We give a plausible-sounding conjecture involving the number of n-equivalence classes of structures of size m which would imply that the complement of a spectrum is also a spectrum.

Ash's functions Nσ ,k count the number of k -equivalence classes of σ -structures of size n . Some conditions on their asymptotic behavior imply the long standing spectrum conjecture. We present a new condition which is equivalent to this conjecture and we discriminate some easy and difficult particular cases.

In this paper, I propose to look closely at certain crucial aspects of the logic of Rawls' argument in Political Liberalism and related subsequent writings. Rawls' argument builds on the notion of comprehensiveness, whereby a doctrine encompasses the full spectrum of the life of its adherents. In order to show the mutual conflict and irreconcilability of comprehensive doctrines, Rawls needs to emphasise the comprehensiveness of doctrines, as their irreconcilability to a large extent emanates from that comprehensiveness. On the other (...) hand, in order to show the possibility and plausibility of the political liberal solution he needs to emphasise that most of these doctrines are reasonable: i.e., they are willing to cede a portion of their authority to political liberalism for the right reasons. Yet, if they are willing to cede a portion of their authority to a political conception they cannot be as comprehensive as we initially thought they were. All these elements highlight the tension in the argument itself. I suggest that many of these tensions can be removed by making Rawls' account more flexible. In this context I propose certain amendments to Rawls' account, which may overcome some of the tensions mentioned above. (shrink)

I hope you have had no trouble identifying this issue of our journal, even if the cover has been changed slightly. I would like to draw your attention to a more essential improvement in the journal's affairs: namely, that the Editorial Board has been enlarged by four new members. These are the following: Douglas Bridges , Ulrich Kohlenbach , H. Dugald Macpherson , and Pavel Pudlak . Please don't hesitate to contact a fellow editor, in particular the managing editor, if (...) you have suggestions for improving either the editorial procedures or the content and form of MLQ.The aims and scope of our journal are unchanged from the original ones developed by Günter Asser. His name is indissolubly connected with the former “Zeitschrift für Mathematische Logik und Grundlagen der Mathematik ”, now known as “Mathematical Logic Quarterly ”. He was one of the two founding editors and then the editor-in-chief of the journal until the 50th volume appeared about one year ago. Single-handedly, and almost incredibly, he showed that it is possible for one man to be the main editor of a successful highlevel scientific journal throughout half a century. He remains involved in and concerned with the editorial process of MLQ. For example, he carefully looks at every article to be published, faithfully checking almost every line of the final layout.On 26 February 2006, Professor Dr. Günter Asser celebrates his 80th birthday. I would like to take this opportunity, on behalf of the whole readership and of all fellow editors of ZML and MLQ throughout the last 51 years, to congratulate him cordially and to wish him good health and all the best for the future.The present issue starts with a paper directly related to G. Asser's spectrum conjecture. Then there are some papers specially dedicated to him, as well as further contributions, as always scrutinised and then recommended by expert referees. So this turns out to be an appropriate birthday issue. (shrink)

Most of the time our utterances are automatically interpreted as speech acts: as assertions, conjectures and testimonies; as orders, requests and pleas; as threats, offers and promises. Surprisingly, the cognitive correlates of this essential component of human communication have received little attention. This book fills the gap by providing a model of the psychological processes involved in interpreting and understanding speech acts. The theory is framed in naturalistic terms and is supported by data on language development and on autism (...) class='Hi'>spectrum disorders. Mikhail Kissine does not presuppose any specific background and addresses a crucial pragmatic phenomenon from an interdisciplinary perspective. This is a valuable resource for academic researchers and graduate and undergraduate students in pragmatics, semantics, cognitive linguistics, psycholinguistics and philosophy of language. (shrink)

