There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.

ABSTRACT:There is considerable overlap between the interests of business ethicists and those of political philosophers. Questions about the moral justifiability of the capitalist system, the basis of property rights, and the problem of inequality in the distribution of income have been of central importance in both fields. However, political philosophers have developed, especially over the past four decades, a set of tools and concepts for addressing these questions that are in many ways quite distinctive. Most business ethicists, on the other (...) hand, consider their field to be primarily a domain of applied ethics, and so adopt methods and conceptual frameworks developed by moral philosophers. In this paper, we discuss some of the salient differences between these two approaches, and suggest some ways in which business ethicists could benefit from taking a more “political philosophy” approach to these questions. Throughout, we underline the importance of seeking greater compatibility among the principles used in normative theorizing about markets, regulations, corporate governance, and business practices. (shrink)

α-recursion lifts classical recursion theory from the first transfinite ordinal ω to an arbitrary admissible ordinal α [10]. Idealized computational models for α-recursion analogous to Turing machine models for classical recursion have been proposed and studied [4] and [5] and are applicable in computational approaches to the foundations of logic and mathematics [8]. They also provide a natural setting for modeling extensions of the algorithmic logic described in [1] and [2]. On such models, an α-Turing machine can complete a θ-step (...) computation for any ordinal θ < α. Here we consider constraints on the physical realization of α-Turing machines that arise from the structure of physical spacetime. In particular, we show that an α-Turing machine is realizable in a spacetime constructed from R only if α is countable. While there are spacetimes where uncountable computations are possible and while they may even be empirically distinguishable from a standard spacetime, there is good reason to suppose that such nonstandard spacetimes are nonphysical. We conclude with a suggestion for a revision of Church’s thesis appropriate as an upper bound for physical computation. (shrink)

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves (...) one no choice but to restrict the use of a certain class of implicational rules including modus ponens. (shrink)

There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. (...) As shown in [1], the threat of paradoxes, such as the Curry paradox, requires care in implementing rules of inference in this context. As in any type-free logic, some traditional rules will fail. The first part of the paper develops a rich collection of inference rules that do not lead to paradox. The second part identifies traditional rules of logic that are paradoxical in algorithmic logic, and so should be viewed with suspicion in type-free logic generally. (shrink)

In this note, we consider constraints on the physical possibility of transfinite Turing machines that arise from how one models the continuous structure of space and time in one's best physical theories. We conclude by suggesting a version of Church's thesis appropriate as an upper bound for physical computation given how space and time are modeled on our current physical theories.

Bidirectional deep brain stimulation (DBS) platforms have enabled a surge in hours of recordings in naturalistic environments, allowing further insight into neurological and psychiatric disease states. However, high amplitude, high frequency stimulation generates artifacts that contaminate neural signals and hinder our ability to interpret the data. This is especially true in psychiatric disorders, for which high amplitude stimulation is commonly applied to deep brain structures where the native neural activity is miniscule in comparison. Here, we characterized artifact sources in recordings (...) from a bidirectional DBS platform, the Medtronic Summit RC + S, with the goal of optimizing recording configurations to improve signal to noise ratio (SNR). Data were collected from three subjects in a clinical trial of DBS for obsessive-compulsive disorder. Stimulation was provided bilaterally to the ventral capsule/ventral striatum (VC/VS) using two independent implantable neurostimulators. We first manipulated DBS amplitude within safe limits (2–5.3 mA) to characterize the impact of stimulation artifacts on neural recordings. We found that high amplitude stimulation produces slew overflow, defined as exceeding the rate of change that the analog to digital converter can accurately measure. Overflow led to expanded spectral distortion of the stimulation artifact, with a six fold increase in the bandwidth of the 150.6 Hz stimulation artifact from 147–153 to 140–180 Hz. By increasing sense blank values during high amplitude stimulation, we reduced overflow by as much as 30% and improved artifact distortion, reducing the bandwidth from 140–180 Hz artifact to 147–153 Hz. We also identified artifacts that shifted in frequency through modulation of telemetry parameters. We found that telemetry ratio changes led to predictable shifts in the center-frequencies of the associated artifacts, allowing us to proactively shift the artifacts outside of our frequency range of interest. Overall, the artifact characterization methods and results described here enable increased data interpretability and unconstrained biomarker exploration using data collected from bidirectional DBS devices. (shrink)

