Machine generated contents note: -- Preface -- Acknowledgements -- Notes on Contributors -- PART I: COMPLEXITY IN ANIMAL MINDS -- Introduction: M.McGonigle-Chalmers -- Relational and Absolute Discrimination Learning by Squirrel Monkeys: Establishing a Common Ground with Human Cognition; B.T.Jones -- Serial List Retention by Non-Human Primates: Complexity and Cognitive Continuity; F.R.Treichler -- The Use of Spatial Structure in Working Memory: A Comparative Standpoint; C.De Lillo -- The Emergence of Linear Sequencing in Children: A Continuity Account and a Formal Model; M.McGonigle-Chalmers&I.Kusel (...) -- Sensitivity to Quantity: What Counts Across Species?; S.T.Boysen&A.M.Yocom -- PART II: COMPLEXITY IN ROBOTS -- Editorial Introduction; D.McFarland -- Towards Cognitive Robotics: Robotics, Biology and Developmental Psychology; M.Lee, U.Nehmzow&M.Rodriguez -- Structuring Intelligence: The Role of Hierarchy, Modularity and Learning in Generating Intelligent Behaviour; J.J.Bryson -- Epistemology, Access, and Computational Models; G.Luger -- Reasoning About Representations in Autonomous Systems: What P´Olya and Lakatos Have To Say; A.Bundy -- PART III: LANGUAGE, EVOLUTION AND THE COMPLEX MIND -- Editorial Introduction; K.Stenning -- How to Qualify for a Cognitive Upgrade: Executive Control, Glass Ceilings, and the Limits of Simian Success; A.Clark -- Private Codes and Public Structures; C.Allen -- The Emergence of Complex Language; W.Hinzen -- Language Evolution: Enlarging the Picture; K.Stenning&M.Van Lambalgen -- Epilogue: Reminiscences of Brendan McGonigle -- Index. (shrink)

Over 50% of the world population will develop a psychiatric disorder in their lifetime.1 In the realm of psychiatric treatment, two primary modalities have been established: pharmacotherapy and psychotherapy. Yet, pharmacological interventions often take precedence as the initial treatment choice despite their comparable outcomes, severe side effects and disputed evidence of their efficacy. This preference for medication foregrounds a vital re-examination of what it means to be invasive in medical treatments, namely in psychiatric care. De Marco et al challenge the (...) standard account of invasiveness, presenting considerations that transcend the traditional criteria of physical intrusion.2 Through case studies centred on treatments for schizophrenia and depression, we aim to (1) reinforce De Marco et al ’s challenge to the standard account of invasiveness and (2) extend the dialogue to the moral imperative of redefining mental invasiveness. Our aims are to broaden the definition of mental invasiveness, aligning with De Marco et al ’s emphasis on context sensitivity, and to include the severity of side effects as a critical factor in this assessment. Redefining what is considered invasive in psychiatric treatment has profound implications for patient care and medical decision-making. Labelling treatments, namely medications, as invasive encourages both patients and healthcare providers to approach these options with a heightened level of scrutiny and care. This is …. (shrink)

Neuropsychiatric disorders such as drug addiction, depression and schizophrenia are often centrally implicated in public health challenges. These conditions impact the individuals affected and have widespread implications, contributing to related crises such as opioid epidemic, rising suicide rates and homelessness. Despite their influence, public health interventions frequently emphasise individual responsibility, overlooking the complex interplay of neurobiological and systemic factors that underpin these disorders. Current public health frameworks, such as the Nuffield Council on Bioethics’ intervention ladder, prioritise efforts that encourage individual (...) behaviour change. Paetkau critiques this emphasis on individual responsibility, emphasising the need to consider more systemic factors, such as social determinants of health, as targets of necessary intervention.1 We aim to reinforce Paetkau’s critique of the intervention ladder by introducing three neuropsychiatric case studies, each highlighting the limitations of an individual-based framework in addressing psychopathology-involved public health issues. We argue that conditions like addiction, depression and serious mental illness undermine the emphasis on individual responsibility in public health and policy interventions. To this end, neuroscience demonstrates that effective public health interventions necessitate a shift from the long-standing emphasis on individual responsibility towards more comprehensive, systems-level interventions. Opioid overdose deaths in the USA have sextupled since 1999, with over 100,000 deaths in 2023 alone.2 The opioid crisis has since remained one of the most pressing public …. (shrink)

The intersection of language, stigma, and neuropsychiatry is an integral area of concern for limited english proficiency (LEP) communities, demanding a greater focus in U.S. healthcare systems. Lan...