David Hume (1711-1776) is widely recognized as one of the most influential and significant critics of religion in the history of philosophy. There remains, nevertheless, considerable disagreement about the exact nature of his views. According to some, he was a skeptic who regarded all conjectures relating to religious hypotheses to be beyond the scope of human understanding – he neither affirmed nor denied these conjectures. Others read him as embracing a highly refined form of “true religion” of some kind. On (...) the other side of this spectrum, it is claimed that Hume was committed to atheism, although due to social conditions at the time, this had to be (thinly) concealed or masked. The aim of this article is to provide an overview of Hume’s core concerns and arguments on this subject and to provide the reader with a framework for interpreting and assessing his various contributions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:How The Mule Got Its Tale: Moretti’s Darwinian BricolageGeoffrey Winthrop-Young* (bio)Franco Moretti. Atlas Of The European Novel. London: Verso, 1998. [AN]Franco Moretti. Modern Epic: The World System From Goethe To García Márquez. Trans. Quentin Hoare. London: Verso, 1996. [ME]1. Darwinian Preliminaries1805: Cousin de Grainville, Le dernier homme. A world in which humans have displaced the oceans dies from ecological exhaustion. 1836: Louis Geoffroy, Napoléon et la conquête du monde. (...) A history in which Napoleon wins at Waterloo and becomes emperor of the world. 1854: Charlemagne-Ischir Defontenay, Star ou Psi de Cassiopée. A distant planetary system filled with its own mythologies, histories and migration patterns.... A litany of lost names and titles: dead, discarded, ignored, out of print, reduced to pulp and brief entries in reference books, known only to experts specializing in early French science fiction. Cut off from each other with little sense of coherence or continuity, two generations of writers had been probing the many possibilities of a new literary form, some of them in highly imaginative ways, but nobody could have foretold the fate of what Félix Bodin had named littérature futuriste. Suddenly, the literary equivalent of a mass extinction wiped out a broad spectrum of conjectural imaginations. Did they deserve their fate? Wrong question. Who is to blame for their disappearance? Cui bono? The prime suspect, no doubt, is Jules Verne. “It was as if SF had for sixty years sought in vain for an institutional ‘landing point,’” surmises Marc Angenot, before pointing out that Verne’s success coincided with, indeed was based on, the repression of a wide array of promising alternatives [64]. Displaying that jovial bluntness which in his days passed for commendable virility, he extracted certain formal features from his environment, eliminated the rest, and engineered his selections into a highly marketable literary model. A lot began with Verne, but a lot ended with him, too.At the outset a rapidly emerging set of random and undirected variations opens up a multiplicity of future possibilities; then a choice is made, a selection that locks in one particular variant while locking out the competition. Subsequently, a winner—who need not be the best or most promising candidate, but who by virtue of his selection manages to impose definite constraints on future developments—spawns a tradition that coasts along until another crisis is heralded by yet another round of proliferation and selection. Readers familiar with Franco Moretti’s work will recognize this Darwinian scenario, which provides the theoretical backbone for his analyses. In the programmatic essay “On Literary Evolution” in the revised edition of Signs Taken for Wonders, it allows him to whittle down the development of the European novel from its experimental phase in the eighteenth century to the victory of the Bildungsroman in the nineteenth century and its subsequent disintegration to what must be the shortest account of the history of the novel ever written: “Novels/novel/novels” [264]. In The Way of the World it helps explain how it was possible for the Bildungsroman “to emerge victorious from that veritable ‘struggle for existence’ between various narrative forms that took place at the [End Page 18] turn of the eighteenth century” [10]. Modern Epic, in turn, uses the Darwinian model to plot the evolution of the hybrid genre announced in its title, while Atlas of the European Novel explains the morphological change novels undergo when they move from one space to another. But why Darwin? Or, since “Darwin” means many different things to many different Darwinists: why this punctuated, nongradualist, highly contingency-tolerant Gouldian Darwin? How much do we gain by applying the proliferation/lock-in sequence to the development of devices, texts, and genres? What motivates the optimism that the Darwinian paradigm may “help us to explain in a new—and better—way numerous questions that literary history has never succeeded in resolving satisfactorily”? [ME 5].But then why raise these arcane questions? Surely, Moretti’s books center on more relevant issues. Atlas is about space—and given the current critical focus on space, what more timely topic could there be? And what more obvious criticism than... (shrink)

