The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation (...) in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

In a recent paper, Montagna proved the undecidability of the first-order theory of diagonalisable algebras. This result is here refined — the set of finitely refutable sentences is shown effectively inseparable from the set of theorems. The proof is quite simple.

(No abstract is available for this citation).

The counterfactual mental state of negligent criminal activity invites skepticism from those who see mental states as essential to responsibility. Here, I offer a revision of the mental state of criminal negligence, one where the mental state at issue is actual and not merely counterfactual. This revision dissolves the worry raised by the skeptic and helps to explain negligence’s comparatively reduced culpability.

In On What Matters, Derek Parfit enters the debate between actualists and possibilists. This debate concerns mere possibilia, possible but non-actual things such as golden mountains and talking donkeys. Roughly, possibilism says that there are such things, and actualism says that there are not. Parfit not only argues for possibilism but also argues that some self-proclaimed actualists are, in fact, unwitting possibilists. -/- I argue that although Parfit’s arguments do not fully succeed, they do highlight a tension within the frameworks (...) of many actualists. Many actualists conscript abstract objects into the role of "possible worlds" to avoid quantifying over mere possibilia. But, in doing so, actualists must quantify over mere possibilia anyway. When we alleviate this tension, a Parfit-friendly form of actualism arguably remains. This form of actualism says that while everything that exists is actual, it is also true in some sense that there are mere possibilia. (shrink)

In common treatments of deontic logic, the obligatory is what is true in all deontically ideal possible worlds. In this article, I offer a new semantics for Standard Deontic Logic with Leibnizian intensions rather than possible worlds. Even though the new semantics furnishes models that resemble Venn diagrams, the semantics captures the strong soundness and completeness of Standard Deontic Logic. Since, unlike possible worlds, many Leibnizian intensions are not maximally consistent entities, we can amend the semantics to invalidate the inference (...) rule which ensures that all tautologies are obligatory. I sketch this amended semantics to show how it invalidates the rule in a new way. (shrink)

Various strands of religious thought distinguish veneration from worship. According to these traditions, believers ought to worship God alone. To worship anything else, they say, is idolatry. And yet many of these same believers also claim to venerate—but not worship—saints, angels, images, relics, tombs, and even each other. But what's the difference? Tim Bayne and Yujin Nagasawa (2006: 302) are correct that “it seems to be extremely difficult to distinguish veneration from worship.” Many have argued throughout history that veneration collapses (...) into worship and that those who venerate saints or icons are guilty of idolatry. In this essay, we distinguish worship from veneration in two stages. First, we give a formal account of their difference. Drawing from St. John of Damascus (c. 675-749 AD), we argue that worship is a determinate of the determinable veneration. Second, we give more substantive accounts of both that explain their differences and similarities. Drawing again from St John, we argue that acts of veneration and worship signify subordination. Their difference, however, lies in the fact that worship alone requires absolute subordination. (shrink)

A framework for pragmatic analysis is proposed which treats discourse as a game, with context as a scoreboard organized around the questions under discussion by the interlocutors. The framework is intended to be coordinated with a dynamic compositional semantics. Accordingly, the context of utterance is modeled as a tuple of different types of information, and the questions therein — modeled, as is usual in formal semantics, as alternative sets of propositions — constrain the felicitous flow of discourse. A requirement of (...) Relevance is satisfied by an utterance (whether an assertion, a question or a suggestion) iff it addresses the question under discussion. Finally, it is argued that the prosodic focus of an utterance canonically serves to reflect the question under discussion (at least in English), placing additional constraints on felicity in context. (shrink)

We can enrich the explanation of how we should treat kid wrongdoers by recognizing that it matters who does the blaming and punishing. That we should think about who does the blaming and punishing is perhaps unsurprising, but it is nonetheless often underappreciated. Here, I offer two lessons about blame and punishment by thinking about who judges kids. First, the right account of moral and legal responsibility should allow that kids may rightly blame each other, and I argue that we (...) can best accommodate this by relativizing the threshold of competence needed for responsibility. Second, although each kid is an individual and, as a result, the implications of immaturity vary signifi- cantly from kid to kid, we should give kids a break as kids, that is, based on our categorizing them as kids. That we should and do categorize in that way reflects the nature of the criminal justice system as an institution and the nature of us as social beings. (shrink)