Some philosophers have claimed that kinds can be construed as mereologically complex structural properties. This essay examines several strategies aimed at construing a certain class of natural kinds, namely isomeric chemical kinds, in accordance with this view. In particular, the essay examines views which posit structural proper parts in addition to micro-constitutive parts to individuate isomeric chemical kinds. It then goes on to argue that the phenomenon of chirality in stereochemistry gives the proponent of kinds-as-complex-properties evidence for positing the existence (...) of causal-cum-dispositional individuating proper parts, in addition to structural parts, for chemical enantiomeric kinds. (shrink)

This paper maintains that at the heart of the post-Reformation debates over the extra Calvinisticum lies the question of what it means to name God’s presence in the world – that is, to say where God is. Because the Lutheran position insists that there can be no proper identification of God’s presence in the world that does not take its bearings from talk about Jesus’ presence, it serves as a means of preventing Christian God-talk from becoming detached from the flesh-and-blood (...) realities of human existence. In this way, the denial of the extra Calvinisticum is a corollary of a theology of the cross – that is, the principle that talk about God is normed by the concrete reality of Jesus. At the same time, the Lutheran genus maiestaticum is rejected as making just the sort of move to which Luther himself objected in the doctrine of transubstantiation: a metaphysical explanation of Jesus’ presence in the world rather than a simple appeal to miracle. (shrink)

The integration of digital phenotyping in psychiatry promises unprecedented insights into mental health, particularly in college settings where mental well-being is a growing concern. The COVID-19...

Abstract Motivation in an automaton, whether it be artificial or animate, is simply that aspect of the total state that determines the behaviour. In an autonomous agent, which has a degree of self?control, the motivational state includes a cognitive evaluation of the likely consequences of possible future behaviour. Such evaluation implies optimization with respect to some motivational criterion.

Discussions of the relationship between perception and cognition often proceed without a definition of these terms. The sensory-modality specific nature of low-level perceptual processes provides a means of distinguishing them from cognitive processes. A more explicit definition of terms provides insight into the nature of the evidence that can resolve questions about the relationship between perception and cognition.

In the Philosophical Investigations, Wittgenstein is sometimes claimed to hold a redundancy theory of truth. The main evidence to support this view, however, comes from a single passage, number 136, which has been misinterpreted. In this essay I argue for an alternative interpretation of the critical passage in question. The purpose behind Wittgenstein’s remarks is not to provide a general theory of truth, per se. Rather, Wittgenstein uses the section as a way to introduce his notion of fit, a notion (...) that will play a more substantial role in his later arguments on following rules. Furthermore, if Wittgenstein did hold something close to a redundancy theory of truth, such a view would illuminate remarks from the earlier notebooks about a crucial Tractarian view rather than his later view from the Investigations: the so-called “Picture Theory”. (shrink)

Abstract The frame problem is a problem that arises when an agent attempts to assess the consequences of future behaviour. Strictly, it is a problem of modelling that arises during planning. The problem arises because many of the possible consequences of a planned action are not really relevant to the decision whether to perform the action. The frame problem is typical of the classical approach to artificial intelligence, but it is evident that animals do not suffer from this problem. In (...) this paper it is suggested that animals can circumvent the frame problem because their decision?making architecture is very different from that traditionally used in artificial intelligence. (shrink)

Correction of sensory transmission delays is an intractable problem, since there is no absolute reference for calibration. Phase-alignment is a practical alternative solution and can be realized by adaptive filters that operate locally with simple error signals.

Currently there is considerable interest in the notion that dorsal and ventral visual systems might differ in their specializations for thought and action. Behavior invariably involves multiple processes such as perception, judgment, and response execution. It is not clear that characteristics of the dorsal and ventral processing streams, as described by Norman, are entirely of a perceptual nature.

Numerous individual differences determine the effectiveness of the multiple external reinforcement contingencies that control drug seeking behavior. Differences in the capacity to frame reinforcement and also the toxic effects of drugs modulate susceptibility to addiction. As a result, not all individuals are at the same degree of risk for addiction.

