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.

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)

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)

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.

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)

This chapter presents an overview of the life, work, and philosophical contributions of Śāntarakṣita (c. 725–788), who is known for his synthesis of Nāgārjuna’s Madhyamaka with elements of the Dignāga-Dharmakīrti tradition of logic and epistemology. His two most important independent treatises, the Compendium of True Principles (Tattvasaṃgraha) and the Ornament of the Middle Way (Madhyamakālaṃkāra), are characterized by an emphasis on the indispensable role of rational analysis on the Buddhist path as well as serious and systematic engagement with competing Buddhist (...) and non-Buddhist schools of thought. Śāntarakṣita employs a pedagogical-rhetorical device of provisionally adopting what he deems to be successively more rational views to reject less rational ones. Using this approach, in the Ornament of the Middle Way, he recommends a gradual path to arrive at an understanding of the Madhyamaka ultimate truth by incorporating Yogācāra idealist ontology into his presentation of conventional truth. In this same text, he presents an influential iteration of the neither-one-nor-many argument for the Madhyamaka ultimate truth, the emptiness of intrinsic nature—i.e., the universal negation of ontologically independent being—leaving a lasting and significant impact on both Indian and Tibetan Madhyamaka Buddhist philosophy. (shrink)

Dharmakīrti’s (c. seventh century) Examination of Relations (Sambandhaparīkṣā) is unique in the Indian Buddhist canon for its being the only extant root text devoted entirely to the topic of the ontological status of relations. But the core thesis of this treatise—that relations are only nominally real—is in prima facie tension with another claim that is central to Dharmakīrti’s epistemology: that there exists some kind of “natural relation” (svabhāvapratibandha) that reliably underwrites inferences. Understanding how Dharmakīrti can consistently rely on natural relations (...) to prop up his presentation of inferential reasoning while at the same time advancing an anti-realist account of relations is critical for making sense of his system of logic and epistemology, which came to be nearly universally adopted in Tibetan Buddhism cutting across traditions. Chomden Rikpé Reldri (1227–1305), who was perhaps the most prolific commentator on logic and epistemology in the history of Tibetan philosophy, composed two texts commenting on the Examination of Relations, neither of which have received any scholarly attention to date. In this paper, I provide an introduction to Chomden Reldri’s two commentaries and consider how they may illuminate Dharmakīrti’s text and also what they reveal about the understanding of Dharmakīrti’s account of relations in early Tibetan scholasticism. I then present a translation of Dharmakīrti’s Examination of Relations together with Chomden Reldri’s commentary, Annotations and Topical Outline of the Examination of Relations (’Brel pa brtag pa’i mchan dang sa bcad gnyis). (shrink)

Perceptual attention is essential to both thought and agency, for there is arguably no demonstrative thought or bodily action without it. Psychologists and philosophers since William James have taken attention to be a ubiquitous and distinctive form of consciousness, one that leaves a characteristic mark on perceptual experience. As a process of selecting specific perceptual inputs, attention influences the way things perceptually appear. It may then seem that it is a specific feature of perceptual representation that constitutes what it is (...) like to consciously attend to an object. In fact conscious attention is more complicated. In what follows, I argue that the phenomenology of conscious attention to what is perceived involves not just a way of perceptually locking on to a specific object. It necessarily involves a way of cognitively locking on to it as well. (shrink)

A uniquely playful and incisive illustrated collection of Zen teaching stories from one of America's best-known and most-respected Zen masters. A Modern Classic. In the tradition of the great koan collections and the extensive records of ancient masters, Robert Aitken--one of America's best-known and most-respected Zen masters--distills a lifetime of teaching down to its essence. Intriguing, playful, and deceptively easy to read, Zen Master Raven is a brilliant encapsulation of Zen in over a hundred koan-like encounters--featuring curious beginners like (...) Mallard and Mole, to teachers-in-training like Porcupine, to the profound wisdom of masters like Brown Bear, Moose Roshi, and Zen Master Raven himself. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations (...) between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified. (shrink)

This article provides a detailed overview of the neuroscience of consciousness.

