We use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.

We investigated the week-to-week effects of a mindfulness intervention on emotional exhaustion, work engagement, and job satisfaction in a field study involving 218 participants who participated and reported their weekly outcomes during the 8-week program. To examine how mindfulness impacted work outcomes, we used intraindividual modeling of the 8-week data. Mindfulness increased over time, and time also had indirect effects on emotional exhaustion, work engagement, and job satisfaction, through mindfulness. Supplementary growth curve analyses on the improvement of mindfulness over time (...) showed a slight decrease in the positive effect of time on mindfulness. (shrink)

Here we address four objections raised by Julien Deonna, John Michael, and Francesca Fardo against a recent account of empathy for pain. First, to what extent must the empathizer share her target’s affective state? Second, how can one interpret neuroscientific findings on vicarious pain in light of recent results challenging the notion of a pain matrix? Third, can one offer a simpler account of how empathy makes one aware of another’s emotion? Finally, to what extent can this account (...) of empathy for pain be generalized to empathy for emotions? (shrink)

Human interactions are often improvised rather than scripted, which suggests that efficient coordination can emerge even when collective plans are largely underspecified. One possibility is that such forms of coordination primarily rely on mutual influences between interactive partners, and on perception–action couplings such as entrainment or mimicry. Yet some forms of improvised joint actions appear difficult to explain solely by appealing to these emergent mechanisms. Here, we focus on collective free improvisation, a form of highly unplanned creative practice where both (...) agents' subjective reports and the complexity of their interactions suggest that shared intentions may sometimes emerge to support coordination during the course of the improvisation, even in the absence of verbal communication. In four experiments, we show that shared intentions spontaneously emerge during collective musical improvisations, and that they foster coordination on multiple levels, over and beyond the mere influence of shared information. We also show that musicians deploy communicative strategies to manifest and propagate their intentions within the group, and that this predicts better coordination. Overall, our results suggest that improvised and scripted joint actions are more continuous with one another than it first seems, and that they differ merely in the extent to which they rely on emergent or planned coordination mechanisms. (shrink)

An English translation of Pierre Bayle's posthumous last book, Entretiens de Maxime et de Themiste (1707), in which Bayle defends his skeptical position on the problem of the evil. This book is often cited and attacked by G.W. Leibniz in his Theodicy (1710). Over one hundred pages of original philosophical and historical material introduce the translation, providing it with context and establishing the work's importance.

Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in (...) constructive geometry, it must be done without a case distinction. Classically, the models of Euclidean geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to different versions of the parallel postulate.We consider three versions of Euclid’s parallel postulate. The two most important are Euclid’s own formulation in his Postulate 5, which says that under certain conditions two lines meet, and Playfair’s axiom, which says there cannot be two distinct parallels to line L through the same point p. These differ in that Euclid 5 makes an existence assertion, while Playfair’s axiom does not. The third variant, which we call the strong parallel postulate, isolates the existence assertion from the geometry: it amounts to Playfair’s axiom plus the principle that two distinct lines that are not parallel do intersect. The first main result of this paper is that Euclid 5 suffices to define coordinates, addition, multiplication, and square roots geometrically.We completely settle the questions about implications between the three versions of the parallel postulate. The strong parallel postulate easily implies Euclid 5, and Euclid 5 also implies the strong parallel postulate, as a corollary of coordinatization and definability of arithmetic. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The independence proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions. “Field elements” in these models are real-valued functions. (shrink)

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...) of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study. (shrink)

Models of ethnic violence have primarily been descriptive in nature, advancing broad or particular social and political reasons as explanations, and neglecting the contributions of individuals as decision-makers. Game theoretic and rational choice models recognize the role of individual decision-making in ethnic violence. However, such models embrace a classical economic theory view of unbounded rationality as utility-maximization, with its exacting assumption of full informational access, rather than a model of bounded rationality, modeling individuals as satisficing agents endowed with evolved domain-specific (...) competences. A newer theoretical framework hypothesizing the existence of a human coalitional psychology, an evolved domain of competence, allows us to make sense of core features of memorial narratives about ethnic violence. Qualitative data from the interviews of fifty-seven participants who were impacted by the Croatian Homeland War support expectations entailed by a coalitional psychology model of ethnic strife. (shrink)