Abstract The values of the healthcare sector are fairly ubiquitous across the globe, focusing on caring and respect, patient health, excellence in care delivery, and multi-stakeholder collaboration. Many individual pharmacists embrace these core values. But their ability to honor these values is significantly determined by the nature of the system they work in. -/- The paper starts with a model of the prevailing pharmacist workforce model in Scotland, in which core roles are predominantly separated into hierarchically disaggregated jobs focused on (...) one professional ‘pillar’: Clinician /Practice Provider; Educator; Leader/Manager; and Researcher. This is the ‘Atomistic’ Model. This skills-segregation yields a workforce of individuals working in isolation rather than collaborating together, and lacking a shared information flow, purpose and identity. Key strategic flaws include suboptimal responsiveness to population and subpopulation needs, inconsistency and inequity of care, an erosion of professional agency, and lower job satisfaction. It is conjectured that this results from a lack of congruence between values, professional ethos, and organizational structure. ‘Atomism’ culminates in a syndrome of widespread professional-level cognitive dissonance. -/- The paper contrasts this with a new emerging workforce vision, The Collaborative Care Model. This new model defines a systems-first-approach, built on the principle that all jobs must include all four professional ‘pillars’. Vertical skills integration, involving education and task sharing, will support sustainability and succession planning. Horizontal skills integration (across practice, leadership and research) is included to improve responsiveness to population need and individual professional agency. The working conditions, supportive ethos, and career structure needed to make the model work are described. Moral theory and workforce theory are used to justify why the model may be more effective for population health, delivering greater job satisfaction for individuals and ultimately helping systematically realize and honor healthcare values. Finally, the paper sketches the first steps needed to implement the model at the national level, starting with the operationalization of new multi-pillar professional curricula across the career spectrum. Potential pitfalls and challenges are also discussed. -/- Co-Authors: 1. Paul Forsyth (PF) Lead Pharmacist Clinical Cardiology, Pharmacy, NHS Greater Glasgow & Clyde. Contribution: Conceptualization; Model Curation; Model Theory; Model Visualization; Writing - original draft (lead author), Writing - review & editing (lead author) 2. Andrew Radley (AR), Consultant in Public Health Pharmacy, NHS Tayside. Contribution: Conceptualization; Model curation; Model Theory; Writing - review & editing 3. Gordon Rushworth (GR), MPharm MSc FFRPS FRPharmS (Consultant). Programme Director, Highland Pharmacy Education & Research Centre, NHS Highland, Inverness. Contribution: Model curation; Writing - review & editing 4. Fiona Marra (FM) National Lead Clinician Scottish Infection and Immunology Network (SPAIIN) / Advanced Pharmacist HCV / HIV, NHS Greater Glasgow & Clyde. Contribution: Model curation; Writing - review & editing 5. Susan Roberts (SR) Associate Postgraduate Pharmacy Dean, NHS Education for Scotland. Contribution: Model curation; Writing - review & editing 6. Roisin O’Hare (RO) Lead Teacher Practitioner Pharmacist, Northern Ireland University Network, Southern Health and Social Care Trust. Contribution: Model curation; Writing - review & editing 7. Catherine Duggan (CD) Chief Executive Officer, International Pharmaceutical Federation (FIP). Contribution: Model curation; Writing - review & editing 8. Barry Maguire (BM) Senior Lecturer, School of Philosophy, Psychology and Life Sciences, The University of Edinburgh. Contribution: Conceptualization; Model Curation; Model Theory; Model Visualization; Supervision; Writing - original draft (senior academic supervisor), Writing - review & editing (senior academic supervisor) -/- . (shrink)

We discuss dividing lines (in model theory) and some test questions, mainly the universality spectrum. So there is much on conjectures, problems and old results, mainly of the author and also on some recent results.