Innes’s “control signals” provides a semiotic perspective for explaining how acts of social control send “signals” about the effectiveness of security mechanisms. A cross-cutting theme infers that “culture and situation matter” in the reception of signals. However, the control signals concept does not explicitly consider the influence that prior experiences may have on present interpretations. Drawing on qualitative research into how members of a residential community perceived control measures within their everyday environment for Glasgow’s 2014 Commonwealth Games, this article outlines (...) the importance of the “pre-signalling” context in influencing how control signals are received. Goffman’s “frame analysis” is used as part of a semiotic framing approach to demonstrate that control signals are framed (or pre-signalled) by the history of relations between sender and receiver of the signal (for example, police and residents). (shrink)

The most comprehensive book on the topic, Thinking about Good and Evil traces salient Jewish ideas about why innocent people seem to suffer, why evil individuals seem to prosper, and God's role in matters of (in)justice, from antiquity to modernity.

This is the story of North Carolina parent choice advocates' push for the creation and expansion of choice policies in the state. The exploration of the politics, ideology, and interests surrounding parent choice in this conversation includes but also stretches beyond the most frequently discussed choice policies of charter schools, school vouchers, and tuition tax credits. Here, Lewis makes the argument that parents push for these policies are closely akin to parents' rejection of busing and redistricting policies in Charlotte-Mecklenburg and (...) Raleigh-Durham, parents' advocating for the state-support of home-schooling options across the state, and parents' pushing for the expansion of magnet and intradistrict choice options. He shows how central to parents' advocacy for all of these policies lies a more foundational desire to reconceputalize public schooling, with parents having much more individual control over how public funding is used for the education of their children. (shrink)

Hegel's very first acknowledged publication was, among other things, an attack on Fichte. In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801 Differenzschrift, Hegel cut his teeth by criticizing Fichte's already widelycriticised Wissenschaftslehre, and by demonstrating that Schelling's philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel's criticisms; indeed he never publicly (...) acknowledged their existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi's criticisms, and to Schelling's; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel's Differenzschrift was left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel's early criticisms of Fichte reappear at every subsequent stage of his career: in the Phenomenology, in the Science of Logic, in the Encyclopaedia, as the final chapter in Hegel's History of Philosophy, and in countless other minor works and documents from the Nachlass and correspondence. (shrink)

This books delineates the seismic shifts of the twentieth century humanities by way of a close examination of the dynamic landscape of modern language, criticism and philosophy. In this manner, it argues that both philosophy and literary criticism have dovetailed in the twenty-first century. Starting out as a survey of literary criticism in its broadest terms, later chapters - which are more expository - assess recent movements within modern literary theory. These are located with respect to the post-Russell and Fregean (...) “linguistic turn” in philosophy. Designed for specialists and non-specialists alike; philosophers, literary critics and even students of the modern critical tradition, the argument takes a novel stance towards modern criticism, language and philosophy, arguing for a return to a more formalist and rhetorical approach to literary criticism, while taking care not to indulge too many “political pathologies” when engaging with texts. (shrink)

Written not by a journalist or politician but rather by a theology professor with a Ph.D. in New Testament studies, Voting by the Bible: The Economic and Foreign Policy Issues begins with the assumption that God intended the Bible to give guidance to every area of life£including how governments should function. Derived from author Wayne Grudemþs magisterial Politics£According to the Bible, this book highlights those economic and foreign-policy issues that have dominated political debate recently. Throughout, author Wayne Grudem (...) supports political positions that would be called more 'conservative' than 'liberal.' However, 'it is important to understand that I see these positions as flowing out of the Bible's teachings rather than positions I hold prior to, or independently of, those biblical teachings,' he writes. 'My primary purpose in the book is not to be liberally or conservative, or Democrat or Republican, but to explain a biblical worldview and a biblical perspective on issues of politics, law, and government.' Concise yet carefully argued, this book is a must-read for any Christian concerned about current debates over the economy, the size and role of government, and the best way forward out of the current recession. Not every reader will agree with the book's conclusions. But by grounding his analysis deeply on Scripture, Grudem has equipped Christians to better understand and respond to some of today's key political debates wisely and in a manner consistent with their primary citizenship as members and ambassadors of the kingdom of God" -- Publisher description. (shrink)

