The paper begins as a response to Tom Rockmore's thesis that contemporary pragmatism is a healthy “confusion” of disparate views. While Rockmore sees the need of some of today's pragmatists to provide a motivation for what he calls “epistemic optimism,” I contend that the crucial question of pragmatism, the problem of pragmatism, is the ontological status of pragmatic meaning. Thus rather than a mere “epistemic optimism,” I call upon pragmatists to assert a fallible yet unabashedly metaphysical optimism. The argument supporting (...) this claim is made in the context of Peirce's “The Architecture of Theories.” In “The Architecture of Theories” Peirce opens the door to a pragmatic metaphysics while at the same time committing the error of subordinating truths and reality to “the long run of inquiry.” Rockmore suggest that the solution may lie in a return to Kant's notion of the “powers of the mind.” However, it is my contention that a solution to this problem cannot be found within Kant at all. I shall argue here that until contemporary pragmatism decisively extracts itself from the Kantian paradigm, the pragmatic philosophic value of pragmatic meaning will always be qualified, conditional and ontologically subordinated, having the same effect upon the standing of pragmatism as a philosophy as well. Moreover, I shall endeavor to show that when the Kantian paradigm is finally abandoned, pragmatism's classic difficulties with realism and what Peircc called “the long run” of scientific inquiry can also be resolved. Kantian “powers of the mind” and constructivist “epistemological optimism” would then be transformed into what I shall call unrestricted pragmatism. On the other hand if the Kantian impediment is not overcome, these difficulties will continue to form the basis of a more sceptical and traditionally restricted pragmatism, one which lacks the confidence desired by both Rockmore and myself. (shrink)

ExtractIn a democracy people are free to express their opinions and question those of others. This is an important personal freedom, and also essential to the very idea of government by discussion. But it has also been held to be instrumentally important because in open public debate true ideas will conquer false ones by their merit, and the people will see the truth for themselves. In other words, democracy has an epistemic function as a kind of truth machine. From this (...) it follows that in a democracy there should be no dogma: no knowledge protected from public challenge and debate. Yet this whole argument is founded on embarrassing misconceptions of the nature of truth and of the working of democracy.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.DEMOCRACY IS NOT A TRUTH MACHINEVolume 12, Issue 33Thomas WellsDOI: https://doi.org/10.1017/S1477175612000309Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. DEMOCRACY IS NOT A TRUTH MACHINEVolume 12, Issue 33Thomas WellsDOI: https://doi.org/10.1017/S1477175612000309Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. DEMOCRACY IS NOT A TRUTH MACHINEVolume 12, Issue 33Thomas WellsDOI: https://doi.org/10.1017/S1477175612000309Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

Rachel Wells turns to the examination of three recent artistic practices, which integrate facts in their work not as an antagonistic other but as a constitutive element to their efficacy and ethics. She argues, that in introducing news, factual actions, or objects with traces of factual events, Alfredo Jaar, Jeremy Deller and Martin Creed use facts in order to retract from the position of art as an expression of artistic freedom and subjectivity and thus as the opposite of fact. Instead, (...) she states that by introducing the factual the artists underline each in their own way the instability of given eptistemological and ethical frameworks. Far from being a mere relativist pose, Wells understands this denial of a stable subjectivist position as a reconfigured sense of “decision”—perhaps in the sense of Nancy’s articulation of a “decision of existence—that lets the factual take precedence over the control in and of the artwork as a heightened form of responsiveness and responsibility. Whereas Jaar uses the factual to engage overt political action, Deller presents facts that avoid taking an overtly critical perspective forcing the viewer to think about political events. Creed in contrast seeks for the interpretation of the past altogether, would avoid to take over the responsibility of taking a position. Whereas David Hume stated famously, that reasoning concerning matter of fact is founded in causality and Immanuel Kant concludes, that responsibility and freedom begins where causality ends, Wells understands the positions of Jaar, Deller and Creed as an attempt to reconcile the realm of the factual and the realm of the moral. Responsibility would then arise exactly out of the insight in the impossibility to ground moral stances in rationality and causality and in an attempt to use causality to demonstrate this impossibility. (shrink)