This essay forms part of an “elegiac symposium” on “what gets lost during paradigm shifts,” and it replies to an earlier contribution to that symposium, “Regarding Change at Ise-Jingu” by Jeffrey M. Perl (14, no. 2 [2008]: 208-20; DOI 10.1215/0961754X-2007-069]) . Andersen argues against or supplements Perl's contention that Japanese attitudes toward change differ radically from those that are standard in the West. Andersen expands on arguments made by Roland Barthes—an explicator and partisan of Japanese thought—to show that at (...) least one Greek myth (that of the unchanging ship Argo) deals with change, originality, updating, fakes, and replication in a way similar to those standard in Japanese culture. Andersen then pursues his argument, as well, with respect to works by Rodin, Sade, and Leonardo da Vinci. (shrink)

In this introduction to part three of the Common Knowledge symposium “Fuzzy Studies: On the Consequence of Blur,” the journal’s editor argues that blur is not a medium of concealment, confusion, or evasion. Making distinctions between kinds of relative unclarity, he reserves the word blur for the kind that results from de-differentiating objects or qualities or states of affairs whose differences have been overstated. To refine what blur is and is not, he compares kinds of unclarity found in images by (...) Giotto, Rubens, Hokusai, Kunitora, Manet, Zeshin, and Richter. With reference to art criticism by Hubert Damisch, Wayne Andersen, Anthony Hughes, Robert Storr, Julian Bell, Christopher Prendergast, and especially T. J. Clark, he agrees that choosing between focus and blur can be a moral decision, though not in the sense for which Clark arraigns the Impressionists. Characterizing the way of seeing that Clark encourages in The Painting of Modern Life as a form of staring, this essay argues that “lean and hungry looking” is indecent, whereas unfocused receptivity is irenic. What Bell calls the “aestheticized halfheartedness” of Manet is redescribed here as a genre of moral heroism, and the essay concludes that it is differentiation that is on morally shaky ground. (shrink)

Jeffrey Stout's "Democracy and Tradition" puts forward a complex argument in favor of American democracy as a healthy and legitimate moral and political tradition in itself. Stout does not dwell on the place of his own work in the "pragmatic" approach to the study of religion in the last thirty years. This paper attempts to situate Stout's work in the approach to religion identified with Mary Douglas and Wayne Proudfoot and to suggest some of the consequences for comparative (...) religious ethics of his making that "pragmatic turn.". (shrink)

Lewis signaling games illustrate how language might evolve from random behavior. The probability of evolving an optimal signaling language is, in part, a function of what learning strategy the agents use. Here we investigate three learning strategies, each of which allows agents to forget old experience. In each case, we find that forgetting increases the probability of evolving an optimal language. It does this by making it less likely that past partial success will continue to reinforce suboptimal practice. The learning (...) strategies considered here show how forgetting past experience can promote learning in the context of games with suboptimal equilibria. (shrink)

Horn (1989) identified a number of irregular or marked negations that are not used in accordance with the standard rule of propositional logic. He concluded that negation was pragmatically ambiguous. Van der Sandt (1991) disputed Horn’s ambiguity claim, and proposed a uniform semantics for all negations. I will provide an informal explanation of van der Sandt’s theory, and develop a number of objections. I show that irregular negations are not anaphoric, as Van der Sandt believes, but compositional. I argue for (...) Geurts’s (1998) view that there are several different rules for irregular negations. I reject the implicature theory in favor of the semantic ambiguity thesis. (shrink)

ABSTRACT Sexting has become a prominent part of adolescent culture. Under current laws, adolescents caught sexting are being arrested, facing child pornography charges, and having to register as sex offenders. State laws on child pornography and child abuse differ throughout the United States and conflict with federal laws, making the ethical obligations for psychologists unclear. The purpose of this article is to promote awareness about legal obligations regarding adolescent sexting, address the ethical dilemma that psychologists face when adolescent sexting is (...) disclosed during psychological treatment, and to provide implications and recommendations for psychologists. (shrink)

This chapter considers two types of fine‐tuning, those dealing with the initial conditions of the universe and those based on fixed parameters. Three approaches have been taken to argue that fine‐tuning does not need any special explanation. The first is an appeal to coincidence. The second is that the data are biased by our own observations. The third has to do with the nature of probability itself. The chapter assesses each of these objections in detail. Many naturalistic explanations have been (...) offered for fine‐tuning. The chapter considers the three most important ones. The first is that future discoveries might show that fine‐tuning was not improbable after all. The second is that other life‐permitting ranges for the fine‐tuned constants (FTCs) might exist, allowing for exotic forms of life unlike ours. The third is that we might live in a multiverse of many different universes all with different values of FTCs. (shrink)

We consider the efficacy of various forms of reinforcement learning with punishment in evolving linguistic conventions in the context of Lewis-Skyrms signalling games. We show that the learning strategy of reinforcement with iterative punishment is highly effective at evolving optimal conventions in even complex signalling games. It is also robust and can be easily extended to a self-tuning variety of reinforcement learning. We briefly discuss some of the virtues of reinforcement with iterative punishment and how it may be related to (...) learning in nature. (shrink)

This paper articulates Epictetus's moral epistemology. The argument of the paper is that the famous Stoic "art of living" is best thought of as a science or kind of knowledge, and that, in his conception of knowledge, Epictetus is an orthodox Stoic, upholding the main tenets of Stoic epistemology. Thus, what exactly the art of living is and how it can be acquired can be better understood by understanding Stoic epistemology.