This paper attempts to show how Adorno’s thought can illuminate our reflections on the future of work. It does so by situating Adorno’s conception of genuine activity in relation to his negativist critical epistemology and his subtle account of the distinction between true and false needs. What emerges is an understanding of work that can guide our aspirations for the future of work, and one we illustrate via discussions of creative work and care work. These are types of work which (...) cater to persistent human needs, albeit ones that are distorted under present social conditions. Adorno’s thought helps us to understand why this is the case. (shrink)

Many contemporary theorists charge that naïve realists are incapable of accounting for illusions. Various sophisticated proposals have been ventured to meet this charge. Here, we take a different approach and dispute whether the naïve realist owes any distinctive account of illusion. To this end, we begin with a simple, naïve account of veridical perception. We then examine the case that this account cannot be extended to illusions. By reconstructing an explicit version of this argument, we show that it depends critically (...) on the contention that perceptual experience is diaphanous, or more minimally and precisely, that there can be no difference in phenomenal properties between two experiences without a difference in the scenes presented in those experiences. Finding no good reason to accept this claim, we develop and defend a simple, naïve account of both veridical perception and illusion, here dubbed Simple, Austere Naïve Realism. (shrink)

Justification for psychiatric paternalism is most easily established where mental illness renders the person mentally incompetent, depriving him of the capacity for rational agency and for autonomy, hence undermining the basis for liberal rights against paternalism. But some philosophers, and no doubt some doctors, have been deeply concerned by the inadequacy of the concept of mental incompetence to encapsulate some apparently appealing cases for psychiatric paternalism. We ought to view mental incompetence as just one subset of a broader justification for (...) psychiatric paternalism. The very basis of liberal limitations on psychiatric paternalism, whether described in terms of rights to autonomy or as respect for differences in values and lifestyles, presupposes a sense of moral persistence, and hence some sufficiently persistent self. Paternalistic intervention is warranted when we are unable to govern our lives in a manner consistent with the goals and values that comprise that ‘self’. One way that can occur is when we lack the mental capacities required for autonomy, such that we are unable to interpret and interact with our environment in order to meaningfully pursue our goals, i.e. mental incompetence. But it can also occur when we are subject to impositions that alter our goals without altering our capacity to pursue them — i.e. when it is our ‘self’ that is impaired rather than our competence. (shrink)

How can we talk meaningfully about the past if it does not exist to be talked about? What gives time its direction? Is time travel possible? This defence of presentism - the view that only the present exists - makes an original contribution to a fast growing and exciting debate.

This study examines the presence and roles of female directors of U.S. Fortune 500 firms, focusing on committee assignments and director background. Prior work from almost two decades ago concludes that there is a systematic bias against females in assignment to top board committees. Examining a recent data set with a logistic regression model that controls for director and firm characteristics, director resource-dependence roles and interaction between director gender and director characteristics, we find that female directors are less likely than (...) male directors to sit on executive committees and more likely than male directors to sit on public affairs committees. There is little if any evidence of systematic gender bias in director assignment to other board committees. We find some evidence that boards evaluate resource dependence differently for women than men. (shrink)

How can we talk meaningfully about the past if it does not exist to be talked about? What gives time its direction? Is time travel possible? This defence of presentism - the view that only the present exists - makes an original contribution to a fast growing and exciting debate.