ABSTRACT Pierre Bayle developed an expansive theory of toleration in his Commentaire philosophique by arguing that tolerance is a universal principle of natural law. However, by situating toleration in natural law rather than positive law, Bayle was brought into theoretical conflict with the Old Testament injunction that the state should punish idolatry. To resolve this conflict, Bayle drew upon the work of early modern Hebraists, particularly the Catholic biblical scholar Richard Simon. Bayle adapted Simon’s idea that theocracy uniquely shaped (...) the institutions of ancient Israel to argue that prohibitions against idolatry should be exclusive to the Hebrew republic. Bayle argued that the Mosaic Law did not punish someone for their sincerely held religious beliefs but only prohibited treason, and these circumstantial laws should not be emulated by other states. This allowed Bayle to contend for the moral veracity of the Old Testament and the notion that toleration is an unconditional principle of natural law. Bayle’s use of Simon displayed the revolutionary potential of textual critical scholarship in the early modern period, as he adapted Simon’s critical ideas to his own aims of promoting religious toleration within the ecclesiastical and civic spheres of his own confessional context. (shrink)

How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common (...) Bayesian formalism. The concepts we review are ambiguities, fusion, multimodality, conflicts, modularity, hierarchies and loops. First, each of these concepts is introduced briefly using some examples from the neuroscience, psychophysics or robotics literature. Then, the concept is formalized using a template Bayesian model. The assumptions and common features of these models, as well as their major differences, are outlined and discussed. (shrink)

Aujourd’hui, les scientifiques sont au moins trilingues : langue maternelle ; langage technique de la discipline ; anglais comme langue véhiculaire. Le plurilinguisme est indispensable à un scientifique parce que la science est inséparable de sa communication, sous ses différents registres, notamment ceux de l’écrit et de l’oral. Il n’est pas de science, en particulier, sans vulgarisation scientifique : en ce sens, être un scientifique, c’est apprendre à traduire la parole des choses. Le monolinguisme, en la matière, n’est pas seulement (...) néfaste : c’est une vue de l’esprit, car les concepts, que ce soit dans les sciences exactes ou les sciences humaines, ne sauraient s’appréhender directement, sans le recours au langage. Lavoisier considérait que les langues étaient « de véritables méthodes analytiques » et, à l’inverse, que « la logique des sciences tient essentiellement à leur langue ». Voilà pourquoi il est bien artificiel d’opposer sciences exactes, sciences humaines et esthétique : il n’y a pas de fossé infranchissable entre les trois, et il est urgent de le redécouvrir.Scientists today are trilingual at least: they have their mother tongue, the technical language of their discipline and English as their vehicular language. Multilingualism is essential to a scientist because science is inseparable from communication in all its different registers, and particularly those of written and oral language. Every kind science of goes hand in hand with scientific popularisation: in this sense, being a scientist means learning to translate what things - rather than people - are saying. Speaking only one language, in this context, is not just a disadvantage: it is an illusion, because concepts, whether in the exact or the human sciences, cannot be grasped directly without the use of language. Lavoisier believed that languages are “analytical methods per se” and that, conversely, “the logic of the sciences essentially lies in their language”. This is why the division between exact sciences, liberal arts and aesthetics is completely artificial: there is no real gap between the three, and we urgently need to rediscover this fact. (shrink)

CpG islands (CGIs) are regions enriched in the dinucleotide CpG; they constitute the promoter of about 60% of mammalian genes. In cancer cells, some promoter‐associated CGIs become heavily methylated on cytosines, and the corresponding genes undergo stable transcriptional silencing. Hypermethylated CGIs attract methyl‐CpG‐binding proteins (MBPs), which have been shown to recruit chromatin modifiers and cause transcriptional repression. These observations have led to the prevalent model that methyl‐CpG‐binding proteins are promoter‐proximal transcriptional repressors. Recent discoveries challenge this idea and raise a number (...) of questions. Here we discuss the following issues: what are other possible roles for the known MBPs? Why are these proteins not essential in mammals? Are there other MBPs left to discover? Could CpG methylation be nonessential? (shrink)

In the study of the process of radicalization, precedence has been given to answering ‘how’ questions over the exact qualification of the concept of radicalization itself. What does it mean to be radicalized? What are the cognitive entailments of such state? What are the features that make radicalization recognizable? We rely on a game theoretic model to characterize the essence of what it is to be radicalized. Our model of the radicalized agent’s rational behavior elucidates his construal of typical social (...) transactions. We further propose that the rationality of the radicalized mind entails a cognitive calibration specifying a modality of thought we call the R.A.S.H. mentality. It incorporates a particular risk preference (that action is always optimal) and attitude (that one’s temerity calls for requital) which are both essential aspects of the radicalized mind. The R.A.S.H. mentality throw in a new light core findings of the radicalization literature. (shrink)

