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.

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.

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)

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)

I focus on problems defining skill and a core theoretical dispute over whether skilled action is largely automatic or consciously controlled. The dominant view in philosophy and psychology has been that skills are automatic, but an emerging body of work suggests that conscious cognition plays a significant role.

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)

The theme of this book is the complex moral psychology of forgiving and remembering in both personal and political contexts. It offers an original account of the moral psychology of interpersonal forgiveness and explores its role in transitional societies. The book also examines the symbolic moral significance of memorialization in these societies and reflects on its relationship to forgiveness.

Should people who perform equal work receive equal pay? Most would say ‘yes’, at least insofar as this question is understood to be asking whether employers should be permitted to discriminate against employees on the basis of race or sex. But suppose the employees belong to all of the same traditionally protected groups. Is (what I call) nondiscriminatory unequal pay for equal work wrong? Drawing an analogy with price discrimination, I argue that it is not intrinsically wrong, but it can (...) be deceptive, in which case it is wrong. (shrink)

This book brings to publication three essays by Rosenstock-Huessy on Nietzsche, and a translation of a chapter from his 'Sociology', clarifying the post-Nietzschean approach of the 'new thinking'.

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)

Consumers spend billions of dollars per year on homeopathic products. But there is powerful evidence that these products don’t work, i.e., they are not medically effective. Should homeopathic products be for sale? I give reason for thinking that the answer is ‘no.’ It has been suggested that the sale of homeopathic products involves deception. This might be so in some cases, but the problem is simpler: it is that these products don’t do what people buy them to do. More precisely, (...) homeopathic products don’t meet the “desire-satisfaction condition,” according to which products for sale in markets should satisfy the desires that people buy them to satisfy. I defend my view against objections, and conclude by acknowledging some of the practical difficulties of banning products people want to buy. (shrink)

This essay assesses Robert Merrihew Adams' contribution to the religion-morality debate in light of questions in philosophical semantics and metaphilosophy, questions Adams raises without addressing directly. It sketches a holistic theory of the use of language in thought in the hope of providing a context for determining the value and philosophical relevance of Adams' semantic claims. It concludes by suggesting that descriptive metaethics should give way to explicitly historical studies, and by maintaining that historians of ethics need not postulate "meanings" (...) in order to make sense of what they do. (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)

This paper examines the problem of ontotheology as it was defined by Martin Heidegger, and how it has subsequently been approached by those philosophers and theologians who have followed in his wake. It argues that Heidegger’s initial analysis of the onto‐theological condition was mistaken by its presumption of a radical divide between philosophy and theology. Furthermore, many of the key thinkers who have followed after Heidegger have merely reinscribed this supposed divide between thought and faith, rather than genuinely questioning the (...) terms Heidegger thought self‐evident. The result, even among some of the most radical and influential contemporary thinkers such as Emmanuel Levinas, John Caputo, and Jean‐Luc Marion, has been a contemporary philosophy deprived of questions of faith and a theology unaccountable to its place in the world. In response to this shortcoming of contemporary philosophical and theological thought, Jacques Derrida has approached the problem of ontotheology from the dual perspective of both thought and faith, and thereby, has provided a new path of thought beyond the problem of ontotheology and towards a renewed appreciation for the possibilities for a genuine philosophical theology. (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)