The book shares Žižek's central problem of how to revitalize the radical political left through theory. It initially follows the argument developed in The Ticklish Subject that contemporary leftist thought is divided by antagonism between a Marxist revolutionary politics founded on Enlightenment philosophy and a politics of identity founded on post-modern post-structuralism. How Žižek used Lacan's theory of character structures is examined here to describe this theoretical deadlock and explain how the dominant contemporary ideologies of liberal tolerant multiculturalism (...) and reactionary "pseudo-fundamentalism" compete to mobilize the individual subject's unconscious drive to enjoyment. The book thus emphasizes the moments in which Žižek hints that Lacanian theory may describe a practice that facilitates the resolution of antagonisms that placate radical leftist politics. It challenges prevalent interpretations of Lacanian ends of analysis, to ultimately connect the psychoanalytic cure to the leftist project of social and political liberation. The Subject of Liberation argues that if Lacan is to be useful to leftist politics, then the left has to develop its own definitions of the post-analytic subject, and proposes one such definition developed out of Lacanian and Zizekian theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 22 (2002) 127-131 [Access article in PDF] Beyond the Usual Alternatives in Buddhist-Christian Dialogue: A Trinitarian Pluralist Approach Harry L. Wells Humboldt State University When I was first asked to present this paper, I was concerned about the assignment —"Beyond the Usual Alternatives." I was told that the usual alternatives were exclusivism, inclusivism, and pluralism. I consider myself a pluralist, so how was I to go beyond (...) what I thought was the best paradigm? But I must make clear that I am a pluralist in the camp of Raimundo Panikkar and not of John Hick, the latter's approach being one that Panikkar has clearly "gone beyond" in my estimation. While pondering the dilemma of how to approach this paper, I auspiciously reencountered the breathtaking profundity of early Christian writings on the nature of reality as Trinitarian. What I found there was an incredibly dynamic notion of reality that refuses to be reductionistic to dualistic modes of analysis. I will do two main things in this paper: I will discuss the Christian experience and understanding of "the mystery of the Living God," including the Trinity and the Christ. In doing this, I will draw upon the book The Roots of Christian Mysticism, by Olivier Clement (New York: New City Press, 1993), whose exposition of these things has been one of rare clarity and wisdom. I will then reflect upon how the Christian Trinitarian reality can serve as a Christian framework for understanding pluralism and interreligious dialogue. If these reflections manage to move us beyond our usual alternatives, it is because they capture a profundity that early Christians knew was eternal and among us. The Mystery of the Living God God is always hidden and universal. That is the mystery of the Living God. Because all things spring forth from God, the world both hides and reveals God's being. God's being is expressed in particular relations that both reveal and conceal; God's being can never be objectified, though it is the horizon in which all things are situated. That is why we can only speak of the living God, as an encounter with God. As Clement points out: "The inexhaustible nature of transcendence is expressed in the profusion of creatures. The universe is the first Bible. Each being manifests the creative word [End Page 127] [the Logos of God] which gives it its identity and attracts it. Each being manifests a dynamic idea, something willed by God. Ultimately each thing is a created name of him who cannot be named" (Clement, p. 27).But to say "willed by God" in a Christian context does not mean a closed monotheism, with a notion of Supreme Being existing objectively independent of the creation. In its very heart, Christianity says God is inexhaustible communion.Dionysius the Areopagite, a pseudonym of an early-fifth-century Christian writer, wrote a treatise called "Divine Names." In it, he speaks of how from all eternity, God lives and reigns in glory, with each ray of glory being a divine Name, and these Names are innumerable. Early Christian writers spoke of these as the powers or energies that spring forth from the unapproachable nature of God that give each created reality, or each emerging manifestation, both its density and transparency. In other words, all things spring forth within God and are modes of the divine presence, receiving its density or particular identity, while clearly being transparent, arising in God. Each creature, each entity names in its own peculiar fashion the divine Names. To say, "from all eternity, God lives and reigns in glory" is to recognize that the very inexhaustible communion that is the cosmos arises from all eternity in the very nature of God. As Gregory Nazianzen proclaims in his work "Dogmatic Poems":... Everything that exists prays to thee And to thee every creature that can read thy universe Sends up a hymn of silence. In thee alone all things dwell. With a single impulse all things find their goal in thee. Thou art the purpose of every creature. Thou art... (shrink)

