Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.

Part intellectual autobiography and part exposition of complex yet contemporary economic ideas, this lively conversation with renowned scholar and public intellectual Kenneth J. Arrow focuses on economics and politics in light of history, current events, and philosophy as well. Reminding readers that economics is about redistribution and thus about how we treat each other, Arrow shows that the intersection of economics and ethics is of concern not just to economists but for the public more broadly. With a foreword (...) by Amartya Sen, this book highlights the belief that government can be a powerful force for good, and is particularly relevant in the current political climate and to the lay reader as well as the economist. (shrink)

Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by (...) two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program. (shrink)

I comment on Amartya Sen's study of the relations between the analysis of freedom and the theory of social choice. Two of his themes are analysed with regard to their contribution to an analytic understanding of the issues. These are: (1) the multiple interpretations of the concept of ‘preferences’ as a foundation for the formal conceptualizations of social choice and freedom; and (2) some issues in the formalization of freedom as a value to be compared with outcomes. Under (2), I (...) mainly point out some difficulties in the existing analyses and mildly support a ‘flexibility’ interpretation of freedom that I have advanced earlier. I conclude with some observations drawn from history and literature which complicate the value bien-pensant thinkers are prone to place on freedom. (Published Online February 16 2006). (shrink)

Cohesion may be based primarily on interpersonal ties or rely instead on the connection between member and group, while groups may cohere temporarily based on the immediate alignment of interests among members or may be tied together more permanently by socio-emotional bonds. Together, these characteristics define four prototypical group types. Cliques and coalitions are based primarily on dyadic ties. Groups of comrades or colleagues rely instead on the connection of members to the group for cohesion, which reduces the marginal cost (...) of increasing group size. The strong glue of socio-emotional cohesion binds cliques and comrades, while coalitions and groups of colleagues are often based on weaker forms of cohesion. The mix of strong and weak adhesives and the greater scalability offered by the member-group bond provide the building blocks for assembling very large societies without overtaxing the social brain. (shrink)

One of the central questions of economics relates to the coordination of individual units within a large organization to achieve the central objectives of that organization. This book examines the problems involved in allocating resources in an economic system where decision-making is decentralized into the hands of individuals and individual enterprises. The decisions made by these economic agents must be coordinated because the input decisions of some must eventually equal the output decisions of others. Coordination arises naturally out of the (...) mathematical theory of optimization but there is still the question of how it can be achieved in practice with dispersed knowledge. The essays here explore the many facets of this problem. Nine papers are grouped under the title 'Economies with a single maximand'. They include papers on static and dynamic optimization, decentralization within firms, and nonconvexities in optimizing problems. Fourteen papers are concerned with 'Economies with multiple objectives'. Among the topics covered here are stability of competitive equilibrium, stability in oligopology, and dynamic shortages. The final part of the book includes three papers on informational efficiency and informationally decentralized systems. Leonid Hurwitcz is the Nobel Prize Winner 2007 for The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, along with colleagues Eric Maskin and Roger Myerson, for his work on the effectiveness of markets. (shrink)

Indigenous Sustainable Wisdom: First Nation Know-How for Global Flourishing’s contributors describe ways of being that reflect a worldview that has guided humanity for 99% of human history; they describe the practical traditional wisdom stemming from Nature-based relational cultures that were or are guided by this worldview. Such cultures did not cause the kinds of anti-Nature and de-humanizing or inequitable policies and practices that now pervade our world. Far from romanticizing Indigenous histories, Indigenous Sustainable Wisdom offers facts about how human beings, (...) with our potential for good and evil behaviors, can live in relative harmony again. Contributions cover views from anthropology, psychology, sociology, leadership, native science, native history, native art. (shrink)

Primatological and archaeological evidence along with anthropological accounts of hunter-gatherer societies indicate that lethal between-group violence may have been sufficiently frequent during our ancestral past to have shaped our evolved behavioral repertoire. Two simulations explore the possibility that heroism (risking one's life fighting for the group) evolved as a specialized form of altruism in response to war. We show that war selects strongly for heroism but only weakly for a domain-general altruistic propensity that promotes both heroism and other privately costly, (...) group-benefiting behaviors. A complementary analytical model shows that domain-specific heroism should evolve more readily when groups are small and mortality in defeated groups is high, features that are plausibly characteristic of our collective ancestral past. (shrink)

Introductory chapter to the book, Indigenous Sustainable Wisdom.

This volume contains a selection of Professor Uzawa's important contributions to mathematical economics. Subjects covered by these nineteen essays include consumption, production, equilibrium, capital, growth, planning, international trade, and the theory of social overhead capital. Written in the 1960s and early 1970s, the papers form a basis upon which economic theory has developed over the last twenty years. The collection includes some of Uzawa's classic contributions, such as 'Preference and Rational Choice in the Theory of Consumption', 'Time Preference, the Consumption (...) Function, and Optimum Asset Holdings', 'Neutral Inventions and the Stability of Growth Equilibrium', 'On a Two-Sector Model of Economic Growth', 'Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth', and 'On the Economics of Social Overhead Capital'. The collection will be useful not only in understanding the nature of the development in economic theory today, but also in reflecting upon the direction toward which economic theory will be advancing in the future. (shrink)