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal "infinitesimal subgroup" G00 such that the quotient G/G00, equipped with the "logic topology", is a compact (real) Lie group. Our first result is that the functor G → G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the o-minimal (...) class='Hi'>spectrum G̃ of G. We prove that G/G00 is a topological quotient of G̃. We thus obtain a natural homomorphism ψ* from the cohomology of G/G00 to the (Čech-)cohomology of G̃. We show that if G00 satisfies a suitable contractibility conjecture then $\widetilde{G^{00}}$ is acyclic in Čech cohomology and ψ* is an isomorphism. Finally we prove the conjecture in some special cases. (shrink)

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen structure. With each (...) new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a single \-sentence \ that codes Kurepa trees to prove the following statements: The spectrum of \ is consistently equal to \ and also consistently equal to \\), where \ is weakly inaccessible.The amalgamation spectrum of \ is consistently equal to \ and \\), where again \ is weakly inaccessible. This is the first example of an \-sentence whose spectrum and amalgamation spectrum are (...) consistently both right-open and right-closed. It also provides a positive answer to a question in Souldatos :533–551, 2014).Consistently, \ has maximal models in finite, countable, and uncountable many cardinalities. This complements the examples given in Baldwin et al. :545–565, 2016) and Baldwin and Souldatos :444–452, 2019) of sentences with maximal models in countably many cardinalities.Consistently, \ and there exists an \-sentence with models in \, but no models in \. This relates to a conjecture by Shelah that if \, then any \-sentence with a model of size \ also has a model of size \. Our result proves that \ can not be replaced by \, even if \. (shrink)

This book puts forward a harmonious analysis of similarities and differences between two concepts—human minds and cultures—and strives for a multicultural spectrum of philosophical explorations that could assist them in pondering the striking pursuit of envisaging human minds and cultures as an essential appraisal of philosophy and the social sciences. The book hinges on a theoretical understanding of the indispensable liaison between the dichotomy of minds and objectivity residing in semantic-ontological conjectures. -/- The ethnographic sense of cultures confines the (...) scope of cultural scientism, an evolutionary paradigm on the functionalist turn, where one could enthral the cultural phenomenon from the contentment of the conflict of scientific quandaries. Hence, cultural relativism concedes that cultures have some descriptive contents, like customs, beliefs, moral codes, other minds, etc., that are followed by an individual or a group of people. However, the notion of societal semiotics embarks on the ‘semiotic conception of culture’ that deploys modernity and values centred on ethical conjectures. -/- Human Minds and Cultures conspicuously attune the cultural edifice of moral minds and cope with the enduring prospects of ethics, genders, laws, and socio-political affairs. Essential reading for anyone with a sparkling interest in human minds and cultures. (shrink)

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen structure. With each (...) new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

Clayton and Stevens argue that political liberals should engage with the religiously unreasonable by offering religious responses and showing that their religious views are mistaken, instead of refusing to engage with them. Yet they recognize that political liberals will face a dilemma due to such religious responses: either their responses will alienate certain reasonable citizens, or their engagements will appear disingenuous. Thus, there should be a division of justificatory labour. The duty of engagement should be delegated to religious citizens. In (...) this comment, I will argue that the division of justificatory labour is indefensible. This dilemma can be avoided if politicians and political philosophers correctly use conjecture, a form of discourse that involves non-public reason. As a conditional response, conjecture avoids alienating any reasonable citizens. Also, if conjecture is given in a sincere and open-minded manner, then the problem of disingenuousness can be overcome. My comment concludes that while the engagement of politicians and political philosophers does not necessarily jeopardize overlapping consensus, they should be permitted, or perhaps even required, to engage with the religiously unreasonable due to the natural duty of justice. (shrink)

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

_Conjectures and Refutations_ is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

Larry Temkin famously argues that what he calls spectrum arguments yield strong reason to reject Transitivity, according to which the ‘all-things-considered better than’ relation is transitive. Spectrum arguments do reveal that the conjunctions of independently plausible claims are inconsistent with Transitivity. But I argue that there is very strong independent reason to reject such conjunctions of claims, and thus that the fact that they are inconsistent with Transitivity does not yield strong reason to reject Transitivity.

ABSTRACT I consider paradoxical spectrum arguments involving transitive relations like ‘better than’. I argue that, despite being formally different from sorites arguments, at least some spectrum arguments arise from vagueness, and that vagueness might often be the most natural diagnosis.

Recent debates within the autism advocacy community have raised difficult questions about who can credibly act as a representative of a particular population and what responsibilities that...