We are pleased to annouce that God’s Companions by Samuel Wells has been shortlisted for the 2007 Michael Ramsey Prize for theological writing. www.michaelramseyprize.org.uk Grounded in Samuel Wells’ experience of ordinary lives in poorer neighborhoods, this book presents a striking and imaginative approach to Christian ethics. It argues that Christian ethics is founded on God, on the practices of human community, and on worship, and that ethics is fundamentally a reflection of God's abundance. Wells synthesizes dogmatic, liturgical, ethical, scriptural, (...) and pastoral approaches to theology in order to make a bold claim for the centrality of the local church in theological reflection. He considers the abundance of gifts God gives through the practices of the Church, particularly the Eucharist. His central thesis, which governs his argument throughout, is that God gives his people everything they need to worship him, be his friends, and eat with him. Wells engages with serious scholarly material, yet sets out the issues lucidly for a student audience. (shrink)

Cytogenetic research has had a major impact on the field of reproductive medicine, providing an insight into the frequency of chromosomal abnormalities that occur during gametogenesis, embryonic development and pregnancy. In humans, aneuploidy has been found to be relatively common during fetal life, necessitating prenatal screening of high‐risk pregnancies. Aneuploidy rates are higher still during the preimplantation stage of development. An increasing number of IVF laboratories have attempted to improve pregnancy rates by using preimplantation genetic diagnosis (PGD) to ensure that (...) the embryos transferred to the mother are chromosomally normal. This paper reviews some of the techniques that are key to the detection of aneuploidy in reproductive samples including comparative genomic hybridization (CGH). CGH has provided an unparalleled insight into the nature of chromosome imbalance in human embryos and polar bodies. The clinical application of CGH for the purposes of PGD and the future extensions of the methodology, including DNA microarrays, are discussed. BioEssays 25:289–300, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Bishop John A.T. Robinson's Honest to God was exceptionally successful. In the decade following its publication more than a million copies were sold in seventeen different languages. Robinson was aware that numerous awkward questions were being asked about traditional Christian beliefs, which it was no longer possible to ignore. His purpose was not so much to question traditional ideas of God as to suggest alternatives for those who found them unsatisfactory . He wanted to convince such persons that an inability (...) to believe what is stated in the Bible or the prayer book does not disqualify them from calling themselves Christians and presenting themselves at church. He speaks of traditional Christian beliefs, as stated in the New Testament, as a ‘language’ and thinks that Christianity should be conveyed to people in a variety of languages. By employing, as he does, the language of such Christian scholars as Bonhoeffer, Tillich and Bultmann, an atheist may find himself able to call himself a Christian. But the old familiar language of the Bible remains more pleasing to most of God's children, particularly to his ‘older children’ , so we must not give it up, although he allows that it is becoming increasingly unpopular, so that without ‘the kind of revolution’ he is advocating, ‘Christian faith and practice … will come to be abandoned’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Life as Dialogue:Remembering RogerHarry WellsI first met Roger when we both attended a colloquium on "Buddhist Thought and Culture" at the University of Montevello, Alabama, in April 1988. Roger read a paper that was thoroughly engaging, called "Becoming a Dialogian: How to do Buddhist-Christian Dialogue without Really Trying." At that point, I was hooked on getting to know this funny little man with a British accent who could deliver (...) an excellent reflection without being bothered by his occasional stammering.What struck me about Roger's paper was that it was meant to engage the one who heard it. It was written with a sense of interpretive transparency—a reflection on experience that was his own but also bigger than his own. It was one of those times where in hearing the account of his experience, one found one's own experience mirrored and affirmed. The paper was an autobiographical reflection on his journey into the interior ambiguity of interreligious dialogue, which at times can be very challenging when one tries truly to listen deeply to the visions of two distinct religious traditions. But his life was testament to the integrity of the journey and to an emergent overarching trust, or faith, that something very real and true was being birthed in the midst of it all.In the paper, which I use as an introductory essay for my Interreligious Dialogue course, he delightfully describes his boyhood "conversions" from one religious tradition to another in his own imagination as his pocket money purchases from Penguin Press "brought the world to my front door." One evening he emerges from his bedroom to inform his parents that he had become a Buddhist. "I had been reading all about it, I explained, and it was clear that I was already a Buddhist. It was as if I were remembering something from a past life. 'That's nice dear' commented my mother, 'have you finished your homework yet?' "He goes on to describe his theological studies, and his ever increasing grasp of, and being grasped by, the Eucharistic celebration. But he recounts:I was now in a quandary. Buddhism made sense to me, Meditation worked, and the Four Noble Truths seemed indeed to be true. But, now Christianity also made sense. In the Bible and the Mass some Power greater, more serene, and more loving than any other power I had known, was trying to contact me. Apparently, it was God, the same God, I presumed, that Buddhism denied.I did not know what to do, other than to be loyal somehow or another to what I had discovered, even though what I had discovered was self-contradictory. [End Page 157]The rest of the paper discusses his journey of that loyalty, becoming a Roman Catholic along the way, and later "the Buddhism erupted and demanded to be taken just as seriously as my Christianity."From that starting point twenty years ago, Roger and I shared our thoughts and reflections along the way at academic conferences and Buddhist-Christian dialogues. I always looked forward to hearing Roger speak, because he had a unique way of taking scholarship seriously by not being stuck in the mold of academic presentation. What I mean is this: Roger thoroughly researched what he was studying, but he is always studied for the engagement of life. As a result, his presentations were always lively in the best sense of that word—"alive," reflection seeking insight, and the "playful" embrace of living life within that insight.Here are some of the ways Roger impacted my life:• Roger taught me about "faith." He helped me learn to trust my experience of being compelled into interreligious experience, which takes immense effort and internal conflict initially but is a "burning in one's bones," to quote the prophet Jeremiah, for those called to be in that stance.• He taught me how to be a better teacher-scholar. He modeled for me the ability to present papers that were written to make a difference in the lives of those present, to connect with them in a way that led me and them to participate in insight as it was manifesting. Scholarship was... (shrink)