Abortion and euthanasia are among the most controversial topics in society today. Abortion is simply any action that intentionally causes the death and removal from the womb of an unborn child. Likewise, Euthanasia is the act of intentionally ending the life of a person who is elderly, terminally ill, or suffering from some incurable injury or disease. In this book, Dr. Wayne Grudem attempts to give an accurate summary of biblical teachings related to abortion and euthanasia, and also to (...) represent fairly the arguments of people who disagree with his positions. (shrink)

Dr. Wayne W. Dyer has researched intention as a force in the universe that allows the act of creation to take place. Here he explores intention - not as something we do - but as an energy we're a part of. We're all intended here through the invisible power of intention - a magnificent field of energy we can access to begin co-creating our lives.

We present a synthetic theory of skilled action which proposes that cognitive processes make an important contribution to almost all skilled action, contrary to influential views that many skills are performed largely automatically. Cognitive control is focused on strategic aspects of performance, and plays a greater role as difficulty increases. We offer an analysis of various forms of skill experience and show that the theory provides a better explanation for the full set of these experiences than automatic theories. We further (...) show that the theory can explain experimental evidence for skill automaticity, including evidence that secondary tasks do not interfere with expert performance, and evidence that experts have reduced memory for performance of sensorimotor skills. (shrink)

The book examines the evolution and current state of corporate social responsibility (CSR), using a five-stage maturity model: defensive, charitable, promotional, strategic and transformative CSR. The first four stages are dubbed CSR 1.0 and characterise most current CSR practice, while the fifth stage is named CSR 2.0 (also transformative or systemic CSR) and describes emergent and future CSR practices. Reasons are given why CSR 1.0 approaches have failed to have any significant impact on the most serious global social, environmental and (...) ethical challenges. The emergent CSR 2.0 will then be explored in detail by elaborating on five principles underlying the new approach, including: creativity, scalability, responsiveness, glocality and circularity. A four-part DNA Model is also introduced, covering value creation, good governance, societal contribution and ecological integrity, which provides the basis for defining and measuring CSR 2.0. Finally, a 70-question CSR 2.0 self-assessment diagnostic tool developed by the author is presented, with sample data to show how the tool can be used for future research and practitioner application. (shrink)

A comprehensive political philosophy, arguing for Christian involvement based on biblical teachings and a Christian worldview. --from publisher description.

Plato, and a wide variety of ancient, Arabic, and medieval Platonisms had a significant influence on Aquinas. The Corpus, with its quasi-Apostolic origin for Aquinas, was his most authoritative and influential source of Neoplatonism. His most influential early sources of Platonism came from Aristotle and Augustine, that is besides the Dionysian Corpus and the Liber. Aquinas greatly acknowledged the Neoplatonic, and the Peripatetic, commentaries and paraphrases he gradually acquired, because they enabled getting to the Hellenic sources. A great part of (...) Aquinas's last writing was devoted to explicating Aristotle's works including the Liber de causis, which was attributed to him. Aquinas wished to understand the philosophical schools such as their characters, the differences between and within them, their memberships, influences, histories, and the extent to which they are complementary. Aquinas gave an extended treatment of the history of philosophy, including lists of differences and agreements between Plato and Aristotle, beginning with ‘the opinions of the ancients and of Plato’ in his On Separate Substances. When Aquinas treated Aristotle in On Separate Substances, he did not leave his Neoplatonic framework behind. There is much more in On Separate Substances concerning the numbers, including an elaborate reasoning that saves the verbally opposed positions of both Proclus and Dionysius. (shrink)

Best-selling author Wayne Grudem explains in detail what the whole Bible says about living as a Christian in this highly practical, biblically based volume on Christian ethics.