This chapter sketches a taxonomy of artificial dispositions where humans play a part in the triggering mechanisms for those dispositions’ manifestations, and those dispositions that require humans for certain kinds of manifestations to be sustained. Thus the way and extent to which a disposition will count as artificial will be a matter of degree. The chapter argues for adopting an approach from the literature on natural kinds, sometimes called an “epistemic” or “pragmatic” turn, and takes aim at a traditional criterion (...) for something’s being real, i.e. mind-independence, while the proposed alternative criterion is a causal criterion. The chapter goes on to address complications for this taxonomy with potential difficulties from mimics, and a variety of dispositions sometimes purported to exist which I’ll call “apocryphal dispositions”. (shrink)

My dissertation addresses a question relevant to metaphysics, philosophy of language, and philosophy of science: What are natural kinds? I explore a view that holds that natural kinds are complex, structural properties that involve causal structure. Causal structure describes the idea that for the many properties associated with natural kinds, these properties are nomically linked - that is causally connected - in such a way that the properties of non-natural kinds are not. After criticizing arguments in favor of a nominalist (...) theory of kinds - one that holds that a natural kind just is to be identified with its class of instances - and after defending the notion of a complex structural property from several prominent objections posed by David Lewis, I apply a causal account of natural kinds to a set of problematic cases, paying special attention to isomeric kinds from chemistry. (shrink)

This paper offers observations on people’s lived experience of the food system in Michigan during the early Covid-19 pandemic as an initial critical foray into the everyday pandemic food world. The Covid-19 crisis illuminates a myriad of adaptive food behaviors, as people struggle to address their destabilized lives, including the casual acknowledgement of the pandemic, then anxiety of the unknown, the subsequent new dependency, and the possible emergence of a new normal. The pandemic makes the injustices inherent in the food (...) system apparent across communities, demonstrating that food injustice destabilizes all members of the food system, regardless of their social location. The challenges of eating in a pandemic also reinforce the importance of building a sustainable food system; the challenges of food sovereignty and food sustainability are inextricably linked, and the pandemic lays this bare. (shrink)

A legal obligation to conduct weapons reviews is a means by which the international community can ensure that States assess whether the use of new types of weapons in armed conflict would raise humanitarian concerns. The use of artificial intelligence in weapon systems greatly complicates the process of conducting reviews, particularly where a weapon system is capable of continuing to ‘learn’ on its own after being deployed on the battlefield. This paper surveys current understandings of the weapons review challenges presented (...) by in situ learning and outlines some concepts which may inform appropriate changes to existing weapons review processes. The main arguments made are that: a distinction should be drawn between learning capabilities that are limited to optimising existing behaviour and capabilities that extend to acquiring new behaviours; and the extent of a weapon system’s learning capabilities should be used as the basis for defining a schedule of weapons reviews. (shrink)

In this paper we address three concepts that are much talked about in the animal robotics community. These concepts are (1) representations, (2) goals, and (3) minimal cognition. We want to distinguish between information as an objective commodity and representation as something which involves a user, i.e. a system which accesses and uses information. Information per se lies out there and exists independently of any system that makes use of it. Representations presuppose design and require a user. We want to (...) distinguish different kinds of purposive behaviour, which involve different notions of goals, which themselves appear to be different from the point of view of the agent, the designer and the naive observer. We want to try to define cognition in terms of the minimal criteria that would be acceptable in view of our definitions of representations and goals. We recognise that full‐blown cognition may require ingredients other than those of minimal cognition. (shrink)

The development of any novel reproductive technology involving manipulation of human embryos is almost inevitably going to be controversial and evoke sincerely held, but diametrically opposing views. The plethora of scientific, ethical and legal issues that surround the clinical use of such techniques fuels this divergence of opinion. During the policy change that was required to allow the use of mitochondrial donation in the UK, many of these issues were intensely scrutinised by a variety of people and in multiple contexts. (...) This extensive process resulted in the publication of several reports that informed the recommendations made to government. We have been intrinsically involved in the development of mitochondrial donation, from refining the basic technique for use in human embryos through to clinical service delivery, and have taken the opportunity in this article to offer our own perspective on the issues it raises. (shrink)

Incidental fndings of potential medical signifcance are seen in approximately 5-8 percent of asymptomatic subjects and 16 percent of symptomatic subjects participating in large computed tomography colonography studies, with the incidence varying further by CT acquisition technique. While most CTC research programs have a well-defned plan to detect and disclose IFs, such plans are largely communicated only verbally. Written consent documents should also inform subjects of how IFs of potential medical signifcance will be detected and reported in CTC research studies.

