open question. (shrink)

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. (...) We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (shrink)

Tyler Burge’s influential arguments have convinced most philosophers that a thinker can have a thought involving a particular concept without fully grasping or having mastery of that concept. In Burge’s (1979) famous example, a thinker who lacks mastery of the concept of arthritis nonetheless has thoughts involving that concept. It is generally supposed, however, that this phenomenon – incomplete understanding, for short – does not require us to reconsider in a fundamental way what it is for a thought to involve (...) a particular concept. In this paper, I argue that the real significance of incomplete understanding has not been appreciated. To the extent that theorists of content address the phenomenon of thoughts involving incompletely grasped contents at all, they tend to assume that some hand-waving about deference to other thinkers who fully grasp the relevant concepts will take care of the inconvenient cases of incomplete understanding. The main lesson of Burge’s arguments is often taken to be that the content of language and thought is socially determined. On this picture, we do not need to change our basic view about what it is to have a concept; we just need to recognize that some thinkers can manage to have a concept by piggybacking on others. In contrast, on the view I defend, taking incomplete understanding seriously forces us to rethink some of our most basic assumptions about the nature of mental content. Deference is a red herring. The role of society in determining the content of thought is not the main lesson, but at most a useful clue as to the nature of mental and linguistic content. (shrink)

Thanks to his unsurpassed eye and his fearless willingness to take a stand, Clement Greenberg (1909 1994) became one of the giants of 20th century art criticism a writer who set the terms of critical discourse from the moment he burst onto the scene with his seminal essays Avant Garde and Kitsch (1939) and Towards a Newer Laocoon (1940). In this work, which gathers previously uncollected essays and a series of seminars delivered at Bennington in 1971, Greenberg provides his most (...) expansive statement of his views on taste and quality in art, arguing for an esthetic that flies in the face of current art world fashions. Greenberg insists despite the attempts from Marcel Duchamp onwards to escape the jurisdiction of taste by producing an art so disjunctive that it cannot be judged that taste is inexorable. He argues that standards of quality in art, the artist's responsibility to seek out the hardest demands of a medium, and the critic's responsibility to discriminate, are essential conditions for great art. The obsession with innovation the epidemic of newness leads, in Greenbergs view, to the boringness of so much avant garde art. He discusses the interplay of expectation and surprise in aesthetic experience, and the exalted consciousness produced by great art. Homemade Esthetics allows us particularly in the transcribed seminar sessions, never before published to watch the critics mind at work, defending (and at times reconsidering) his theories. His views, often controversial, are the record of a lifetime of looking at and thinking about art as intensely as anyone ever has. (shrink)

EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of${\rm{\Delta }}_2^0$functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)