In 1952, Waldemar Gurian, founding editor of The Review of Politics, commissioned Eric Voegelin, then a professor of political science at Louisiana State University, to review Hannah Arendt’s recently published The Origins of Totalitarianism . She was given the right to reply; Voegelin would furnish a concluding note. Preceding this dialogue, Voegelin wrote a letter to Arendt anticipating aspects of his review; she responded in kind. Arendt’s letter to Voegelin on totalitarianism, written in German, has never appeared in print before. (...) She wrote two drafts of it, the first and longest being the more interesting. It contained an early reference to her thinking about the relationship among plurality, politics, and philosophy. It also invoked her notion of the compelling “logic” of totalitarian ideology. But this was not the letter Voegelin received. Because of this, he misunderstood significant parts of her argument. Below, the two versions of Arendt’s letter are translated. They are prefaced by a translation of Voegelin’s initial message to Arendt. An introduction compares Arendt’s letters, offers context, and provides a snapshot of Arendt’s and Voegelin’s perceptions of each other. Their views of political religion and human nature are also highlighted. Keyed to Arendt and Voegelin’s letters are pertinent aspects of the debate in The Review of Politics that followed their epistolary exchange. (shrink)

The two center time dependent Dirac equation, for an electron in the external field of two colliding ultrarelativistic heavy ions is considered. In the ultrarelativistic limit, the ions are practically moving at the speed of light and the electromagnetic fields of the ions are confined to the light fronts by the extreme Lorentz contraction and by the choice of gauge, designed to remove the long-range Coulomb effects. An exact solution to the ultrarelativistic limit of the two-center Dirac equation is found (...) by using light-front variables and a light-fronts representation. Previously unexplained experimental results obtained at CERN's SPS are explained in this way and predictions are made as to where one should look, in momentum space, and in space-time, if one wants to study and observe non-perturbative electromagnetic pair-production effects in extremely relativistic heavy-ion collisions. (shrink)

The expectation is fulfilled, but in an unexpected way. 'The first studies toward this book were addressed to topics in the field of ethics' ; but our author, like Wagner composing 'Der Ring des Nibelungen', found himself becoming preoccupied with prolegomena. To these the present volume is wholly devoted. In order to establish its fundamental thesis that valuation is a form of empirical knowledge, two preparatory discussions are called for. An analysis of empirical knowledge in general is one of these; (...) but there is an inquiry properly prior even to this, an examination of the topic of meaning. The articulation of the book is accordingly tripartite; and Book I Meaning and Analytic Truth, Book II Empirical Knowledge, and Book III Valuation are of roughly equal length. (shrink)

