This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

Some philosophers have recently argued that contrary to the traditional view, good scientific theories can in fact be logically inconsistent. The literature is now full of case-studies that are taken to support this claim. I will argue however that as of yet no-one has managed to articulate a philosophically interesting view about the role of logically inconsistent theories in science that genuinely goes against tradition, is plausibly true, and is supported by any of the case studies usually given.

Abstract:Ratnākaraśānti (ca. 970–1040) holds three conflicting positions: luminosity (prakāśa) is the ultimately real nature of consciousness; luminosity and appearances (ākāras) are identical; and appearances are false (alīka) because they are targeted by the neither-one-nor-many argument. But why is luminosity not false, too, given its identity with appearances? In response to this worry, Ratnākaraśānti develops a notion of identity (tādātmya) that lets him claim that, although luminosity and appearance are composed of the same stuff, they are not identical in every respect. (...) On the basis of this, he limits the scope of the neither-one-nor-many argument such that it targets appearances but not luminosity. Other philosophers (and possibly Ratnākaraśānti himself) then further limit the argument's scope, showing that it also does not target experiences of pleasure (sukha) and, crucially for their buddhology, the innate bliss (sahajānanda) that characterizes the experience of buddhahood. (shrink)

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the (...) second law are merely artifacts of this questionable justification. *Received October 2006; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e-mail: [email protected]. (shrink)

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes (...) be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view. (shrink)

Gadamer's aesthetics demonstrates that the experience of art is grounded in the objectivities of language, history and tradition. By treating words and images as transmittable placeholders for meanings and concepts, hermeneutics gives a persuasive account of how artworks communicate. Davey demonstrates how hermeneutics transforms aesthetic reflection into a poignant attentive practice that is open to the unexpected. This new "poetics" is relevant not only to the understanding of art but also to showing, explaining and defending the cognitive content of (...) the humanities. Hermeneutic aesthetics provides a sound basis for re-thinking humanities disciplines as critical-creative practices able to re-envision the future. (shrink)

Although the inferring of explanations plays an important role in both our everyday lives and in the workings of science, I argue that inference to the best explanation as it is commonly conceived is often not the best way to capture this sort of reasoning. I suggest that a different form of reasoning – so-called immediate explanatory inference – is instead often much better suited to this task. This is a form of inference in which we are justified in believing (...) explanations for the evidence before us purely in virtue of this evidence, and not in virtue of the evidence plus some general principle or rule of non-deductive reasoning. I defend the idea of such a notion of inference, and argue that it plays a central role in both ordinary life and science. (shrink)

This paper considers Jñānaśrīmitra’s defense of manifestation as the criterion of ultimate existence. In the first section, "Asatkhyāti and Adhyavasāya: making sense of manifestation as the criterion of the real", I show the way that, in response to Ratnākaraśānti’s Nirākāravāda, Jñānaśrīmitra argues for a sharp distinction between manifestation and determination in an effort to establish that the manifestation of something unreal is incoherent. The unreal, he thinks, is only ever determined; it is never manifest to consciousness, properly speaking. In the (...) second section, “To be manifest is to be locked away in a single awareness-event”, I turn to one of the consequences of this view that Jñānaśrīmitra embraces: what manifests is only what appears in a single moment of conscious awareness. In the third section, “The scope of neither-one-nor-many: Jñānaśrīmitra’s Interpretation of PV 3.220–221”, I consider one of the problems this raises: how is it that an appearance with mutually opposed parts manifests in one and the same unitary moment of awareness? Jñānaśrīmitra solves this problem by appealing to the nature of manifestation and its distinction from determination: what is manifest, even if it is variegated, is nondual and indivisible; distinctions arise only on the basis of determination. I trace the details of this solution in the context of his discussion of an important pair of verses from Dharmakīrti. Finally, in the last section, “The marvelous nonduality of variegated awareness-events”, I turn to the surprising buddhological consequences of this solution. (shrink)