Hegel's very first acknowledged publication was, among other things, an attack on Fichte. In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801Differenzschrift, Hegel cut his teeth by criticizing Fichte's already widelycriticisedWissenschaftslehre, and by demonstrating that Schelling's philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel's criticisms; indeed he never publicly acknowledged their (...) existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi's criticisms, and to Schelling's; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel'sDifferenzschriftwas left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel's early criticisms of Fichte reappear at every subsequent stage of his career: in thePhenomenology, in theScience of Logic, in theEncyclopaedia, as the final chapter in Hegel'sHistory of Philosophy, and in countless other minor works and documents from theNachlassand correspondence. (shrink)

Hegel’s very first acknowledged publication was, among other things, an attack on Fichte.1 In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801 Differenzschrift, Hegel cut his teeth by criticizing Fichte’s already widely-criticized Wissenschaftslehre, and by demonstrating that Schelling’s philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel’s criticisms; indeed he never publicly (...) acknowledged their existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi’s criticisms, and to Schelling’s; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel’s Differenzschrift was left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel’s early criticisms of Fichte reappear at every subsequent stage of his career: in the Phenomenology, in the Science of Logic, in the Encyclopaedia, as the final chapter in Hegel’s History of Philosophy, and in countless other minor works and documents from the Nachlass and correspondence. (shrink)

This book posits that a sustainable future is possible without abandoning Capitalism. In its present form as Consumer Capitalism, the organization of the global economy is clearly unsustainable. But Capitalism is a malleable concept that has assumed a variety of forms since the 17th Century, and it can be altered as needed. In Part I of this book, Wayne Henry sets out an economic model for a sustainable form of Capitalism, referred to in the literature as Natural Capitalism. In (...) Part II, he abandons exposition in favour of rigorous philosophical analysis and critiques the older but still dominant narrative that underlies Classical Liberalism. The narrative will be reconstructed with great care and analyzed to understand why it has been so powerful and enduring, and, of course, why it is no longer appropriate for our present circumstances. In Part III, he investigates Classical Liberalism and globalized capitalism, the economic system it licenses, from a normative perspective. Finally, in the conclusion, Henry draws the threads of the discussion together in a way that emphasizes the differences between the two narratives, Classical Liberalism on the one hand, and the contemporary version of Progressive Liberalism that nurtures and supports Natural Capitalism on the other. This book will be of interest to a broad range of scholars and curious laypersons interested in a clear and interdisciplinary presentation of the issues arising out of climate change, including corporate governance, social and environmental policy, declining social capital and the capacity of democratic institutions to deal effectively with sustainability. It will be particularly relevant for students and instructors of philosophy, history, economics, political science, social policy and environmental sociology. (shrink)

Andrew Wayne discusses some recent attempts to account, within a Bayesian framework, for the "common methodological adage" that "diverse evidence better confirms a hypothesis than does the same amount of similar evidence". One of the approaches considered by Wayne is that suggested by Howson and Urbach and dubbed the "correlation approach" by Wayne. This approach is, indeed, incomplete, in that it neglects the role of the hypothesis under consideration in determining what diversity in a body of evidence (...) is relevant diversity. In this paper, it is shown how this gap can be filled, resulting in a more satisfactory account of the evidential role of diversity of evidence. In addition, it is argued that Wayne's criticism of the correlation approach does not indicate a serious flaw in the approach. (shrink)

Theorising Education shows basic theoretical moves for the educational imagination by stripping each move down to its most elementary function. The author opens out five basic theoretical moves - each one able to be used with the others, so that, by the end of the book, you will have the beginnings of a theoretical tool kit. This tool kit will enable you to imagine possible educational worlds different from ones you may have already encountered. A first of its kind, Theorising (...) Education is for the person who wants to learn how to think about education in an active, imaginative and systematic way."--Publisher's website. (shrink)

A shift in focus, of the sort recently advocated by David Wallace, towards consideration of work in nonequilibrium statistical mechanics has the potential for far-reaching consequences in the way we think about the foundations of statistical mechanics. In particular, consideration of the approach to equilibrium helps to pick out appropriate equilibrium measures, measures that are picked out by the dynamics as "natural' measures for systems in equilibrium. Consideration of the rationale for using such measures reveals that the scope of their (...) legitimate employment is much more limited than an appeal to a Principle of Indifference would suggest. These points are illustrated by use of a toy model that I call the parabola gadget. (shrink)

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1952.