Introduction US data reveal a Caesarean rate discrepancy between insured and uninsured patients, with the C-section rate highest among the privately insured. The data have prompted concern that financial incentives associated with insurance status might influence American physicians' decisions to perform Caesarean deliveries. Objective To determine whether differences in medical risk factors account for the apparent Caesarean rate discrepancy between Medicaid and privately insured patients in Michigan, USA. Method A retrospective review was performed of 617 269 live birth deliveries in (...) Michigan hospitals during 2004–8. All live birth records that were able to be linked to their mothers' hospital discharge records were utilised. Diagnosis-related group codes from the hospitalisation records were used to identify Caesarean deliveries. Regression models determined Caesarean probability for the time period under study, adjusted for insurance type, maternal age, race, maternal medical conditions, multiple births, prematurity and birth weight. Results From 2004 to 2008, Caesarean rates were 33% for privately insured patients and 29% for Medicaid patients. The probability of Caesarean delivery was significantly greater for privately insured than Medicaid patients on univariate analysis (OR 1.2, 95% CI 1.19 to 1.22) but not on multivariate analysis (adjusted OR 1.01, 95% CI 0.99 to 1.02). Conclusion No significant disparity was found in the odds of Caesarean delivery between privately insured and Medicaid patients in Michigan after adjusting for other Caesarean risk factors. A positive disparity would have provided de facto evidence that financial incentives play a role in physician decision-making regarding Caesarean delivery. (shrink)

Research demonstrates that women experience disgust more readily and with more intensity than men. The experience of disgust is associated with increased attention to disgust-related stimuli, but no prior study has examined sex differences in attention to disgust facial expressions. We hypothesised that women, compared to men, would demonstrate increased attention to disgust facial expressions. Participants completed an eye tracking task to measure visual attention to emotional facial expressions. Results indicated that women spent more time attending to disgust facial expressions (...) compared to men. Unexpectedly, we found that men spent significantly more time attending to neutral faces compared to women. The findings indicate that women’s increased experience of emotional disgust also extends to attention to disgust facial stimuli. These findings may help to explain sex differences in the experience of disgust and in diagnoses of anxiety disorders in which disgust plays an important role. (shrink)

Those who wish to claim that all facts about grounding are themselves grounded (“the meta-grounding thesis”) must defend against the charge that such a claim leads to infinite regress and violates the well-foundedness of ground. In this paper, we defend. First, we explore three distinct but related notions of “well-founded”, which are often conflated, and three corresponding notions of infinite regress. We explore the entailment relations between these notions. We conclude that the meta-grounding thesis need not lead (...) to tension with any of the three notions of “well-founded”. Finally, we explore the details of and motivations for further conditions on ground that one might add to generate a conflict between the meta-grounding thesis and a well-founded constraint. We explore these topics by developing and utilizing a formal framework based on the notion of a grounding structure. (shrink)

Epistemological theories of knowledge and justification draw a crucial distinction between one's simply havinggood reasons for some belief, and one's actually basingone's belief on good reasons. While the most natural kind of account of basing is causal in nature--a belief is based on a reason if and only if the belief is properly caused by the reason--there is hardly any widely-accepted, counterexample-free account of the basing relation among contemporary epistemologists. Further inquiry into the nature of the basing relation is therefore (...) of paramount importance for epistemology. Without an acceptable account of the basing relation, epistemological theories remain both crucially incomplete and vulnerable to errors that can arise when authors assume an implausible view of what it takes for beliefs to be held on the basis of reasons. Well-Founded Beliefbrings together seventeen essays written by leading epistemologists to explore this important topic in greater detail. The collection is divided thematically to cover a wide range of issues related to the epistemic basic relation. The first section of essays covers the nature of the basing relation and attempts to articulate defensible accounts of what it takes to believe on the basis of a reason. Section II explores the kind of things that can be reasons on the basis of which we hold beliefs. Finally, the last section addresses the basing relation as it bears on particular problems in epistemology, such as skepticism, the analysis of knowledge, and the contingencies of our epistemic upbringing. (shrink)