Crossing the Stream, Leaving the Cave brings philosophers from two of the world's great philosophical traditions--Platonic and Indian Buddhist--into joint inquiry on topics in metaphysics, epistemology, mind, language, and ethics. An international team of scholars address selected questions of mutual concern to Buddhist and Platonist: How can knowledge of reality transform us? Will such transformation leave us speechless, or disinterested in the world around us? What is cause? What is self-knowledge? And how can dreams shed light on waking cognition? What (...) do the paradoxes thrown up by abstract thought about fundamental notions such as being and unity reveal? Is it possible to attain unity in ourselves, and should we even try? Would doing so make us happy--and is such happiness consistent with both contemplation of reality and action in the world? With close readings of texts by Buddhaghosa, Nagarjuna, Vasubandhu, Dignaga, Bhaviveka, Santideva; by Plato, Plotinus, Porphyry, Olympiodorus, and Damascius (among others), these studies consider not just the different answers Buddhists and Platonists might give to these questions, but also the criticisms they might bring to each other's positions, the sort of arguments they use, and the use they put these arguments to. Bringing Platonic and the Buddhist perspectives jointly to bear creates a cosmopolitan philosophical exchange which yields greater conceptual clarity on the questions and the terms in which they are cast, reveals unnoticed conceptual connections, and opens up new possibilities for addressing central philosophical concerns. (shrink)

This book will remain timeless in its study of Aristotle's objective grasp of reality. The book's uniqueness lies in its aim of letting Aquinas himself speak on the subject of metaphysics. The work embraces both a history of philosophy and Aristotle's subsequent reasoning toward God as pure act.

Pierre Bourdieu is now recognized as one of the key contemporary critics of culture and the visual arts. Art Rules analyses Bourdieu's work on the visual arts to provide the first overview of his theory of culture and aesthetics. Bourdieu's engagement with both postmodernism and the problem of aesthetics provides a new way of analyzing the visual arts. His interest is in how artistic fields function and the implications their processes have for art and artistic practice. Art Rules applies (...) Bourdieu's theory of practice to the three fields of museums, photography and painting. These practical examples are used as a springboard to address visual arts in the 21st Century and to establish Bourdieu's rules of art. (shrink)

Peer review is a widely accepted instrument for raising the quality of science. Peer review limits the enormous unstructured influx of information and the sheer amount of dubious data, which in its absence would plunge science into chaos. In particular, peer review offers the benefit of eliminating papers that suffer from poor craftsmanship or methodological shortcomings, especially in the experimental sciences. However, we believe that peer review is not always appropriate for the evaluation of controversial hypothetical science. We argue that (...) the process of peer review can be prone to bias towards ideas that affirm the prior convictions of reviewers and against innovation and radical new ideas. Innovative hypotheses are thus highly vulnerable to being “filtered out” or made to accord with conventional wisdom by the peer review process. Consequently, having introduced peer review, the Elsevier journal Medical Hypotheses may be unable to continue its tradition as a radical journal allowing discussion of improbable or unconventional ideas. Hence we conclude by asking the publisher to consider re-introducing the system of editorial review to Medical Hypotheses. (shrink)

Rethinking the Body and Its Boundaries Content Type Journal Article Category Editorial Pages 1-6 DOI 10.1007/s11673-011-9353-8 Authors Leigh E. Rich, Department of Health Sciences (Public Health), Armstrong Atlantic State University, 11935 Abercorn Street, Savannah, GA 31419, USA Michael A. Ashby, Palliative Care and Persistent Pain Services, Royal Hobart, Hospital, Southern Tasmania Area Health Service, and School of Medicine, Faculty of Health Sciences, University of Tasmania, 1st Floor, Peacock Building, Repatriation Centre, 90 Davey Street, Hobart, TAS 7000 Australia Pierre-Olivier (...) Méthot, ESRC Centre for Genomics in Society (Egenis), University of Exeter, Byrne House, St German’s Road, Exeter, EX4 4PJ UK Journal Journal of Bioethical Inquiry Online ISSN 1872-4353 Print ISSN 1176-7529 Journal Volume Volume 9 Journal Issue Volume 9, Number 1. (shrink)

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...) philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (shrink)