Most phobias are focussed on a small number of fear-inducing stimuli (e.g., snakes, spiders). A review of the evidence supporting biological and cognitive explanations of this uneven distribution of phobias suggests that the readiness with which such stimuli become associated with aversive outcomes arises from biases in the processing of information about threatening stimuli rather than from phylogenetically based associative predispositions or “biological preparedness.” This cognitive bias, consisting of a heightened expectation of aversive outcomes following fear-relevant stimuli, generates and maintains (...) robust learned associations between them. Some of the features of such stimuli which determine this expectancy bias are estimates of how dangerous they are, the semiotic similarity between them and their aversive outcomes, and the degree of prior fear they elicit. Ontogenetic and cultural factors influence these features of fear-relevant stimuli and are hence important in determining expectancy bias. The available evidence does not exclude the possibility that both expectancy biases and specific evolved predispositions coexist, but the former can explain a number of important findings that the latter cannot. (shrink)

Although the canonical distribution is one of the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. This is due in part to the fact that there is no clear consensus on what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. I examine some traditional views as to what sort of thing we should take the canonical distribution to represent. I argue that a less explored alternative, according (...) to which the canonical distribution represents a time ensemble of sorts, has a number of advantages that rival interpretations lack. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e‐mail: [email protected]. (shrink)

Recently, a new problem has arisen for an Anscombean conception of intentional action. The claim is that the Anscombean’s emphasis on the formally causal character of practical knowledge precludes distinguishing between an aim and a merely foreseen side effect. I propose a solution to this problem: the difference between aim and side effect should be understood in terms of the familiar Anscombean distinction between acting intentionally and the intention with which one acts. I also argue that this solution has advantages (...) over an alternative that has already been endorsed in the literature: it is a better fit for the Anscombean theory, and it naturally accommodates intuitions about the moral significance of aiming vs. merely foreseeing. (shrink)

The present book is true to its title. A collection of articles that stems from a symposium of the same name at the University of Hamburg in 2017, the authors here bring different perspectives to bear on the philosophical and historical relations between Buddhism and scepticism. Though this is relatively well-trodden ground, the insightful studies here shed new light on the matter. We find historical studies of the possible links between Pyrrhonism and Buddhism ; a defense of Nāgārjuna's philosophical scepticism (...) as of the Pyrrhonian variety ; considerations of the role of sceptical doubt in less expected places, such as in Dharmakīrti's and Vasubandhu's... (shrink)

Recent studies of spider phobia have indicated thatfearof spiders is closely associated with the disease-avoidance response of disgust. It is argued that the disgust-relevant status of the spider resulted from its association with disease and illness in European cultures from the tenth century onward. The development of the association between spiders and illness appears to be linked to the many devastating and inexplicable epidemics that struck Europe from the Middle Ages onwards, when the spider was a suitable displaced target for (...) the anxieties caused by these epidemics. Such factors suggest that the pervasive fear of spiders that is commonly found in many Western societies may have cultural rather than biological origins, and may be restricted to Europeans and their descendants. (shrink)

How do words and images function hermeneutically? How does hermeneutic practice work? Answering these questions and more, Nicholas Davey develops the hermeneutical foundations of creative practice. In doing so, he not only uncovers the significance of philosophical hermeneutics for the arts and the humanities, but defends the humanities as a whole from the current scepticism inspired by deconstruction and post-structuralism. Taking Gadamer's language ontology as its cue, this pioneering volume not only addresses certain weaknesses that Davey observes in (...) Gadamer's thought but further takes Gadamerian thinking beyond Gadamer himself. In particular, Davey investigates the productive value of negativity that is central to hermeneutics and to wider spheres of creative learning. Advocating a renewed confidence in hermeneutics and the humanities, Negative Hermeneutics and the Question of Practice reveals how hermeneutical thinking provides a map of the dynamics within creative practice, eliminating the need for an externally imposed 'theory' of the arts. (shrink)

The conflicting positions of the two early eleventh century Yogācāra scholars, Ratnākaraśānti and his critic Jñānaśrīmitra, concerning whether or not consciousness can exist without content are inseparable from their respective understandings of enlightenment. Ratnākaraśānti argues that consciousness can be contentless —and that, for a buddha, it must be. Mental content can be defeated by reasoning and made to disappear by meditative cultivation, and so it is fundamentally distinct from the nature of consciousness, which is never defeated and never ceases. That (...) mental content is thus separable from the nature of consciousness is unimaginable to Jñānaśrīmitra, who argues that all mental content cannot be so defeated, nor can it disappear completely, and who concludes that Ratnākaraśānti’s commitment to this idea can be based on nothing but faith. Contra Jñānaśrīmitra, I will suggest that Ratnākaraśānti’s view is based not only on faith, but is also driven by a certain theory of buddhahood, the implications of which he is committed to working out. Because Ratnākaraśānti’s theory of buddhahood is developed in part in his tantric work, our understanding of his position benefits from our reading it in this context, wherein buddhahood and the most effective techniques for attaining it are explored. (shrink)