The semantic fluency task is commonly used as a measure of one’s ability to retrieve semantic concepts. While performance is typically scored by counting the total number of responses, the ordering of responses can be used to estimate how individuals or groups organize semantic concepts within a category. I provide an overview of this methodology, using Alzheimer’s disease as a case study for how the approach can help advance theoretical questions about the nature of semantic representation. However, many open questions (...) surrounding the validity and reliability of this approach remain unresolved. (shrink)

Sayyid Qutb and Fethullah Gülen are two of the most important Muslim leaders and intellectuals of the twentieth century: the two are similar not only for their focus on the relationship between Islam and politics, but also for their lifelong commitments to education. For both Qutb and Gülen, schools were a means through which society itself could be made more just and, ultimately, more Islamic, and for both, their philosophy of education and broader political projects were at once pragmatic and (...) implicitly and explicitly for Qutb contrasted with American pragmatism. Their differing pedagogies are illustrative of their larger visions: for Qutb, Muslim education must be a “total world” in which Islam is protected from secular contagion, while for Gülen, Muslim education can move more slowly through largely secular means. For Gülen, Islam can work outside of and within a secular system; for Qutb, the system must be changed. (shrink)

This article examines the way in which selfhood is constructed in direct-to-consumer advertisements for antidepressant medications. The sample consists of advertisements that appeared in nine popular magazines between 1997 and 2005, television commercials that ran between 2003 and 2005, and online promotional Web sites. The analysis is divided into three sections. First, it is argued that the ads rely on metaphors of communication, information exchange, and plenitude to construct a relationship between biology and selfhood. Second, in offering the choice for (...) antidepressant treatment, the ads grant individuals a new capacity for the exercise of personal agency. Third, the author describes antidepressants as pills that perform a narrative “magic.” In contrast to religious and psychoanalytic narratives that required individuals to incorporate disavowed elements of their selves into an ongoing life narrative, antidepressants are medications that allow individuals to put aside, or jump over, inexplicable and painful moments in their life. (shrink)

Abstract: C. S. Peirce's psychological analysis of belief, doubt, and inquiry provides insights into the nature of scientific knowledge. These in turn can be used to construct an account of scientific knowledge where the notions of belief, truth, rational justification, and inquiry are determined by the relationships that must hold between these notions. I will describe this account of scientific knowledge and some of the problems it faces. I will also describe the close relationship between pragmatic and naturalized accounts of (...) scientific knowledge. (shrink)

This article aims to provide an account of self-reflexivity through recent debates that pertain to thinking about contemporary network culture. It focuses on the shifts from the mechanistic to the organic, and then towards the post-organic, pertaining particularly to current debates around an understanding of systems and structures. Although it employs a wide variety of disciplines, ranging from philosophy to mathematics, this article traces the lineage from modern art towards thinking about systems. This work is part of an ongoing research (...) objective that is directed towards practice-based research, particularly aimed at art practice that seeks to intersect with emerging network thinking and culture. One of the intentions of this article is to consider the account of self-reflexivity towards the implication of a ‘system as the medium’ in contemporary art practice, which is found in the writing of Francis Halsall. The research is part of an agenda that seeks to explore the conditions of production in contemporary culture, as a supplement to practice-based research. This article frames the debates around self-reflexivity through the chapter entitled ‘Strange loops’ by Mark C. Taylor, which is found in his book The Moment of Complexity: Emerging Network Culture (2001). It traces the lineage that Francis Halsall provides in his book Systems of Art: Art, History and Systems Theory (2008), and seeks to provide an account of self-reflexivity towards his consideration of the system as medium, found in the chapter entitled ‘Systems aesthetics and the system as medium’. In this chapter, Halsall provides an inclusive account of the medium that arguably covers the extent of contemporary art practices, through his contribution to system aesthetics. The account of self-reflexivity introduced in this article follows a parallel pathway to some of the major points in Halsall’s development of the system as medium. These include the ontologically stable modernist art object; the impact of cybernetics and information theory on art practice and discourse; and art that seeks to intersect with the environment. (shrink)