The celebrated career of a venerated scholar inspires incisive new contributions to the field of Indian and Tibetan Buddhism. Particularly known for his groundbreaking and influential work in Tibetan studies, Matthew Kapstein is a true polymath in Buddhist and Asian studies more generally; possessing unsurpassed knowledge of Tibetan culture and civilization, he is also deeply grounded in Sanskrit and Indology, and his highly accomplished work in these cultural and civilizational areas has exemplified a whole range of disciplinary perspectives. Reflecting something (...) of the astonishing range of Matthew Kapstein’s work and interests, this collection of essays pays tribute to a luminary in the field by exemplifying some of the diverse work in Buddhist and Asian studies that has been impacted by his scholarship and teaching. Engaging matters as diverse as the legal foundations of Tibetan religious thought, the teaching careers of modern Chinese Buddhists, the history of Bhutan, and the hermeneutical insights of Vasubandhu, these essays by students and colleagues of Matthew Kapstein are offered as testament to a singular scholar and teacher whose wide-ranging work is unified by a rare intellectual selflessness. (shrink)

This article is a response to the 1999 article `On the Cunning of Imperialist Reason' by Pierre Bourdieu and Loïc Wacquant, in which US intellectuals such as myself were accused of engaging in `imperialist reason' through scholarly and institutional efforts to impose a US paradigm of racial relations upon Brazilian society and scholarship. This article makes three principal points in relation to Bourdieu and Wacquant's charges. First, their critique relies on presumptions and critical analytical methods which privilege the nation-state (...) and culture as the sole object for comparative analysis, and, second, as a consequence ignore how Afro-Brazilian politics and the US civil rights movement intersect within the political contexts and histories of transnational black politics. The intersecting affiliations of transnational black politics across territorial and nation-state boundaries problematize any characterization of international and inter-state relations as the inevitable interaction of politically discrete, territorially sovereign entities. Bourdieu and Wacquant's self-entrapment within the analytic category of the territorial nation leads them to imprison and caricature US African-American politics and thought within the geographic boundaries of the USA. Their assertions, however, provide an opportunity to consider the so-called US civil rights movement within the larger context of black struggles for racial equality in various parts of the world. Third, Bourdieu and Wacquant's attack is in some ways consistent with Wacquant's demonstrated habit of decontextualizing black cultural production and presenting such decontextualization as a virtue or strength, as evidenced in some of his writings on boxing in the United States. This final linkage is crucial, I believe, in understanding how the indiscriminate use of sociological categories and the refusal to engage the specific peculiarities of the tensions between politics and culture in Brazil are symptomatic of a wider misrecognition of black agency more generally in Wacquant's writings. (shrink)

We consider a computational model comparing the possible roles of and in phonetic decoding, demonstrating that these two routes can contain similar information in some communication situations and highlighting situations where their decoding performance differs. We conclude that optimal decoding should involve some sort of fusion of association and simulation in the human brain.

In face of the multiple controversies surrounding the DSM process in general and the development of DSM-5 in particular, we have organized a discussion around what we consider six essential questions in further work on the DSM. The six questions involve: 1) the nature of a mental disorder; 2) the definition of mental disorder; 3) the issue of whether, in the current state of psychiatric science, DSM-5 should assume a cautious, conservative posture or an assertive, transformative posture; 4) the role (...) of pragmatic considerations in the construction of DSM-5; 5) the issue of utility of the DSM – whether DSM-III and IV have been designed more for clinicians or researchers, and how this conflict should be dealt with in the new manual; and 6) the possibility and advisability, given all the problems with DSM-III and IV, of designing a different diagnostic system. Part 1 of this article took up the first two questions. Part 2 took up the second two questions. Part 3 now deals with Questions 5 & 6. Question 5 confronts the issue of utility, whether the manual design of DSM-III and IV favors clinicians or researchers, and what that means for DSM-5. Our final question, Question 6, takes up a concluding issue, whether the acknowledged problems with the earlier DSMs warrants a significant overhaul of DSM-5 and future manuals. As in Parts 1 & 2 of this article, the general introduction, as well as the introductions and conclusions for the specific questions, are written by James Phillips, and the responses to commentaries are written by Allen Frances. (shrink)