A growing number of philosophers are concerned with the epistemic status of culturally nurtured beliefs, beliefs found especially in domains of morals, politics, philosophy, and religion. Plausibly, worries about the deep impact of cultural contingencies on beliefs in these domains of controversial views is a question about well-foundedness: Does it defeat well-foundedness if the agent is rationally convinced that she would take her own reasons for belief as insufficiently well-founded, or would take her own belief as (...) biased, had she been nurtured in a different psychographic community? This chapter will examine the proper scope and force of this epistemic location problem. It sketches an account of well and ill-founded nurtured belief based upon the many markers of doxastic strategies exhibiting low to high degrees of inductive risk: the moral and epistemic risk of ‘getting it wrong’ in an inductive context of inquiry. (shrink)

This is the Editor's Introduction to "Well-Founded Belief: New Essays on the Epistemic Basing Relation" (Routledge, 2020).

We present a sequent calculus for the Grzegorczyk modal logic $\mathsf {Grz}$ allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic $\mathsf {Grz}$ proof-theoretically.

We consider Hilbert-style non–well-founded derivations in the Gödel-Löb provability logic GL and establish that GL with the obtained derivability relation is globally complete for algebraic and neighbourhood semantics.

Fixpoint semantics are provided for ambiguity blocking and propagating variants of Nute's defeasible logic. The semantics are based upon the well-founded semantics for logic programs. It is shown that the logics are sound with respect to their counterpart semantics and complete for locally finite theories. Unlike some other nonmonotonic reasoning formalisms such as Reiter's default logic, the two defeasible logics are directly skeptical and so reject floating conclusions. For defeasible theories with transitive priorities on defeasible rules, the logics (...) are shown to satisfy versions of Cut and Cautious Monotony. For theories with either conflict sets closed under strict rules or strict rules closed under transposition, a form of Consistency Preservation is shown to hold. The differences between the two logics and other variants of defeasible logic—specifically those presented by Billington, Antoniou, Governatori, and Maher—are discussed. (shrink)

Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, three-valued, semantics uses ΦP, which extends TP to Kleene’s strong three-valued logic. Both these approaches generalize to cover logic programming systems based on a wide class of logics, provided only that the underlying structure be that of a bilattice. This was presented in earlier papers. Recently well-founded semantics has become influential for classical logic programs. We show how the well-founded approach (...) also extends naturally to the same family of bilatticebased programming languages that the earlier fixpoint approaches extended to. Doing so provides a natural semantics for logic programming systems that have already been proposed, as well as for a large number that are of only theoretical interest. And finally, doing so simplifies the proofs of basic results about the well-founded semantics, by stripping away inessential details. (shrink)

Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call M-types. We derive existence results for M-types in locally cartesian closed pretoposes with a natural numbers object, using their internal logic. These are then used to prove stability of such categories with M-types under various topos-theoretic constructions; namely, slicing, formation of coalgebras (...) , and sheaves for an internal site. (shrink)

According to Alan Millar, justified beliefs are well-founded beliefs. Millar cashes out the notion of well-foundedness in terms of having an adequate reason to believe something and believing it for that reason. To make his account of justified belief compatible with perceptual justification he appeals to the notion of recognitional ability. It is argued that, due to the fact that Millar’s is a knowledge-first view, his appeal to recognitional abilities fails to offer an explanatory account of familiar (...) cases in the literature and, as a consequence, of the notion of perceptual justification. (shrink)

George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build (...) models in which foundation fails in prescribed ways. In particular, we obtain models in which every relation is isomorphic to the membership relation on some set as well as models of Aczel's anti-foundation axiom (AFA). We suggest that Fregean extensions provide a natural way to envisage non-well-founded membership. (shrink)

The generality problem is perhaps the most notorious problem for process reliabilism. Several recent responses to the generality problem have claimed that the problem has been unfairly leveled against reliabilists. In particular, these responses have claimed that the generality problem is either (i) just as much of a problem for evidentialists, or (ii) if it is not, then a parallel solution is available to reliabilists. Along these lines, Juan Comesaña has recently proposed solution to the generality problem—well-founded reliabilism. (...) According to Comesaña, the solution to the generality problem lies in solving the basing problem, such that any solution to the basing problem will give a solution to the generality problem. Comesaña utilizes Conee and Feldman’s evidentialist account of basing (Conee and Feldman’s well-foundedness principle) in forming his version of reliabilism. In this paper I show that Comesaña’s proposed solution to the generality problem is inadequate. Well-founded reliabilism both fails to solve the generality problem and subjects reliabilism to new damning verdicts. In addition, I show that evidentialism does not face any parallel problems, so the generality problem remains a reason to prefer evidentialism to reliabilism. (shrink)

