[688/2197] In many economic matters there arises a paradox that may be related to what in logic courses is called the “sophism of the heap of wheat”. Among the sophisms bequeathed to us by the Greeks, none is worthier to have come down through the centuries than this “sophism of the heap of wheat”; indeed this no mere puzzle, but a topical example of a frequent difficulty, as much in practical life as in pure speculation.One grain of (...) wheat does not make a heap; neither do two grains; nor do three grains; \(\ldots \) on the other hand, if a million grains are gathered, we can agree that they constitute a heap. What is the exact limit? Should we say that 2,342 grains, for instance, do not make a heap, whereas 2,343 grains do? This is obviously ridiculous. There appears no logical way out of this dead-end; it is therefore not possible to know what a heap of wheat is.The expression of the sophism can be varied in many ways; a classification of these expressions will not be unhelpful. (shrink)

In a providential account of the changing relation between political economy and economics, the late nineteenth-century development of economics is identified with the rational choice model; and the revival of political economy in the late twentieth century comes with the export of this model to politics and the other social sciences. An alternative prudential account locates the revival of political economy with a significant qualification to the rational choice model. This qualification restores an eighteenth- and nineteenth-century view of rule-following to (...) human agency. This essay sets out these accounts and draws the conclusion that the choice of one over the other matters, not least for the practice of contemporary politics. (shrink)

The present offers a pragmatic solution of the Heap Paradox, based on the idea that vague predicates are “indexical” in the sense that their denotation does not only depend on the context of their use, but it is a function of the context. The analysis is based on the following three claims. The borderlines of vague terms are undetermined in the sense that though they may be determined in some contexts, they may differ from one context to the (...) next. Vagueness serves the important communicative function, enabling speakers to identify entities as objects (as things we can talk about) in terms of some quantitative differences between the “object” and its background in the context. Thus, in some contexts we can naturally partition the group of men uniquely so as to distinguish the bald from the not-bald. Whether a man with a given hair number is among the bald in a given context depends not only on his own hair number but also on the hair number of others in that context. This provides the background for the claim that when we assert that John is bald, we presuppose that there is a unique demarcation to the bald in that context. I consider the truth of the Paradox’s statements in contexts where the presupposition is true and in contexts where it is false. The analysis yields that the contradiction is avoided because though each of the statements is often true, never are all the sentences in the Paradox true together. (shrink)

This paper uses evidence from laboratory experiments to identify a variety of tribalisms. This is important because some tribalisms encourage zerosum thinking and others do not; and some are not developed by Buchanan. This, in turn, supplies new insights into Buchanan’s project of identifying the kinds of environment that encourage his sense of moral progress. In particular, current levels of inequality become a significant barrier to moral progress not only because they create an economic form of tribalist zero-sum thinking but (...) they also undermine the scope for positive-sum. (shrink)

This article examines, experimentally, whether inequality affects the social capital of trust in non-market and market settings. We consider three experimental treatments, one with equality, one with inequality but no knowledge of the income of other agents, and one with inequality and knowledge. Inequality, particularly when it is known, has a corrosive effect on trusting behaviours in this experiment. Agents appear to be less sensitive to known relative income differentials in markets than they are in the non-market settings, but trust (...) in markets appears generally more vulnerable to the introduction of inequality than in the non-market setting. (shrink)

One might expect that, in pure coordination games, coordination would become less frequent as the number of options increases. Contrary to this expectation, we report an experiment which found more frequent coordination when the option set was unrestricted than when it was restricted. To try to explain this result, we develop a method for eliciting the general rules that subjects use to identify salient options in restricted and unrestricted sets. We find that each such rule, if used by all subjects, (...) would generate greater coordination in restricted sets. However, subjects tend to apply different rules to restricted and unrestricted sets. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities (...) of Borel’s essay is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are (...) heaps of sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. -/- Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case . (shrink)

Barry Maguire has recently argued that the nature of normative support for affective attitudes like fear and admiration differs fundamentally from that of reasons. These arguments appear to raise new and serious challenges for the popular ‘reasons-first’ view according to which normative support of any kind comes from reasons. In this paper, I show how proponents of the reasons-first view can meet these challenges. They can do so, I argue, if they can successfully meet some other well-known challenges to their (...) view: distinguishing between right and wrong kinds of reasons, distinguishing between reasons, enablers, and defeaters, and providing an account of the relation between reasons and rationality. Whether proponents of the reasons-first view can meet these other challenges remains controversial. I do not try to settle these questions here, but rather show that the debate about the nature of normative support for affective attitudes is not going to be settled in isolation from them. (shrink)

By offering an original elucidation of the notion of the imagination in the writings of Immanuel Kant, Johann Fichte, and Cornelius Castoriadis, this book addresses and brings to the fore the significance of the imagination as the ontological source of human creation.

"The enterprise initiative is probably the most significant political and cultural influence to have affected Western and Eastern Europe in the last decade. In this book, academics from a range of disciplines debate Mary Douglas's distinctive Grid Group cultural theory and examine how it allows us to analyse the complex relation between the culture of enterprise and its institutions. Mary Douglas, Britain's leading cultural anthropologist, contributes several chapters."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved.

