This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device and the quality of the programs it learns successfully. There are results to the effect that, thanks to small increases in generality of a learning device, the computational complexity of some successfully learned programs is provably unalterably suboptimal. There are also results in which the complexity of successfully learned programs is asymptotically optimal and the learning device is general, but, still thanks to the generality, some of (...) those optimal, learned programs are provably unalterably information deficient—in some cases, deficient as to safe, algorithmic extractability/provability of the fact that they are even approximately optimal. For these results, the safe, algorithmic methods of information extraction will be by proofs in arbitrary, true, computably axiomatizable extensions of Peano Arithmetic. (shrink)

Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, equation image. Other cases are done for all transfinite notations in a very natural, proper subsystem equation image of equation image, where equation image (...) has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in equation image. (shrink)

John MacFarlane explores how we might make sense of the idea that truth is relative. He provides new, satisfying accounts of parts of our thought and talk that have resisted traditional methods of analysis, including what we mean when we talk about what is tasty, what we know, what will happen, what might be the case, and what we ought to do.

Recent reports of the discovery of a “God module” in the human brain derive from the fact that epileptic seizures in the left temporal lobe are associated with ecstatic feelings sometimes described as an experience of the presence of God. The brain area involved has been described as either (a) the seat of an innate human faculty for experiencing the divine or (b) the seat of religious delusions.In fact, religious experience is extremely various and involves many parts of the brain, (...) including some that are prehuman in their evolutionary history and some that are characteristically human. In the continuing integration of such experiences, spiritual formation takes place. Thus the entire human brain might be described as a “God module.”Such a process is only possible because of the brain's complexity. The human brain is the most complex entity for its size that we know of. As used here, complexity is a specialized term denoting the presence of a web of interlinked and significant connections—the more intricate the web, the more complex the entity. Complex systems develop only in a milieu that provides both lawfulness and freedom, and they tend to be self‐organizing, becoming more complex and more effective as a result of both inward and outward experience. The evidence suggests that both personal growth and spiritual growth are processes of complexification of character, and of the brain itself. This thesis is tested in light of the work of William James and James W. Fowler. (shrink)

A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central (...) topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

R.W. Ashby maintained that people and animals do not have to remember as much as one might think since considerable information is stored in the environment. Presented herein is an everyday, quantitative example featuring calculation of the number bits of memory that can be off-loaded to the environment. The example involves one’s storing directions to a friend’s house. It is also argued that the example works with or without acceptance of the extended mind hypothesis. Additionally, a brief supporting argument for (...) at least a form of this hypothesis is presented. (shrink)

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. (...) Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight. (shrink)

“Gettier cases” have played a major role in Anglo-American analytic epistemology over the past fifty years. Philosophers have grouped a bewildering array of examples under the heading “Gettier case.” Philosophers claim that these cases are obvious counterexamples to the “traditional” analysis of knowledge as justified true belief, and they treat correctly classifying the cases as a criterion for judging proposed theories of knowledge. Cognitive scientists recently began testing whether philosophers are right about these cases. It turns out that philosophers (...) were partly right and partly wrong. Some “Gettier cases” are obvious examples of ignorance, but others are obvious examples of knowledge. It also turns out that much research in this area of philosophy is marred by experimenter bias, invented historical claims, dysfunctional categorization of examples, and mischaracterization by philosophers of their own intuitive judgments about particular cases. Despite these shortcomings, lessons learned from studying “Gettier cases” are leading to important insights about knowledge and knowledge attributions, which are central components of social cognition. (shrink)

A generator program for a computable function (by definition) generates an infinite sequence of programs all but finitely many of which compute that function. Machine learning of generator programs for computable functions is studied. To motivate these studies partially, it is shown that, in some cases, interesting global properties for computable functions can be proved from suitable generator programs which cannot be proved from any ordinary programs for them. The power (for variants of various learning criteria from the literature) of (...) learning generator programs is compared with the power of learning ordinary programs. The learning power in these cases is also compared to that of learning limiting programs, i.e., programs allowed finitely many mind changes about their correct outputs. (shrink)

When we say that someone knows something we are making a value judgment—we are saying that there is something intellectually good or right about the person’s belief, or about the way she believes it, or perhaps about her. We are saying, for example, that her belief is intellectually better than someone else’s mere opinion. Notice that we might make this sort of value judgment even if the two persons agree. Suppose that two people agree that the earth is the third (...) planet from the sun. Nevertheless, we might think that one person knows this while the other person merely believes it. If so, we are making a value judgment—we are saying that there is something intellectually better going on in the case of knowledge. Another way to put the point is to say that knowledge is a normative notion. There is something normatively better about the case of knowledge, as opposed to the case of mere opinion, or even the case of true opinion. Finally, saying that someone knows something is not the only sort of value judgment we can make about her belief. Even if we agree that some belief falls short of knowledge, we might nevertheless judge that it is justified, or rational, or reasonable, or responsible. In each such case, we are saying that there is something normatively better about the case in question, as opposed to the case of mere opinion, or even the case of true opinion. (shrink)