With the growth of neuroscience research, new neuroscience and society (NeuroX) fields like neuroethics, neurolaw, neuroarchitecture, neuroeconomics, and many more have emerged. In this article we report on lessons learned about mentoring students in the interdisciplinary space of neuroscience and society. We draw on our experiences with the recently launched Dana Foundation Career Network in Neuroscience & Society. This resource supports educators and practitioners mentoring students aiming to apply neuroscience in diverse fields beyond medicine and biomedical science. Through our programming, (...) we identified three key lessons: (1) students are interested in exploring a wide range of neuroscience and society intersections; (2) outreach to underserved institutions generates avenues for students to join NeuroX conversations; and (3) by offering free access to online NeuroX resources and a network of subject-matter experts, the Career Network joins many partners helping to bridge the gap between neuroscience and society. (shrink)

Paradoxes of Freedom is a study of the philosophical and historical concept of liberty. Centring his argument upon the Romantic exaltation of freedom, Thomas McFarland identifies freedom as one of the three chief transcendences, along with love and religion, by which humanity orientates itself. McFarland indicates, by an examination ranging from Shakespeare and Luther to the writings of Nietzsche and Wagner, both the reasons for the supreme valuation of freedom and the nature of the hindrances, in theory and (...) fact, that enmesh the actual realization of freedom. (shrink)

Since Hegel, the idea of an end of art has become a staple of aesthetic theory. This book analyzes its role and its rhetoric in Hegel, Nietzsche, Benjamin, Adorno, and Heidegger in order to account for the topic's enduring persistence. In addition to providing a general overview of the main thinkers of post-Idealist German aesthetics, the book explores the relationship between tradition and modernity. For despite the differences that distinguish one philosopher's end of art from another's, all authors treated here (...) turn the end of art into an occasion to thematize and to reflect on the very thing that modernism cannot or should not be: tradition. As a discourse, the end of art is one of our modern traditions. (shrink)

According to a subjectivist view of some concept, C, there is an a priori implication of subjective responses in C's application or possession conditions. Subjectivists who intend their view to be descriptive of our practice with C will hold that it is possible for there to be true empirical claims which explain such responses in terms of certain things being C. Mark Johnston's "missing-explanation argument" employs a substitution principle with a view to establishing that these strands of subjectivism are inconsistent. (...) I suggest that Johnston's substitution principle survives an attempt by Alex Miller to show that it is unreliable, but that it is prey to a counterexample which cannot be explained away by the proponent of the missing-explanation argument. I conclude that the missing-explanation argument poses no threat to subjectivism. (shrink)