The presentation of these two projects the metaLAB (at) Harvard complements Jeffrey Schnapp's interview published in the section Perspectives of this issue of Humanist Studies and the Digital Age. The first project, A Flitting Atlas of the Human Gaze, performs an art historical experiment. The second project, Their Names, is an online Denkmal or monument that visualizes the names of 28,000+ fatal encounters with American police dating from the year 2000 up until the death of George Floyd on May (...) 25, 2020. (shrink)

Lots of contextually sensitive expressions appear to have context invariant meanings that do not by themselves suffice to secure semantic values for those expressions in context. For example, suppose I say 1. She is smart. where I do not demonstrate any female, I don’t intend that some female is the semantic value of my use of ‘she’, no female is uniquely salient in the context of utterance, and no female has been under discussion. It would appear in such a case (...) that the context invariant meaning of ‘she’ does not secure a semantic value in context for my use of ‘she’, resulting in infelicity. After all, what would that semantic value in context be? This appears to show that the context invariant meaning of ‘she’ does not by itself secure semantic values in context for it. The class of expressions that are like ‘she’ in this respect is quite large. It arguably includes simple and complex demonstratives, tense, expressions taking implicit arguments, gradable adjectives, quantifiers, ‘only’, possessives, conditionals, modals and more. I call these expressions supplementives to highlight the fact that their context invariant meanings need to be supplemented in context for them to secure semantic values in context. I claim that supplementives differ from each other in the following two ways: 1. The degree to which normal speakers are explicitly aware that the expression is contextually sensitive. 2. The degree to which ordinary speakers are explicitly aware of what sort of semantic value in context the expression takes. I hold the view that semantic values in context for supplementives are fixed by recognizable speaker intentions. However, I argue that given the differences between supplementives with respect to 1 and 2, the intentions fixing the semantic values in context of supplementives that differ with respect to 1 and 2 will themselves be different, while still all being speaker intentions that some entity o be the semantic value of the use of the supplementive in context. (shrink)

In this case study, I address the procedural ethics of conversation analysis (CA) and the collection of naturally occurring mundane interactions. I draw from the challenges that emerged from the institutional ethics review of the HIV, health and interaction study (the H2I Study), a CA project that sought to identify the practices through which normative assumptions of HIV and other health conditions are produced in conversations. Consistent with CA’s preference for naturally occurring interactions, the H2I Study collected and analysed everyday (...) telephone calls involving people living with HIV. This article offers practical strategies CA researchers might use to navigate two ethical concerns raised about the collection of naturally occurring mundane interactions. The first questions the merits of collecting naturally occurring mundane interactions. For those unfamiliar with CA, the specific advantages of analysing naturally occurring mundane interactions may not be self-evident. This places an evidentiary burden on CA researchers to warrant the collection of this type of data. To address this concern, I suggest demonstrating in ethics applications the analytic value of CA using publicly available interactions. The second concern questions the use of verbal consent necessary for the collection of naturally occurring mundane interactions. Like most CA research, the H2I Study required flexible informed consent protocols appropriate for spontaneous and unpredictable interactions. Drawing from within and outside the CA literature, I offer three rationales for the use of verbal consent. This article is written as a practical resource for conversation analysts seeking approval from their research ethics board (REB) and for REBs who might be unfamiliar with CA research. This article contributes to a small but growing body of literature that documents not only the kinds of challenges CA researchers encounter from institutional ethics review, but the specific procedural ethics they may employ to secure ethics approval. (shrink)

It is Heidegger who asks what there is to be thought after the end of metaphysics, and indeed his own work is never far from a response to the question. This is neither to say that there is only one such response, nor even to suppose that Heidegger’s thinking provides only one response. To be sure, the origin of the question is not difficult to identify. Metaphysics, as the grounding of known beings in some anterior or first being, comes to (...) its end as thinking becomes capable of grasping it as a sum of relations. This occurs when thinking is awakened to the difference between inquiring about beings , including the first being, and asking the question of the meaning of Being . In an important sense, then, the “end” of metaphysics coincides with the appearing of its place within a more primordial horizon. Attending more closely to the historical configuration of this metaphysics, Heidegger often concentrates on the recurrence, or else the persistence, of an urge in thinkin .. (shrink)

An examination of the salient literature on hospital clinical directorates (CDs) is presented. A critique of the largely managerialist, instrumental, hortatory and normative extant literature about CDs is offered. In analysing the literature this way the earlier promotional and critical literature is eschewed in favour of an evaluative approach. CDs are then reconceptualised by locating them within two overarching accounts of social structure—formalised, prescribed frameworks, and enacted, patterned interactions—following the kinds of distinctions made by Giddens, Weick, social action and institutional (...) theorists. Social structure as it relates to culture is also considered, following Martin. Such an approach facilitates an understanding of the general weaknesses of health service perspectives and methods of analysis, and exposes the strengths of Giddens–Weick type paradigms. (shrink)