Anyone who has ever worked with a variety \ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one—but until now there has been no abstract definition. Here we provide one. After deriving some basic properties of a restricted Priestley dual category \ of such a variety, we give a characterisation, in terms of \, of finitely generated discriminator subvarieties of \. As an application of our characterisation, we (...) give a new proof of Sankappanavar’s characterisation of finitely generated discriminator varieties of distributive double p-algebras. A substantial portion of the paper is devoted to the application of our results to Cornish algebras. A Cornish algebra is a bounded distributive lattice equipped with a family of unary operations each of which is either an endomorphism or a dual endomorphism of the bounded lattice. They are a natural generalisation of Ockham algebras, which have been extensively studied. We give an external necessary-and-sufficient condition and an easily applied, completely internal, sufficient condition for a finite set of finite Cornish algebras to share a common ternary discriminator term and so generate a discriminator variety. Our results give a characterisation of discriminator varieties of Ockham algebras as a special case, thereby yielding Davey, Nguyen and Pitkethly’s characterisation of quasi-primal Ockham algebras. (shrink)

This paper explores the philosophical stakes of eighth–twelfth-century Sanskrit debates about tantric initiation ( abhiṣeka ). I propose that three models of tantric initiation emerged in this period, in part in response to the Dharmakīrtian model of the gradual development of yogic perception. According to one, the true glimpse view, initiation gives a glimpse of precisely the experience of buddhahood, which is then made firm in post-initiatory practice. According to another, the exemplary glimpse view, the initiatory glimpse is only exemplary (...) of what buddhahood is like. Post-initiatory practice is necessary to transform the practitioner's attitude toward that glimpse, which eventually results in an experience of buddhahood itself. Finally, others advanced a no glimpse view: only the experience of reality itself in post-initiatory practice can result in an experience of buddhahood. I explore these three views through a close engagement with some representative texts from the period. (shrink)

To engage with the subtle philosophical implications of the hermeneutical term “lived experience” (Erlebnis) requires a referential differentiation not customary within Anglo‐Saxon empirical thought. Within Erlebnisse, the meaning of the terms understanding and experience become coterminous. In Gadamer's mind, “Erlebnis” is more a psychological category of experience whereas “Erfahrung” denotes a hermeneutical category of experience which explains its recursive nature. Epistemologically speaking, Erlebnisse represent circular units of experience. Erlebnisse understood as units of intense, immediate, personal feeling can only ever convey (...) the psychological predicament of the reading subject. Gadamer's philosophical language probes the limits of conventional usage when he implies that Erfahrungen would be better thought of as distinct occasions in ongoing processes of encounter, negotiation, and engagement. Gadamer's philosophy of Erfahrung exposes the arrogance, presumption, and folly of any claim to economic and political certainty that does not acknowledge or calculate for alternative outcomes. (shrink)

This paper was delivered at the 2009 annual conference of the National Council on Ethics in Human Research. It is a reflective piece based on many years of experience with human research ethics and the role of Research Ethics Boards in human participant research.

Why is it that even strong formal theories of truth fail to prove their own consistency? Although Field has addressed this question for many theories of truth, I argue that there is an important and attractive class of theories of truth that he omitted in his analysis. Such theories cannot prove that all their axioms are true, though unlike many of the cases Field considers, they do not prove that any of their axioms are false or that any of their (...) rules of inference are not truth preserving. I argue that it is the fact that such theories are not finitely axiomatizable that stops them from proving their own consistency. (shrink)