Should a philosophical account of perceptual knowledge accord a justificatory role to sensory experiences? This discussion raises problems for an affirmative answer and sets out an alternative account on which justified belief is conceived as well-founded belief and well-foundedness is taken to depend on knowledge. A key part of the discussion draws on a conception of perceptual-recognitional abilities to account for how perception gives rise both to perceptual knowledge and to well-founded belief.

A complete list of Finsler, Scott and Boffa sets whose transitive closures contain 1, 2 and 3 elements is given. An algorithm for deciding the identity of hereditarily finite Scott sets is presented. Anti-well-founded sets, i. e., non-well-founded sets whose all maximal ∈-paths are circular, are studied. For example they form transitive inner models of ZFC minus foundation and empty set, and they include uncountably many hereditarily finite awf sets. A complete list of Finsler and Boffa (...) awf sets with 2 and 3 elements in their transitive closure is given. Next the existence of infinite descending ∈-sequences in Aczel universes is shown. Finally a theorem of Ballard and Hrbáček concerning nonstandard Boffa universes of sets is considerably extended. (shrink)

From a classical proof that the gcd of natural numbers a1 and a2 is a linear combination of the two, we extract by Gödel's Dialectica interpretation an algorithm computing the coefficients. The proof uses the minimum principle. We show generally how well-founded recursion can be used to Dialectica interpret well-founded induction, which is needed in the proof of the minimum principle. In the special case of the example above it turns out that we obtain a reasonable (...) extracted term, representing an algorithm close to Euclid's. (shrink)

Every set can been thought of as a directed graph whose edge relation is ∈. We show that many natural examples of directed graphs of this kind are indivisible: for every infinite κ, for every indecomposable λ, and every countable model of set theory. All of the countable digraphs we consider are orientations of the countable random graph. In this way we find indivisible well‐founded orientations of the random graph that are distinct up to isomorphism, and ℵ1 that (...) are distinct up to siblinghood. (shrink)

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the (...) chosen axiomatisation for the class of small maps. (shrink)

We show that there are universes of sets which contain descending ϵ-sequences of length α for every ordinal α, though they do not contain any ϵ-cycle. It is also shown that there is no set universe containing a descending ϵ-sequence of length On. MSC: 03E30; 03E65.

In this paper, we show that non-well-founded sets can be defined constructively by formalizing Hallnäs' limit definition of these within Martin-Löf's theory of types. A system is a type W together with an assignment of ᾱ ∈ U and α̃ ∈ ᾱ → W to each α ∈ W. We show that for any system W we can define an equivalence relation = w such that α = w β ∈ U and = w is the maximal bisimulation. (...) Aczel's proof that CZF can be interpreted in the type V of iterative sets shows that if the system W satisfies an additional condition (*), then we can interpret CZF minus the set induction scheme in W. W is then extended to a complete system W * by taking limits of approximation chains. We show that in W * the antifoundation axiom AFA holds as well as the axioms of CFZ -. (shrink)

We construct by diagonalization a non-well-founded primitive recursive tree, which is well-founded for co-r.e. sets, provable in Σ1 0. It follows that the supremum of order-types of primitive recursive well-orderings, whose well-foundedness on co-r.e. sets is provable in Σ1 0, equals the limit of all recursive ordinals ω1 ck . RID=""ID="" Mathematics Subject Classification (2000): 03B30, 03F15 RID=""ID="" Supported by the Deutschen Akademie der Naturforscher Leopoldina grant #BMBF-LPD 9801-7 with funds from the Bundesministerium für (...) Bildung, Wissenschaft, Forschung und Technologie. RID=""ID="" I would like to thank A. SETZER for his hospitality during my stay in Uppsala in December 1998 – these investigations are inspired by a discussion with him; S. BUSS for his hospitality during my stay at UCSD and for valuable remarks on a previous version of this paper; and M. MÖLLERFELD for remarks on a previous title. (shrink)