Neuropsychiatric disorders introduce distinct challenges to clinical decision-making. Affected patients often experience impairments or absences in rationality, lucidity and cogni-emotional capacities, rendering it difficult for them to engage in the decision-making process. In turn, dynamics of the patient-physician relationship become strained, including when physicians employ bioethical principlism or moral case deliberation to arrive at ethically justified courses of action–both of which require sufficient communication and rationality that may be impaired or altogether absent in the presence of psychopathology. The complexity of (...) neuropsychiatric conditions therefore compels interrogation towards how ethics consultations are currently constructed and conducted when full communication or rational decision-making cannot be assumed. Delany et al, for example, present a robust, methodical framework for ethical deliberation.1 Such methodologies for facilitating ethical decision-making, although valuable in predominant contexts, assume full participant engagement and decision-making capacities (eg, independent moral agency). Neuropsychiatric disorders complicate this assumption, making it difficult for patients with limited decision-making capacity to engage meaningfully in proposed ethics consultations.2 This paper will explore how neuropsychiatric disorders complicate the assumptions of full participant engagement underlying ethical frameworks. It will argue that, by adapting ethics consultations to function as a ‘mental prosthesis’, clinicians can better navigate the ethical challenges posed by neuropsychiatric disorders, helping to ensure that patient autonomy is upheld even in cases of impaired cognitive …. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:'Difficult Patient':A Reflective EssayDaniel McFarlandThe patient who sat across from me knew too much about all brain tumors. According to her, she would never know enough about the one sitting uncomfortably close to her brain's temporal lobe. In her quest for the 'right' answer to her meningioma problem, she became certain that its surgical removal would upend her life, leaving her in neurological taters.She was a small business owner (...) of a practice dedicated to medical massage. Indubitably, she had helped countless clients heal themselves of medical mishaps and avoid or recover from the tyranny of [End Page E13] a medical community that did not always provide respectable, hospitable care. She was certain a craniotomy would end her business, nullifying everything she had spent her life building. She became fluent in the legalese needed to transfer or sell her business in anticipation of surgery. To stave off losing her life's work from a surgical mishap, she sought opinions from a dozen neurosurgeons. They reassured her that a routine surgery like this would be effective with little chance of neurological collateral damage. She did not believe them. In her business she had treated numerous exhausted professionals. Many surgeons with whom she worked professionally frequently referred patients to her. She had seen the poor self-care that many surgeons and doctors brought on themselves in the form of unrelenting stress, drinking, bad eating habits, and even drugs. This made her nervous and untrusting about the care she could receive at the hands of an overworked or impaired surgeon. She scheduled appointments with every neurosurgeon she could find and interviewed them relentlessly, looking for the slightest sign of incompetence, unprofessionalism, antipathy, or lapse in compassion. Given her insistence and dogged nature, she usually found what she was looking for. She would bring her research to the appointments and interview the neurosurgeons on what other doctors had opined. If they were incredulous of research she brought or a technique on which she inquired, they were summarily dismissed.At first glance, which is likely all that she got from many of her visits, these encounters put a spotlight on a 'difficult' patient refusing care. The deeper look that my patient deserved revealed a personal narrative of the oldest child who survived a broken home riddled with drug use and prostitution. She learned to rely on only herself for protection. She took unapologetic control of her fate. Her own mother had at one time offered my patient work as a prostitute. Her father was no better in providing protection and a decent upbringing. He had left her as an eight-year-old with the neglectful mother and four younger siblings to fend for herself, which she did against the odds. She suffered physical, emotional, and spiritual abuse.As an adult, her strong sense of selfhood and boundaries allowed her to have a guarded relationship with both of her parents at a comfortable emotional distance. Her mission and passionate drive to help others heal saved her life. In healing others, she was healing herself. Importantly, her experience marked for her indelibly that while she could do this for herself, others were not reliable and could not heal her. She had only ever trusted and relied upon herself. She was the only one who had never let her down. She was terrified that this might be the first time. The potential surgery risked her cognition, physical capacities, and ability to care for herself. The risk was too great.We met numerous times, uncovering her past, reliving the stories of her tumultuous background, and examining how she established her place in the world away from the horrors of her insecure childhood. She took in my reaction to her stories and saw the horror on my face when I tried to imagine a world where one's parents were not only neglectful but the source of danger. Through my reaction, she may have begun to have some compassion for her own story and put the pieces together. One several occasions, she became enraged when I didn't meet her expectations, or I didn't entertain the diatribe of neurosurgical scholarly work.On one of those... (shrink)

Most philosophers today will acknowledge the pitfalls of confusing metaphysical and semantic issues. Many are also familiar with the classic semi-formalargument that has come to be known as ‘the Slingshot’ and the various philosophical ends to which this argument has been deployed. The combination of the argument’s relatively simple theoretical machinery and its wide range of applications make it ripe for abuse. The slingshot was originally conceived as a semantic argument about designation; what it suggests, but does not prove, is (...) that the closest analogue to singular term reference for any expression is that expression’s semantic extension. In order to derive more metaphysically robust conclusions, however, many classical deployments of the argument make use of several methodologically suspicious tactics. By cataloguing the more frequent abuses of the argument, we may remind ourselves of a valuable philosophical lesson. (shrink)

Since the publication of Edmund Gettier's challenge to the traditional epistemological doctrine of knowledge as justified true belief, Roberts and Wood claim that epistemologists lapsed into despondency and are currently open to novel approaches. One such approach is virtue epistemology, which can be divided into virtues as proper functions or epistemic character traits. The authors propose a notion of regulative epistemology, as opposed to a strict analytic epistemology, based on intellectual virtues that function not as rules or even as skills (...) but as habits of the heart. To that end, they divide the task of clarifying and expounding their notion in the book's two parts.In the first part, Roberts and Wood examine various components that constitute their notion of regulative epistemology. The first are the epistemic goods or goals that drive the epistemic process. What is needed, claim Roberts and Wood, is an enriched notion of these goods rather than the restricted notion of justified true belief. Epistemic agents are more than calculating devices in that …. (shrink)

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

On what grounds will the rational man become a Christian? It is often assumed by many, especially non-Christians, that he will become a Christian if and only if he judges that the evidence available to him shows that it is more likely than not that the Christian theological system is true, that, in mathematical terms, on the evidence available to him, the probability of its truth is greater than half. It is the purpose of this paper to investigate whether or (...) not this is a necessary and sufficient condition for the rational man to adopt Christianity. (shrink)