In lieu of an abstract, here is a brief excerpt of the content:Drama on the Run:A Prelude to Mapping the Practice of Process DramaPamela Bowell (bio) and Brian Heap (bio)In the current educational climate prevailing in a number of countries, increased emphasis is being placed on the concept of "the artist in schools." Funding is being channeled to support a range of initiatives and schemes that are designed to bring arts professionals from all the art forms into the classroom (...) where they place their artistic talents, knowledge, and insights alongside the pedagogic skills of the teacher.We see exciting projects in which artists work with children in school—visual artists to create murals, musicians to compose and perform operas, dancers to choreograph new ballets, and actors and directors to devise plays. Many of the outcomes are of high quality, and the children who have been fortunate enough to be involved have enjoyed the experiences and have gained a great deal from them. This would seem to be a state of affairs to be applauded unreservedly, as such projects surely enrich the lives of the pupils and schools in which they take place. In one sense, of course, this is undeniably true, and we have no intention of suggesting otherwise. However, in reality, this is a much more complex situation. It raises a number of key issues for us as educational practitioners who work in the field of applied theatre, sharing with others, as Judith Ackroyd describes, "a belief in the power of the theatre form to address something beyond the form itself."1The most critical issue is the perceived separation of the artist from the teacher that can sometimes be encouraged by artists in schools projects. We sense a dangerous precedent here. It becomes all too easy for two erroneous assumptions to be made, namely that teachers cannot be considered to be artists in their own right, while artists on the other hand can be accorded [End Page 58] the status of teacher. In our own experience too, the nature of educational funding can be extremely volatile, subject to all kinds of shifts in the prevailing political and economic climate, as well as adjustments to the ways in which funding is applied according to the social and educational priorities of the time. Too frequently, education falls victim to what might be described as "the-flavor-of-the-month syndrome."Those who are involved with teacher education, both pre- and in-service, make superhuman efforts to respond with alacrity to the new demands as courses are reviewed and reorganized accordingly. The trainees of the next generation find themselves with a new "party line" to toe as their courses conform to the new priority. This is all well and good—until the priority changes and gaps suddenly appear in the knowledge or skills or understanding of teachers. What was received wisdom becomes a deficit model as focus changes, and the circle is now expected to be squared.Under these circumstances, it would seem a more prudent policy to train teacher-artists who would have the ability to meld their pedagogical understanding and skill with an aesthetic craft and sensibility than to rely on visiting artists as the "natural" or "normal" providers of arts education. This would ensure not only that teachers would make better, more informed use of visiting artists but also that children's expertly guided engagement with the arts would be a permanent and enduring aspect of their regular schooling rather than a "special" event subject to the vagaries of arts funding or policy. This might seem an easy statement to make for people such as ourselves, who have spent whole careers working as teacher-artists within the field of drama in education. But it might seem an altogether more daunting prospect for teachers, or intending teachers, who are not specialists in the arts.Having spent a great deal of our respective careers working in teacher education, we are very conscious of this possibility. To this end, our research collaboration has been centered on exploring and coming to understand more fully, clearly, and precisely how the teacher functions as an artist within the particular genre of applied theatre known as process drama. Embedded within the increase of our... (shrink)

Taking inspiration from the vast breadth of Castoriadis’ oeuvre, this article provides an ongoing elucidation of the being of human as creation ex nihilo. It does so by engaging with Castoriadis’ reflections on the vis formandi pertaining to the human condition and his tentative introduction to the concept of the ‘human Nonconscious’. Across many of his essays, Castoriadis refers to the vis formandi of the being of human as an ‘a-causal’ and as a corporeal power of formation and of creation. (...) Associated with the defunctionalized and the corporeal dimensions of the radical imagination, these two domains of formation and of creation are, for Castoriadis, fundamental to the ontology of the being of human. By exploring Castoriadis’ theoretical and practical reflections on the vis formandi of the being of human and the role he accords the two dimensions of the radical imagination, this article offers a new mode of thinking about the being of human as creation ex nihilo – one that addresses the mind body divide by proposing that the human Nonconscious can be envisaged as the dominion of the embodied imagination. (shrink)

This article examines, experimentally, whether inequality affects the social capital of trust in non-market and market settings. We consider three experimental treatments, one with equality, one with inequality but no knowledge of the income of other agents, and one with inequality and knowledge. Inequality, particularly when it is known, has a corrosive effect on trusting behaviours in this experiment. Agents appear to be less sensitive to known relative income differentials in markets than they are in the non-market settings, but trust (...) in markets appears generally more vulnerable to the introduction of inequality than in the non-market setting. (shrink)

This chapter contains sections titled: Fingers Running Up and Down the Back of My Arm Am I Really Free? Determinism Kant, Freedom, and Alternate Natures ‘Nature’ Isn't a System Embodied Freedom: It Develops! The Response Part of Responsibility In the Space Created by that Fluid Emergence.