AimTo explore new mothers' knowledge of newborn screening, and their attitudes towards issues surrounding sample retention and the potential for blood screening samples to be used for research.MethodsA self-administered mail survey was sent to women who gave birth in Perth, Western Australia during January 2005. A total of 600 women completed the survey.ResultsIt was found that women were aware of newborn screening, however desired further information in order to acquire a more comprehensive knowledge of the test. Further, women reported discomfort (...) with the long-term storage of cards, but they were supportive of using blood samples for medical research, contingent upon the samples being de-identified and parental consent provided.ConclusionsNew mothers need to be provided with comprehensive information about the newborn screening test at a time which is conducive for the assimilation of this information. In addition, whilst supporting health related research using newborn screening samples, new mothers are keen for ethical issues to be sufficiently addressed prior to samples being systematically stored for extended periods of time. (shrink)

It is often supposed that we can use mathematics to capture the time evolution of any physical system. By this, I mean that we can capture the basic truths about the time evolution of a physical system with a set of mathematical assertions, which can then be used as premises in arbitrary mathematical arguments to deduce more complex properties of the system. ;I would like to argue that this picture of the role of mathematics in physics is incorrect. Specifically, I (...) shall assert: ;The Deduction Failure Thesis: Bodies of knowledge in physics are generally not closed under otherwise valid mathematical argument forms. ;The Representation Failure Thesis: We cannot assume that the state of any system, together with its fundamental laws, can be captured by some set of mathematical assertions or equations. In fact, it is more likely that the world is not representable by a set of mathematical assertions or equations than that it is. ;The dissertation largely consists of arguments for these two theses. (shrink)

Describing a physical system in idealized terms involves making claims about the system that we know to be literally false. Because of this, it is not clear how calculations involving idealizations can generate justified belief and explain facts about the world. I argue that this puzzling aspect of idealizations cannot be explained away by talking about approximations, as is often supposed. I develop a different account of how justified beliefs and explanations can be generated from idealized descriptions of physical systems. (...) My account involves a type of contextualism about the truth of mathematical descriptions of physical systems. (shrink)

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fundamentally flawed, and will show that some puzzles sometimes associated with the second (...) law are merely artifacts of this incorrect justification. (shrink)

A series of arguments are presented by De Jong & Merckelbach which suggest that biological preparedness has been received significantly less critically than it should have been. I agree fully with their assessment. Cuthbert raises four questions about the applicability of the expectancy bias hypothesis to selective associations in human conditioning. This response argues that none of these four examples is necessarily problematic for the hypothesis.

Although canon-formation is, as Lecker suggests, a product of rhetoric and textual choices of critics, it is also a product of economic forces, political conflicts, and cultural expectations of coherence, “order,” and unitary explanation. Conditioned by some or all of these, an essay ostensibly skeptical of canons, as this one appears to be, can find itself nevertheless contributing to the thing it questions. In attempting to attribute the formation of a single national canon to a specific period , to a (...) specific and allegedly homogeneous group of actors , and to a specific social phenomenon , Lecker’s essay becomes another constructor of canonical text and theory. Behind its arguments that a canon suddenly came into being are fairly precise assumptions not only about “Canadian critics” but also about what constitutes canonicity, and about the relative legitimacy of canonicity claims. “At the end of World War II, Canadian literature was not taught as an independent subject in Canadian schools. There was no canon,” his essay begins . Is a school curriculum the only possible context for the attainment of literary “legitimacy”? Can there be no canon if a literature has no curriculum, education publishers, or “academic critics,” or if it has not been institutionalized as an “independent” subject? Frank Davey, chair of the department of English at York University, is the author of From There to Here: A Guide to English Canadian Literature Since 1960 , Surviving the Paraphrase , Margaret Atwood: A Feminist Poetics , and Reading Canadian Reading . He is also the editor of Open Letter and the on-line magazine Swiftcurrent. He is currently working on a study of nationalist ideologies in Canadian fiction entitled National Arguments. (shrink)

Can we acquire apriori knowledge of mathematical facts from the outputs of computer programs? People like Burge have argued (correctly in our opinion) that, for example, Appel and Haken acquired apriori knowledge of the Four Color Theorem from their computer program insofar as their program simply automated human forms of mathematical reasoning. However, unlike such programs, we argue that the opacity of modern LLMs and DNNs creates obstacles in obtaining apriori mathematical knowledge from them in similar ways. We claim though (...) that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them after all, even though the original machines are entirely opaque to us and the proofs they output may not, themselves, be human-surveyable. (shrink)