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism: that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor even as 'probable'. Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us (...) understand the difficulties of the problems which we try to solve. This is how we become better acquainted with our problem, and able to propose more mature solutions: the very refutation of a theory - that is, of a tentative solution to our problem - is always a step forward that takes us nearer the truth. And this is how we can learn from our mistakes. As we learn from our mistakes our knowledge grows, even though we may never know - that is, know for certain. Since our knowledge can grow, there can be no reason here for despair of reason. And since we can never know for certain, the can be no authority here for any claim to authority, for conceit over our knowledge, or for smugness. The essays and lectures of which this book is composed apply this thesis to many topics, ranging from problems of the philosophy and history of the physical and social sciences to historical and political problems. (shrink)

The notion of minimal, basic, pre-reflective or core self is currently debated in the philosophy of mind, cognitive sciences and developmental psychology. However, it is not clear which experiential features such a self is believed to possess. Studying the schizophrenic experience may help exploring the following aspects of the minimal self: the notion of perspective and first person perspective, the ‘mineness’ of the phenomenal field, the questions of transparency, embodiment of point of view, and the issues of agency and ownership, (...) considered as different and less fundamental than the feeling of mineness. Two clinical vignettes of patients with the diagnosis of schizophrenia will be presented: the first one, illustrating early illness stages, and the second case, of chronic schizophrenia, symptomatically marked by persistent hallucinations. Through their analysis, we will discuss the experiential dimensions of minimal self. (shrink)

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

This chapter examines the spectrum inversion hypothesis as an argument against certain kinds of account of what it’s like to be conscious of color. The hypothesis aims to provide a counterexample to accounts of what it’s like to be conscious of color in non-qualitative terms, as well as to accounts of what it’s like to be conscious of color in terms of the representational content of conscious visual states (which, according to some philosophers, is in turn given an account (...) in non-qualitative terms). I explain the hypothesis’s reasoning in sections 1 and 2. I then take up background issues: since the counterexample provided by the hypothesis is typically given as a possibility rather than an actuality, I briefly discuss the kind of possibility involved in section 3, and the methodologies used to evaluate the plausibility of possibilities in section 4. In section 5, I describe some general considerations that are commonly used against the spectrum inversion hypothesis. I take up attempts to support the hypothesis with findings from color science in section 6. I end with comments skeptical of both the motivation for the spectrum inversion hypothesis and the methodology used to support it. (shrink)

§1. Introduction. By and large, definitions of a differentiable structure on a set involve two ingredients, topology and algebra. However, in some cases, partial information on one or both of these is sufficient. A very simple example is that of the field ℝ where algebra alone determines the ordering and hence the topology of the field:In the case of the field ℂ, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the ield but (...) this will be too coarse to give a diferentiable structure.A celebrated example of how partial algebraic and topological data determines a differentiable structure is Hilbert's 5th problem and its solution by Montgomery-Zippin and Gleason.The main result which we discuss here is of a similar flavor: we recover an algebraic and later differentiable structure from a topological data. We begin with a linearly ordered set ⟨M, <⟩, equipped with the order topology, and its cartesian products with the product topologies. We then consider the collection of definable subsets of Mn, n = 1, 2, …, in some first order expansion ℳ of ⟨M, <⟩. (shrink)

Bianchi, Stanley, and Sutander argue in an insightful, cogent manner for the consideration of harm reduction as an ethically-defensible, non-paternal management approach for capable persons...

It is common in philosophy of language to recognise two different kinds of linguistic meaning: literal or conventional meaning, on the one hand, versus communicated or conveyed meaning, on the other. However, once we recognise these two types of meaning, crucial questions immediately emerge; for instance, exactly which meanings should we treat as the literal (semantic) ones, and exactly which appeals to a context of utterance yield communicated (pragmatic), as opposed to semantic, content? It is these questions and, specifically, how (...) we should model the relationship between semantic content and utterance context, that is the topic of this chapter. We explore five contemporary answers to this modelling question, considering the benefits and challenges of each, before closing by examining some potential new directions for debates in this area. (shrink)

The Conjectural Body combines continental philosophy with musicology, popular music studies, and feminist, critical race, and postcolonial theories to offer a unique perspective on issues of gender, race, and the philosophy of music. It is one of the few books in philosophy to take popular music seriously, and is one of the few books in continental feminism to privilege music over the visual.