In order to determine whether a particular course of conduct is ethically permissible it is important to have a concept of what it means to be harmed. The dominant theory of harm is the counterfactual account, most famously proposed by Joel Feinberg. This determines whether harm is caused by comparing what actually happened in a given situation with the ‘counterfacts’ i.e. what would have occurred had the putatively harmful conduct not taken place. If a person's interests are worse off than (...) they otherwise would have been, then a person will be harmed. This definition has recently faced challenges from bioethicists such as John Harris, Guy Kahane and Julian Savulescu who, believing it to be severely flawed, have proposed their own alternative theories of the concept. In this article I will demonstrate that the shortcomings Harris, Kahane and Savulescu believe are present in Feinberg's theory are illusory and that it is their own accounts of harm that are fraught with logical errors. I maintain that the arguments presented to refute Feinberg's theory not only fail to achieve this goal and can be accommodated within the counterfactual account but that they actually undermine the theories presented by their respective authors. The final conclusion will be that these challenges are misconceived and fail to displace the counterfactual theory. (shrink)

This paper aims to demonstrate the contemporary relevance of Adorno’s thought for business ethicists working in the critical tradition by showing how his critique of modern social life anticipated, and ofers continuing illumination of, recent technological transformations of capitalism. It develops and extrapolates Adorno’s thought regarding three central spheres of modern society, which have seen radical changes in light of recent technological developments: work, in which employee monitoring has become ever more sophisticated and intrusive; leisure consumption, in which the algorithmic (...) developments of the culture industry have paved the way for entertainment products to dominate us; and political discourse, in which social media has exacerbated the anti-democratic tendencies Adorno warned of in the mid-twentieth century. We conclude by presenting, as a rejoinder to these developments, the contours of an Adornian ethics of resistance to the reifcation and dehumanisation of such developments. (shrink)

Many want to know what bitcoin is and how it works. But bitcoin is as complex as it is controversial, and relatively few have the technical background to understand it. In this paper, I offer an accessible on-ramp for understanding bitcoin in the form of a model. My model reveals both what bitcoin is and how it works. More specifically, it reveals that bitcoin is a fictional substance in a massively coauthored story on a network that automates and distributes jobs (...) normally entrusted to centralized publishing institutions. My model therefore falsifies a popular view according to which each bitcoin is a chunk of code. (shrink)

Digital medicine is a medical treatment that combines technology with drug delivery. The promises of this combination are continuous and remote monitoring, better disease management, self-tracking, self-management of diseases, and improved treatment adherence. These devices pose ethical challenges for patients, providers, and the social practice of medicine. For patients, having both informed consent and a user agreement raises questions of understanding for autonomy and informed consent, therapeutic misconception, external influences on decision making, confidentiality and privacy, and device dependability. For providers, (...) digital medicine changes the relationship where trust can be verified, clinicians can be monitored, expectations must be managed, and new liability risks may be assumed. Other ethical questions include direct third-party monitoring of health treatment, affordability, and planning for adverse events in the case of device malfunction. This article seeks to lay out the ethical landscape for the implementation of such devices in patient care. (shrink)

As a graduate student in Linguistics at UMass/Amherst in the 1980s, I was fortunate to be exposed to a number of new developments bearing on the relationship between formal semantics and pragmatics. In the 1970s under the influence of Cresswell, Lewis, Montague, and Partee, enormous progress in semantics was made possible by narrowing the focus of the field mainly to the consideration of the conventional, truth conditional content of an indicative utterance, calculated compositionally as a function of the semantic contributions (...) of its parts and its syntactic structure. Context was typically relegated to the background, in the form of indices of evaluation, though occasionally popping out for more serious consideration, as in the work of Kaplan, Karttunen, and Stalnaker. But eventually the nature of the rigorous formal enterprise itself, confronted with phenomena like Geach’s donkey sentences, presupposition projection, and the context-dependence of tense and aspect, forced the field into a more careful, thorough reconsideration of the relationship between context and content. Hence were born the dynamic theories of interpretation, beginning with Hans Kamp (1981) and Irene Heim (1982), who were both at UMass during my stay there, Heim completing her dissertation and Kamp on the faculty in Philosophy. Such frameworks posit a dynamic interchange between content and context, each dependent on the other, even in the course of interpreting a single utterance. Mats Rooth was also a graduate student at UMass at that time, and wrote his influential dissertation (1985) proposing an alternative semantics for the interpretation of prosodic focus, inter alia shedding light on how focus contributes to the contextual domain restriction of various operators. (shrink)