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)

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.

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)

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)

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)

ABSTRACTIn keeping with the dominant view that skills are largely automatic, the standard view of memory systems distinguishes between a representational declarative system associated with cognitive processes and a performance-based procedural system. The procedural system is thought to be largely responsible for the performance of well-learned skilled actions. Here we argue that most skills do not fully automate, which entails that the declarative system should make a substantial contribution to skilled performance. To support this view, we review evidence showing that (...) the declarative system does indeed play a number of roles in skilled action. (shrink)

This chapter presents the main formalism of the book, which is used in subsequent chapters to describe a variety of concepts in Husserlian phenomenology, and thereby unify them. A dynamical systems approach to Husserl is introduced, and several dynamical laws of Husserlian phenomenology are described. The first is an expectation rule according to which expectations are determined by what a person knows, sees, and does. The second is a learning rule according to which background knowledge is updated in a specific (...) way when experiences fulfill or frustrate prior expectations. In addition to these rules, a “supervenience function” is described, which associates how a thing is seen with a “trail set,” the set ways that thing is expected to look, relative to all possible ways of moving around it. This function further illustrates the explanatory dimension of phenomenology described in Chap. 2, whereby how we immanently experience things is determined by how we expect them to look relative to counterfactual movement patterns. (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)

In conventional identity politics subjective differences are understood negatively, as gaps to be overcome, as lacks of sameness, as evidence of failed or incomplete unity. In _Alterity Politics _Jeffrey T. Nealon argues instead for a concrete and ethical understanding of community, one that requires response, action, and performance instead of passive resentment and unproductive mourning for a whole that cannot be attained. While discussing the work of others who have refused to thematize difference in terms of the possibility or impossibility (...) of sameness—Levinas, Butler, Derrida, Foucault, Deleuze, Guattari, Zizek, Jameson, Heidegger, Bakhtin—Nealon argues that ethics is constituted as inexorable affirmative response to different identities, not through an inability to understand or totalize the other. _Alterity Politics_ combines this theoretical itinerary with crucial discussions of specific and diverse sites of literary and cultural production—the work of William S. Burroughs, Amiri Baraka, Andy Warhol, Ishmael Reed, Rush Limbaugh, and Vincent Van Gogh—along with analyses of the social formation of subjects as found in identity politics, and in multicultural and whiteness studies. In the process, Nealon takes on a wide variety of issues including white male anger, the ethical questions raised by drug addiction, the nature of literary meaning, and the concept of “becoming-black.” In seeking to build an ethical structure around poststructuralist discourse and to revitalize the applied use of theoretical concepts to notions of performative identity, _Alterity Politics_ marks a decisive intervention in literary theory, cultural studies, twentieth-century philosophy, and performance studies. (shrink)

The author integrates, expands, and deepens his previous publications about irregular (or "metalinguistic") negations. A total of ten distinct negatives-several previously unclassified-are analyzed. The logically irregular negations deny different implicatures of their root. All are partially non-compositional but completely conventional. The author argues that two of the irregular negative meanings are implicatures. The others are semantically rather than pragmatically ambiguous. Since their ambiguity is neither lexical nor structural, direct irregular negatives satisfy the standard definition of idioms as syntactically complex expressions (...) whose meaning is non-compositional. Unlike stereotypical idioms, idiomatic negatives lack fixed syntactic forms and are highly compositional. The final chapter analyzes other "free form" idioms, including irregular interrogatives and comparatives, self-restricted verb phrases, numerical verb phrases, and transparent propositional attitude and speech act reports. (shrink)

Recent research into the nature of self in artificial and biological systems raises interest in a uniquely determining immutable sense of self, a “metaphysical ‘I’” associated with inviolable personal values and moral convictions that remain constant in the face of environmental change, distinguished from an object “me” that changes with its environment. Complementary research portrays processes associated with self as multimodal routines selectively enacted on the basis of contextual cues informing predictive self or world models, with the notion of the (...) constant, per-vasive and invariant sense of self associated with a multistable attractor set aiming to ensure personal integrity against threat of disintegrative change. This paper proposes that an immutable sense of self emerges as a global attractor which can be described as a project ideal self-situation embodied in frontal medial processes during more or less normal adolescent development, and that thereafter serves to orient agency in the more or less free development of embodied potentials over the life course in effort to realize project conditions, phenomenally identified with the felt pull towards this end as purpose of and source of meaning in life. So oriented, life-long self-development aims to embody solutions to problems at different timescales depending on this embodied purpose, ultimately in the service of evolutionary processes securing organism populations against threats of disintegrative change over timespans far beyond that of the individual. After characterizing the target sense of self, research circling this target is briefly surveyed. Self as global project and developmental neural correlates are proposed. Then, the paper discusses some implications for research in biological and artificial systems. Building from earlier work in cognitive neurorobotics, discussion affirms the value of reinforcement rituals including prayer in metaphysical self-development, considers implications for value alignment and rights associated with free will in the context of artificial intelligence and robot religion, and concludes by emphasizing the importance of self-development toward project ideals as source of meaning in life in the current social-political environment. (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)

In 2018, Daniela Frauchiger and Renato Renner published an article in Nature Communications entitled ‘Quantum theory cannot consistently describe the use of itself.’ The argument has been attacked as flawed from a variety of interpretational perspectives. I clarify the significance of the result as a sequence of actions and inferences by agents modeled as quantum systems evolving unitarily at all times. At no point does the argument appeal to a ‘collapse’ of the quantum state following a measurement.