Knowledge sets the standard for appropriate assertion and recent evidence suggests that it might also set the standard for appropriate belief and decision‐making. Governments spend hundreds of millions of dollars to support the creation, transfer, and mobilization of knowledge. Philosophers have created a dizzying array of Gettier case thought experiments. In doing so, many have been guilty of experimenter bias. This includes some original players who helped set the agenda for decades to come. Cognitive scientists recently began seriously investigating (...) knowledge judgments. The study of Gettier cases was motivated by work in psychology showing important cultural differences in reasoning styles and moral judgments. The nominal category Gettier case includes a variety of cases with radical structural differences that are extremely important in both theory and ordinary practice, so important as to render the nominal category, as the authors have inherited it, utterly useless. (shrink)

We investigate a new paradigm in the context of learning in the limit, namely, learning correction grammars for classes of computably enumerable (c.e.) languages. Knowing a language may feature a representation of it in terms of two grammars. The second grammar is used to make corrections to the first grammar. Such a pair of grammars can be seen as a single description of (or grammar for) the language. We call such grammars correction grammars. Correction grammars capture the observable fact that (...) people do correct their linguistic utterances during their usual linguistic activities. We show that learning correction grammars for classes of c.e. languages in the TxtEx-model (i.e., converging to a single correct correction grammar in the limit) is sometimes more powerful than learning ordinary grammars even in the TxtBe-model (where the learner is allowed to converge to infinitely many syntactically distinct but correct conjectures in the limit). For each n ≥ 0, there is a similar learning advantage, again in learning correction grammars for classes of c.e. languages, but where we compare learning correction grammars that make n + 1 corrections to those that make n corrections. The concept of a correction grammar can be extended into the constructive transfinite, using the idea of counting-down from notations for transfinite constructive ordinals. This transfinite extension can also be conceptualized as being about learning Ershov-descriptions for c.e. languages. For u a notation in Kleene's general system $(O,\, < _o )$ of ordinal notations for constructive ordinals, we introduce the concept of an u-correction grammar, where u is used to bound the number of corrections that the grammar is allowed to make. We prove a general hierarchy result: if u and v are notations for constructive ordinals such that $u\, < _o \,v$ , then there are classes of c.e. languages that can be TxtEx-learned by conjecturing v-correction grammars but not by conjecturing u-correction grammars. Surprisingly, we show that— above "ω-many" corrections—it is not possible to strengthen the hierarchy: TxtEx-learning u-correction grammars of classes of c.e. languages, where u is a notation in O for any ordinal, can be simulated by TxtBe-learning ω-correction grammars, where ω is any notation for the smallest infinite ordinal ω. (shrink)

What is it reasonable to believe about our most successful scientific theories such as the general theory of relativity or quantum mechanics? That they are true, or at any rate approximately true? Or only that they successfully ‘save the phenomena’, by being ‘empirically adequate’? In earlier work I explored the attractions of a view called Structural Scientific Realism (hereafter: SSR). This holds that it is reasonable to believe that our successful theories are (approximately) structurally correct (and also that this is (...) the strongest epistemic claim about them that it is reasonable to make). In the first part of this paper I shall explain in some detail what this thesis means and outline the reasons why it seems attractive. The second section outlines a number of criticisms that have none the less been brought against SSR in the recent (and as we shall see, in some cases, not so recent) literature; and the third and final section argues that, despite the fact that these criticisms might seem initially deeply troubling (or worse), the position remains viable. (shrink)

Experiences of embodied remembering are familiar and diverse. We settle bodily into familiar chairs or find our way easily round familiar rooms. We inhabit our own kitchens or cars or workspaces effectively and comfortably, and feel disrupted when our habitual and accustomed objects or technologies change or break or are not available. Hearing a particular song can viscerally bring back either one conversation long ago, or just the urge to dance. Some people explicitly use their bodies to record, store, or (...) cue memories. Others can move skilfully, without stopping to think, in complex and changing environments thanks to the cumulative expertise accrued in their history of fighting fires, or dancing, or playing hockey. The forms of memory involved in these cases may be distinct, operating at different timescales and levels, and by way of different mechanisms and media, but they often cooperate in the many contexts of our practices of remembering. (shrink)

The doctrine of precedent, as it has evolved within the common law, has at its heart a form of reasoning—broadly speaking, alogic—according to which the decisions of earlier courts in particular cases somehow generalize to constrain the decisions of later courts facing different cases, while still allowing these later courts a degree of freedom in responding to fresh circumstances. Although the techniques for arguing on the basis of precedent are taught early on in law schools, mastered with relative ease, and (...) applied on a daily basis by legal practitioners, it has proved to be considerably more difficult to arrive at a theoretical understanding of the doctrine itself—a clear articulation of the underlying logic. (shrink)