In face of the multiple controversies surrounding the DSM process in general and the development of DSM-5 in particular, we have organized a discussion around what we consider six essential questions in further work on the DSM. The six questions involve: 1) the nature of a mental disorder; 2) the definition of mental disorder; 3) the issue of whether, in the current state of psychiatric science, DSM-5 should assume a cautious, conservative posture or an assertive, transformative posture; 4) the role (...) of pragmatic considerations in the construction of DSM-5; 5) the issue of utility of the DSM - whether DSM-III and IV have been designed more for clinicians or researchers, and how this conflict should be dealt with in the new manual; and 6) the possibility and advisability, given all the problems with DSM-III and IV, of designing a different diagnostic system. Part I of this article will take up the first two questions. With the first question, invited commentators express a range of opinion regarding the nature of psychiatric disorders, loosely divided into a realist position that the diagnostic categories represent real diseases that we can accurately name and know with our perceptual abilities, a middle, nominalist position that psychiatric disorders do exist in the real world but that our diagnostic categories are constructs that may or may not accurately represent the disorders out there, and finally a purely constructivist position that the diagnostic categories are simply constructs with no evidence of psychiatric disorders in the real world. The second question again offers a range of opinion as to how we should define a mental or psychiatric disorder, including the possibility that we should not try to formulate a definition. The general introduction, as well as the introductions and conclusions for the specific questions, are written by James Phillips, and the responses to commentaries are written by Allen Frances. (shrink)

In the conclusion to this multi-part article I first review the discussions carried out around the six essential questions in psychiatric diagnosis – the position taken by Allen Frances on each question, the commentaries on the respective question along with Frances’ responses to the commentaries, and my own view of the multiple discussions. In this review I emphasize that the core question is the first – what is the nature of psychiatric illness – and that in some manner all further (...) questions follow from the first. Following this review I attempt to move the discussion forward, addressing the first question from the perspectives of natural kind analysis and complexity analysis. This reflection leads toward a view of psychiatric disorders – and future nosologies – as far more complex and uncertain than we have imagined. (shrink)

The Routledge Handbook of Indian Buddhist Philosophy is an outstanding reference source to the principal philosophers in the diverse Buddhist traditions of India, from the early Pāli writings to the twentieth century. The Handbook provides thorough coverage of the most significant figures, texts and debates that animate Buddhist philosophy. A key feature is the attention given to the ideas and works of particular Buddhist thinkers, placing the author at the centre of inquiry. Forty chapters by an international team of contributors (...) are divided into eight clear sections, each of which includes an introduction by the editors: Buddhas as Philosophers Poet Philosophers Abhidharma Philosophers Philosophical Founders Early Period Philosophical Commentators (fifth - eighth century) Middle Period Philosophical Commentators (eighth - ninth century) Late Period Philosophical Commentators (tenth - twelfth century) Modern Philosophers. Essential reading for students and researchers in Eastern and comparative philosophy and especially Buddhist philosophy, The Routledge Handbook of Indian Buddhist Philosophy will also be of interest to those studying Buddhism in religious studies and related subjects. (shrink)

Matthew Lipman is an American philosopher who conceived, in the 1970s, a method to help children think in an autonomous, critical and reasonable way. This method is a global approach which aims to develop the personal as well as the intellectual, the moral and the social aspects of the person; it is an educative project in the broad sense of the term. This holistic project takes the form of a program of philosophy for students from five to fifteen years old. (...) The philosophical content is adapted to the children's interests and needs and is presented in the form of novels which relate semantic, logic, esthetic and ethic experiences of daily life. (shrink)

In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, most recently, (...) Michael Dummett. Intuitionists can either point out the intuitionistc invalidity of the inference from the claim that all truths are knowable to the insane conclusion that all truths are known, or they can outright demur from asserting the existence of forever-unknown truths, perhaps questioning—as Dummett now suggests—the applicability of the Principle of Bivalence to a certain class of empirical statements. I argue that if intuitionists reject strict finitism—the view that all truths are knowable by beings just like us—the prospects for either proposal look bleak. (shrink)

Contextualist approaches to the Liar Paradox postulate the occurrence of a context shift in the course of the Liar reasoning. In particular, according to the contextualist proposal advanced by Charles Parsons and Michael Glanzberg, the Liar sentence L doesn’t express a true proposition in the initial context of reasoning c, but expresses a true one in a new, richer context c', where more propositions are available for expression. On the further assumption that Liar sentences involve propositional quantifiers whose domains (...) may vary with context, the Liar reasoning is blocked. But why should context shift? We argue that the paradox involves principles of contextualist reflection that explain, by analogy with well-known reflection principles for arithmetic, why context must shift from c to c' in the course of the Liar reasoning. This provides a diagnosis of the Liar Paradox—one that equally applies to two revenge arguments against contextualist approaches, one recently advanced by Andrew Bacon, the other mentioned by Charles Parsons and more recently revived by Cory Juhl. (shrink)