A Sheaf Model of Contradictions and Disagreements. Preliminary Report and Discussion

We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b) measure how strong it is; (c) and do something about it, e.g. suggest ways to reconcile inconsistent advice. This model naturally represents the distinction between contradictions and disagreements. It is based on the idea of representing natural language sentences as formulas with parameters sitting on lattices, creating partial orders based on predicates shared by theories, and building sheaves on these partial orders with products of lattices as stalks. Degrees of disagreement are measured by the existence of global and local sections. Limitations of the sheaf approach and connections to recent work in natural language processing, as well as the topics of contextuality in physics, data fusion, topological data analysis and epistemology are also discussed.Comment: This paper was presented at ISAIM 2018, International Symposium on Artificial Intelligence and Mathematics. Fort Lauderdale, FL. January 3 5, 2018. Minor typographical errors have been correcte

Towards a classification of continuity and on the emergence of generality

This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

The limits of local politics: local socialism and the local economy in the 1980s; a case study of Sheffield's economic policies

The analysis of local politics has too often been partial and one-sided. Dominant approaches to its study have tended to emphasise either the institutions of local government, or the logic of the local state, or (more recently) its relationship to localities. This thesis seeks to bring together a range of different approaches in ways which make it easier to explore the processes of local politics, acknowledging that no single approach is likely to provide all the answers. But it argues that those debates which build links between politics and geography, around the notion of locality , are particularly helpful, as long as they do not lose sight of politics within the state (as expressed, for example, in Rhodes' discussion of policy networks), and (following Duncan, Goodwin, Halford, and Savage) as long as localities are not understood as coherent expressions of underlying relations. Following a critical discussion of the locality debates (associated with the ESRC's Changing Urban and Regional System programme), it is suggested that notions of local growth coalition (as developed by Cox and Mair) and urban corporatism (as developed by Harvey) may be helpful in analysing change at local level. This suggestion is taken further through a case study of the development of 'local socialism' and of local economic policies in Sheffield in the 1980s. The concluding chapter seeks to set out the lessons which can be drawn from the Sheffield experience, relating back to the earlier arguments, as well as suggesting ways of integrating those conclusions with the analyses of the state developed by Jessop at a more abstract level

Systematizing God\u27s Law: Rabbanite Jurisprudence In The Islamic World From The Tenth To The Thirteenth Centuries

This study examines the jurisprudential writings of medieval Rabbanites, Jews in the Islamic world who saw themselves as heirs to the talmudic tradition. Rabbanite Jews were the first to author systematic accounts of talmudic law, which they attempted to transform from an amorphous, dialectical, and discursive corpus into a structured, elegant, and logical system. In so doing, they sought to impose a coherent structure on their legal traditions that would be compatible with larger theological, philosophical, and epistemological ideas. By subjecting Rabbanite legal theory to diachronic and synchronic analysis, this dissertation demonstrates that Rabbanites were involved in a multilayered conversation that engaged their talmudic past, Rabbanite and non-Rabbanite coreligionists, and elements of the Islamic intellectual tradition that were most helpful for the explanation and reconsideration of their own tradition. While Rabbanite legal theory drew heavily on talmudic ideas, it was, at its core, profoundly contemporary, spurred by both Qaraite and Islamic legal theory, among many other factors. This study concentrates on Rabbanite thinking about two, frequently intertwined, topics: the nature and scope of extra-scriptural traditions, known as Oral Torah, and the methodology to be used in enumerating the 613 commandments, which, talmudic legend claims, were given to Moses at Sinai. Acknowledging earlier scholarship on these topics, this study presents a more holistic picture of Rabbanite legal theory. Particular attention is paid to the Judeo-Arabic writings of Moses Maimonides (1138-1204), the Rabbanite author who appears to have been most explicitly concerned with problems of legal theory. Other central figures include Saʿadya ben Joseph Gaon (882-942), Daniel ben Saʿadya ha-Bavli (fl. early thirteenth c.), and Abraham ben Moses Maimonides (1186-1237)

Rural life in English poetry of the mid-eighteenth century

This thesis examines several mid-eighteenth century poems, assessing their portrayal of rural life, its literary and historical significance, and the aesthetic and ideological issues it presents. An introductory essay on developments in rural poetry sets the scene for two extended essays. The first essay is a comparative reading of the subject of rural labour in three poems: James Thomson’s The Seasons (1726-44), Stephen Duck’s The Thresher’s Labour (1730, 1736) and Mary Collier’s The Woman’s Labour (1739). The viewpoints of a professional poet (Thomson), a farm labourer (Duck), and a working woman (Collier) are compared in relation to kinds of work all three address as well as to individual labouring subjects. The responses of the three poets to such related issues as folk traditions, forms of charity and other ‘compensations’, are also compared. Some surprising similarities as well as instructive differences are located; and an interesting picture of idealistic and realistic, male-oriented and female-oriented attitudes to labour and labour-related themes emerges

Conquering the Highlands

Ecology; Deforestation; Scotlan

Post-Truth Imaginations

This book engages with post-truth as a problem of societal order and for scholarly analysis. It claims that post-truth discourse is more deeply entangled with main Western imaginations of knowledge societies than commonly recognised. Scholarly responses to post-truth have not fully addressed these entanglements, treating them either as something to be morally condemned or as accusations against which scholars have to defend themselves (for having somehow contributed to it). Aiming for wider problematisations, the authors of this book use post-truth to open scholarly and societal assumptions to critical scrutiny. Contributions are both conceptual and empirical, dealing with topics such as: the role of truth in public; deep penetrations of ICTs into main societal institutions; the politics of time in neoliberalism; shifting boundaries between fact – value, politics – science, nature – culture; and the importance of critique for public truth-telling. Case studies range from the politics of nuclear power and election meddling in the UK, over smart technologies and techno-regulation in Europe, to renewables in Australia. The book ends where the Corona story begins: as intensifications of Modernity’s complex dynamics, requiring new starting points for critique