How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as Lorenzo Valla and (...) Rudolph Agricola, Paduan Aristotelians such as Agostino Nifo, Jacopo Zabarella, and members of the medical faculty, writers on philosophy of mind such as the Englishman John Case, writers of reasoning handbooks, and Francis Bacon. (shrink)

“Interpretation” is a term that encompasses both the most esoteric and the most fundamental activities of our lives, from analyzing medical images to the million ways we perceive other people’s actions. Today, we also leave interpretation to the likes of web cookies, social media algorithms, and automated markets. But as John Frow shows in this thoughtfully argued book, there is much yet to do in clarifying how we understand the social organization of interpretation. On Interpretive Conflict delves into four (...) case studies where sharply different sets of values come into play—gun control, anti-Semitism, the religious force of images, and climate change. In each case, Frow lays out the way these controversies unfold within interpretive regimes that establish what counts as an interpretable object and the protocols of evidence and proof that should govern it. Whether applied to a Shakespeare play or a Supreme Court case, interpretation, he argues, is at once rule-governed and inherently conflictual. Ambitious and provocative, On Interpretive Conflict will attract readers from across the humanities and beyond. (shrink)

Makes the case that the different stances Aristotle and Socrates take toward politics can be traced to their divergent accounts of friendship.

Depth Calls to Depth: Jungian Psychology and Spiritual Direction in Dialogue draws on the author's dual background as a certified Jungian analyst and psychologist as well as a spiritual director with a master's degree in theology. Over the last several decades, spiritual direction has moved beyond its monastic origins to become a major force in contemporary spirituality. Its emphasis on direct spiritual experience offers a natural parallel to Jung's model of psychospiritual healing. This book describes how Jungian dreamwork can enhance (...) the practice of spiritual direction. There is much interest in Jung's thought in spiritual circles but little informed understanding of the details of his model and its application to work with individuals. In an effort to meet this need, chapters alternate between descriptions of Jung's approach, augmented by extensive case material and accounts of spiritual direction sessions. In this way, the book combines a comprehensive summary of Jung's main ideas and methodologies with vignettes that illustrate their practical application. Larger issues regarding the relationship between psychology and spirituality are discussed as well as Jung's complicated relationship with the Christian tradition. The author's background in Ignatian spirituality and the work of mystics like Meister Eckhart allow him to demonstrate how these approaches can bridge gaps between the Christian and Jungian models of spiritual growth. Parallels to 12-Step spirituality also are explored. (shrink)

There is a limited understanding amongst scientists, students and the public about realizing trust in scientific findings. This should be a paramount objective, or is it only about career ambition? What is the role of the individual? Scientists and the public need to know more about the link between the philosophy of science and the science research methods. There is a limited understanding of why accuracy is important and that it is not the same as precision. Also, there is often (...) the need to measure an approximation of a real system and the classic case is reductionism in biology versus whole organism biology. The author brings these topics together in terms of trusting in science. (shrink)

Exposing and illustrating how an ongoing engagement with nihilistic alienation may contribute to, rather than detract from, the value of life, Cinematic Nihilism both challenges and builds upon past scholarship that has scrutinised nihilism in the media, but which has generally over-emphasisedits negative and destructive aspects. Through case studies of popular films, including Prometheus, The Dark Knight Rises, Dawn of the Dead and The Human Centipede, and with chapters on Scotland's cinematic portrayal as both a site of "nihilistic sacrifice" (...) and as "nowhere in particular", this bookpresents a necessary corrective, re-emphasising the constructive potential of cinematic nihilism and casting it as a phenomenon that need not be overcome. (shrink)

I set out the factors which tempt people into reading Ernst Mach's book The Analysis of Sensations as putting forward either a version of phenomenalism or a version of neutral monism, and then assess the strengths and weaknesses of these two readings. I present an ‘internal’ view of that text, showing that it by no means mandates the phenomenalist reading, and that a case for something more like the neutral monist reading can be made from within that book, indeed (...) largely from within its famous first chapter. (shrink)

In this paper I present a variant of the “Sleeping Beauty” case that shows that the “halfer” approach to the original Sleeping Beauty problem is incompatible with an extremely plausible principle pertaining to cases of disagreement. This principle says that, in “nonpermissive” contexts, the weight you give to a disputant’s view ought to be proportional to your estimation of the strength of the disputant’s epistemic position with respect to the disputed proposition. In requiring such proportionality, the principle denies the (...) possibility of what I will call “robustly perspectival” contexts. Given the plausibility and widespread acceptance of this principle, its incompatibility with the halfer approach to Sleeping Beauty gives us an apparently powerful new argument against the halfer position and for the alternative “thirder” view. But I am a halfer, not a thirder. So I go on to argue that despite the principle’s intuitive plausibility, there are good reasons for thinking that the case presented here does involve a robustly perspectival context and that the principle should be rejected. I suggest that the lesson that we should draw from this case is not that we should accept the thirder view, but rather that rationality can be perspectival in a robust way that many may find quite surprising. (shrink)