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett’s limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.

I shall conclude with a methodological moral. I have tried to show that there are several fundamentally different kinds of fear. One is a pure propositional attitude, one is partially a bodily state, and one is a relation between a person and a nonpropositional object. Other emotions come in similar varieties, such as hope and happiness, but with significant differences. The state of happiness, for example, does not entail any particular bodily state or feeling. So one lesson is this: it (...) is hard to generalize about “the emotions.” Further detailed, analytical studies of particular emotions are needed before a “general theory of the emotions” can be fruitfully attempted. (shrink)

Sociologists of education often emphasize goods that result from a practice (external goods) rather than goods intrinsic to a practice (internal goods). The authors draw from John Dewey and Alasdair MacIntyre to describe how the same practice can be understood as producing “skills” that center external goods or as producing habits (Dewey) or virtues (MacIntyre), both of which center internal goods. The authors situate these concepts within sociology of education’s stratification paradigm and a renewed interest in the concept of alienation, (...) contrasting the concepts of skills, habits, and virtues to capital, credentials, and habitus. They close by connecting the argument to broader critiques of procedural liberalism and the ideology of meritocracy, then giving suggestions for an expanded sociology of education beyond the stratification paradigm. (shrink)

I formulate the interpretation problem of quantum mechanics as the problem of identifying all possible maximal sublattices of quantum propositions that can be taken as simultaneously determinate, subject to certain constraints that allow the representation of quantum probabilities as measures over truth possibilities in the standard sense, and the representation of measurements in terms of the linear dynamics of the theory. The solution to this problem yields a modal interpretation that I show to be a generalized version of Bohm's hidden (...) variable theory. I argue that unless we alter the dynamics of quantum mechanics, or accept a for all practical purposes solution, this generalized Bohmian mechanics is the unique solution to the problem of interpretation. (shrink)

Three errors of "The Blind Watchmaker" theory are examined with Aristotelian thought.

A question dating to Mardešić and Prasolov’s 1988 work [S. Mardešić and A. V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc. 307(2) (1988) 725–744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits [Formula: see text] [Formula: see text] of a certain inverse system [Formula: see text] indexed by [Formula: see text] to simultaneously vanish. An equivalent formulation (...) of this question is that of whether it is consistent for all [Formula: see text]-coherent families of functions indexed by [Formula: see text] to be trivial. In this paper, we prove that, in any forcing extension given by adjoining [Formula: see text]-many Cohen reals, [Formula: see text] vanishes for all [Formula: see text]. Our proof involves a detailed combinatorial analysis of the forcing extension and repeated applications of higher-dimensional [Formula: see text]-system lemmas. This work removes all large cardinal hypotheses from the main result of [J. Bergfalk and C. Lambie-Hanson, Simultaneously vanishing higher derived limits, Forum Math. Pi 9 (2021) e4] and substantially reduces the least value of the continuum known to be compatible with the simultaneous vanishing of [Formula: see text] for all [Formula: see text]. (shrink)

This chapter contains sections titled: Action Intentional vs Unintentional Action Autonomous Action Action for Reasons References Further reading.

I critically examine Cappelen and Lepore’s definition of and tests for indexicality, and refine them to improve their adequacy. Indexicals cannot be defined as expressions with different referents in different contexts unless linguistic meaning and circumstances of evaluation are held constant. I show that despite Cappelen and Lepore’s claim that there are only a handful of indexical expressions, their “basic set” includes a number of large and open classes, and generates an infinity of indexical phrases. And while the tests can (...) be used effectively to combat contextualism concerning ‘knows’ and ‘actual,’ many expressions not in their basic set test positive for indexicality, including quantifier nouns, weather reports, and comparative adjectives. I rebut their claim that context-shifting arguments inevitably lead to radical contextualism, and that if there were any indexicals beyond their basic set, communication would be impossible. (shrink)

This paper responds to the focus issue on exemplarity that includes contributions by Kyle Lambelet, Brian Hamilton, and Gustavo Maya. The paper calls attention to ancient, medieval, and modern precedents that ought to inform our thinking about the ethical and political significance of exemplars.

Kant repeatedly uses the biangle as an example of an impossible figure. In this paper, I offer an account of these passages and their significance for the possibility of geometry as a science. According to Kant, the constructibility of the biangle would signal the failure of geometry. Whereas Wolff derives the no-biangle proposition from the axiom that between two points there can be only one straight line, Kant gives it axiomatic status as a synthetic a priori principle possessing immediate certainty. (...) Because we are unable to generate a schema for the biangle, the failure of the attempt to construct it is intuitively clear. The parallel between mathematical and empirical concepts is instructive because both involve the synthesis of disparate intuitions into a unity. We do not, strictly speaking, even possess a well-formed concept of the biangle, because its representation cannot fulfill certain basic requirements of concept formation. (shrink)