This paper reviews some of the key responses to Hahn's famous retiring remarks and argues that none has satisfactorily addressed Hahn's suggestion that a discipline does not need to consciously discuss its foundations as it can rely on an evolutionary process to select them. The paper presents a general counter to Hahn on this point which, when applied to contemporary economics, supplies a strong case for the study of methodology now. The particular strength of the case now turns on the (...) current ferment at the foundations of the discipline over the rational choice model. (shrink)

In the epilogue to Memory, History, Forgetting, Paul Ricoeur introduces an overlooked “vertical” axis into the problem of forgiveness. This verticality runs from the “depth” of fault to the “height” of forgiveness. For Ricoeur, forgiveness only appears an impossible “exchange” if one excludes this verticality from the question. Instead, he calls forgiveness “difficult” because it traverses from height to depth. This article argues that Ricoeur’s notion of the horizontal and the vertical in Memory, History, Forgetting is best understood as an (...) allusion to his account of time and eternity in Chapter 1 of Time and Narrative, volume 1, even though Ricoeur himself does not explicitly make this connection. In light of the ontological tenor of this connection, the author also suggests a slight modification of Ricoeur’s account, calling forgiveness “improbable” rather than difficult. (shrink)

In the epilogue to Memory, History, Forgetting, Paul Ricoeur introduces an overlooked “vertical” axis into the problem of forgiveness. This verticality runs from the “depth” of fault to the “height” of forgiveness. For Ricoeur, forgiveness only appears an impossible “exchange” if one excludes this verticality from the question. Instead, he calls forgiveness “difficult” because it traverses from height to depth. This article argues that Ricoeur’s notion of the horizontal and the vertical in Memory, History, Forgetting is best understood as an (...) allusion to his account of time and eternity in Chapter 1 of Time and Narrative, volume 1, even though Ricoeur himself does not explicitly make this connection. In light of the ontological tenor of this connection, the author also suggests a slight modification of Ricoeur’s account, calling forgiveness “improbable” rather than difficult. (shrink)

Though Bernard Lonergan is often counted among the so-called “Transcendental Thomists”, this article offers a re-appraisal of his theory of understanding with a renewed emphasis on its a posteriori, rather than a priori, approach. For Lonergan, because understanding is experienced, it can be investigated empirically. It is the further conviction of the author that the experience in which understanding gives itself is a bodily experience. This is the case both in how the experience emerges from biological processes, but also appears (...) within the “phenomenological body” of human conscious awareness. Lonergan’s cognitional theory is compared with Maurice Blondel’s theory of embodied reason to elucidate the former and with Eugene Gendlin’s notion of a bodily “felt-experience” to elucidate the latter. A few final, exploratory comments are made with regard to the dynamics of symbolization, formulation, and expression by linking Gendlin’s work with Lonergan’s Verbum articles. (shrink)

Healthcare practitioners are often presented with vulnerable encounters where their professional experience is insufficient when dealing with patients who suffer from illnesses such as chronic pain. How can one otherwise understand chronic pain and develop practices whereby medical healthcare practitioners can experience alternative ways of doing their practice? This essay describes how a group of researchers have, over a number of years, developed improvised participatory theatre as a means of engaging healthcare practitioners, patients and other lay people in situations where (...) it is legitimate to reappraise their practice and reunderstand the nature of an illness such as chronic pain. One conclusion was to consider that it is a relational rather than an individual phenomenon that in turn demands alternative practice. Through iterative workshop processes of improvised theatre, participants are encouraged to experience the vulnerable, the unknown, and the need to be alternatively present when dealing with patients whose situation is imbued with suffering. (shrink)

Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...) and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

This research investigates an integrated problem of construction scheduling and resource allocation. Inspired by complex construction practices, multi-time scale resources are considered for different length of terms, such as permanent staff and temporary workers. Differing from the common stochastic optimization problems, the resource price is supposed to be an uncertain parameter of which probability distribution is unknown, but observed data is given. Hence, the problem here is called Data-Driven Construction Scheduling and Multiscale Resource Allocation Problem. Based on likelihood robust optimization, (...) a multiobjective programming is developed where project completion time and expected resource cost are minimized simultaneously. To solve the problem efficiently, a double-layer metaheuristic comprised of Multiple Objective Particle Swarm Optimization and interior point method named MOPSO-interior point algorithm is designed. The new solution presentation scheme and decoding process are developed. Finally, a construction case is used to validate the proposed method. The experimental results indicate that the MOPSO-interior point algorithm can reduce resource cost and improve the efficiency of resource utilization. (shrink)

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19 th century: Dr Bernard Bolzano’s Paradoxien . This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.

_Paradoxes of the Infinite_ presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19 th century: Dr Bernard Bolzano’s _Paradoxien_. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.

_Paradoxes of the Infinite_ presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19 th century: Dr Bernard Bolzano’s _Paradoxien_. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction to the masterpiece, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.