Principlism : the Borg of bioethics -- A common morality for hedgehogs : Bernard Gert -- Getting down to cases : the revival of casuistry in bioethics -- Nice story but so what : narrative and justification in ethics -- Dewey and Rorty's pragmatism and bioethics -- Freestanding pragmatism in bioethics and law -- A method in search of a purpose : the internal morality of medicine -- Method to rule them all? Reflective equilibrium in bioethics -- Concluding reflections : (...) method in bioethics : the very idea. (shrink)

Where do we find ourselves? -- Not with syllables but men -- Essaying America -- Living multiplicity: a matter of course -- Emerson, race, and the conduct of life -- Reforming ethical life -- Emerson and the case of philosophy -- Abbreviations for Emerson's works.

This chapter contains sections titled: McCloud's Definition Pictures and Comics Panels, Panels Everywhere Seeing‐in and Closure Pictureless Comics? Wordless Prints, Unprinted Words Spaces Between Words The Air of Non‐Pictures A Continuum of Cases Comic Books and Ideal Books Notes References.

A powerful case for the importance of universities as an antidote to the “secular dogmatism” that increasingly infects political discourse John Sexton argues that over six decades, a “secular dogmatism,” impenetrable by dialogue or reason, has come to dominate political discourse in America. Political positions, elevated to the status of doctrinal truths, now simply are “revealed.” Our leaders and our citizens suffer from an allergy to nuance and complexity, and the enterprise of thought is in danger. Sexton sees (...) our universities, the engines of knowledge and stewards of thought, as the antidote, and he describes the policies university leaders must embrace if their institutions are to serve this role. Acknowledging the reality of our increasingly interconnected world—and drawing on his experience as president of New York University when it opened campuses in Abu Dhabi and Shanghai—Sexton advocates for “global network universities” as a core aspect of a new educational landscape and as the crucial foundation-blocks of an interlocking world characterized by “secular ecumenism.”. (shrink)

Things that don't exist -- Fictional object nominalism -- Fictional object realism -- Meinongianism -- God's existence and nonexistence -- Contingency and nonexistence -- Perfection and divine existence -- Nonexistence and creatures -- Ex nihilo and nonexistence -- Infinite existence and countless nonexistents -- Providence and freedom -- Nonexistents and middle knowledge -- Evil as nonexistence.

A fascinating book demonstrating the influence of alchemy and esoteric traditions on the mature art of Marcel Duchamp.

_A groundbreaking examination of a central question in international relations: Do states act rationally?_ To understand world politics, you need to understand how states think. Are states rational? Much of international relations theory assumes that they are. But many scholars believe that political leaders rarely act rationally. The issue is crucial for both the study and practice of international politics, for only if states are rational can scholars and policymakers understand and predict their behavior. John J. Mearsheimer and Sebastian (...) Rosato argue that rational decisions in international politics rest on credible theories about how the world works and emerge from deliberative decision‑making processes. Using these criteria, they conclude that most states are rational most of the time, even if they are not always successful. Mearsheimer and Rosato make the case for their position, examining whether past and present world leaders, including George W. Bush and Vladimir Putin, have acted rationally in the context of momentous historical events, including both world wars, the Cold War, and the post–Cold War era. By examining this fundamental concept in a novel and comprehensive manner, Mearsheimer and Rosato show how leaders think, and how to make policy for dealing with other states. (shrink)

The Intelligent Nation proposes a systemic and radical transformation of the organisation, management, ownership and performance of the services of the state by capitalising on the potential offered by contemporary information capability and fulfilling the rights and obligations both to and of citizens. In this book, John Beckford shows how, by adopting the principles of an intelligent organisation, the state can thrive and meet the needs of its citizens. He proposes a complete rethink of the state as the enabler (...) or provider of public services. In particular, he points to the failure of the public sector to significantly emulate the massive gains in productivity and customer focus experienced in both manufacturing and services (e.g. finance, retailing, insurance). Governance and all public services must be redesigned to align to the contemporary needs of the citizen and exploit the power of information to enable a transformation of their effectiveness, redefine efficiency, and support human-based services in crucial areas. Each chapter provides the key learning points, a discussion of the problem in theory and practice, integrated case studies, and discussion points. Written in an accessible style, the book provides thought-provoking supplemental reading for masters and undergraduate students reading organization theory, organization development, political science, public administration, healthcare, information systems, and business and management science. (shrink)