In a fifty-two–line interpolation appearing towards the end of many Romance of the Rose manuscripts, the narrator compares the female image over the entry to the tower of Jealousy—the one at which Venus fires her burning arrow—to the head of Medusa. This passage entered the Rose manuscript tradition in the late thirteenth or early fourteenth century, possibly within the lifetime of Jean de Meun; it recurs throughout the fourteenth and fifteenth centuries. A reading of the Medusa interpolation raises the (...) important critical issue of significant variants in a manuscript tradition and the evidence they offer for a medieval reading of the text in question. A close examination of the Medusa passage expands our understanding of the reception of the Rose during the twenty or thirty years immediately following the completion of Jean de Meun's continuation. An inquiry into the relevance of Medusa to the Rose, and in particular to this moment in the Rose, helps us to appreciate something of what the poem may have meant for its first readers. As I will show, the Medusa passage participates in a larger mythographic program extending throughout the conjoined Rose, exploring the nature of feminine sexuality and its effects on men. (shrink)

In this article I discuss Martha Nussbaum’s cosmopolitan educational ideal and its theoretical underpinnings. I argue that, in spite of its merits, it overlooks the historical-relational dimension of cross-cultural encounters and the impediments posed by unresolved historical conflicts to the goal of cultural reconciliation. I suggest a rehabilitation of the historical-relational dimension by applying the insights of Paul Ricoeur to this context. My steps comprise a description of Nussbaum’s position, an exploration of its shortcomings, an interpolation of Ricoeur’s ideas and (...) some concomitant suggestions. (shrink)

In this article I discuss Martha Nussbaum’s cosmopolitan educational ideal and its theoretical underpinnings. I argue that, in spite of its merits, it overlooks the historical-relational dimension of cross-cultural encounters and the impediments posed by unresolved historical conflicts to the goal of cultural reconciliation. I suggest a rehabilitation of the historical-relational dimension by applying the insights of Paul Ricoeur to this context. My steps comprise a description of Nussbaum’s position, an exploration of its shortcomings, an interpolation of Ricoeur’s ideas and (...) some concomitant suggestions. (shrink)

Why is the future so different from the past? Why does the past affect the future and not the other way round? The universe began with the Big Bang - will it end with a `Big Crunch'? Now in paperback, this book presents an innovative and controversial view of time and contemporary physics. Price urges physicists, philosophers, and anyone who has ever pondered the paradoxes of time to look at the world from a fresh perspective, and throws fascinating new light (...) on some of the great mysteries of the universe. (shrink)

The book aims at a comprehensive account of the relationship between Wittgenstein s Tractatus Logico-Philosophicus and Russell s philosophy as it developed between 1903 and 1918. The focus is on the central nucleus of the Tractatus, i.e., on its ontology and the picture theory of language. On Russell s side, the multiple-relation theory of judgment has been chosen as the leading theme around which the presentation of several other issues is organized. Whereas the similarity between Russell s and Wittgenstein s (...) problems is pointed out, the deep difference between their solutions is acknowledged, in particular with reference to the opposition between objects and names on the one hand, and facts and propositions on the other.". (shrink)

I propose that, in addition to the commonly recognized increase of entropy, two more time arrows influence living beings. The increase of damage reactions, which produce aging and genetic variation, and the decrease of the rate of entropy production involved in natural selection are neglected arrows of time. Although based on the statistical theory of the arrow of time, they are distinguishable from the general arrow of the increase of entropy. Physiology under healthy conditions only obeys the increase (...) of entropy arrow. But aging, death, and evolution are determined by the other time arrows as well. Paradoxes emerge from conflicts among the specific determinisms associated with each arrow. These conflicts, along with uncertainties intrinsic to the low-number statistics of the arrows of damage reactions and decrease of the rate of production of entropy, highlight the limits of determinism at different levels of biology and its dependence on time span and number of organisms. The recognition of the three time arrows opens new perspectives for the problem of compatibility of the flow of time in physics and psychology. (shrink)

This paper extends the classical extension theorem established by Edward Szpilrajn (Fundamenta Mathematicae, 16, pp. 386–389, 1930). Szpilrajn's theorem states that every quasi‐ordering has an ordering extension. Because of its usefulness in various themes of economics, it has been applied by many researchers. Important generalizations have been presented by two authors, Kenneth Arrow and Kotaro Suzumura, among others. First, we provide concise proofs of four extension theorems by Szpilrajn, Arrow and Suzumura. We then show an extension of their (...) extension theorems. (shrink)

In this paper, I draw on postphenomenology and material engagement theory to consider the material and emergent character of sociality in Homo faber. I approach this through the context of the bow and arrow, which is a technology that has received recent attention in cognitive archeology as a proxy for assessing criteria that made early human cognition distinct from that of other hominins. Through an ethnographic case study, I scrutinize the forms of knowledge that are required to use the (...) technology in the dynamic field of environmental practices that constitute the hunt. I demonstrate that the learning of the skill is a transformational process where beginners develop self and intentionality by attuning subjective capacities for sensory awareness and creative responsiveness. Through mutual participation, the bow and arrow aligns disposition and rapport among those whose life processes are shaped by the skill. As a mechanism of shared experience, the bow and arrow generates a community can together perceive and act creatively in an impermanent world. Through these observations, I argue that early human sociality was built not on a pre-evolved capacity for symbolic representation but on technical experience, and I consider important questions this raises about the nature of evolutionary processes at work in the development of communities through time. (shrink)

I offer a novel solution to Zeno’s paradox of The Arrow by introducing nilpotent infinitesimal lengths of time. Nilpotents are nonzero numbers that yield zero when multiplied by themselves a certain number of times. Zeno’s Arrow goes like this: during the present, a flying arrow is moving in virtue of its being in flight. However, if the present is a single point in time, then the arrow is frozen in place during that time. Therefore, the (...) class='Hi'>arrow is both moving and at rest. In “Zeno’s Arrow, Divisible Infinitesimals, and Chrysippus,” White suggests using an infinitesimal value as the length of the present. Contra Zeno, this allows the arrow to be moving in the present, rather than frozen in place. In this paper, I follow the basic outline of White’s solution but argue that his solution suffers from arbitrariness and a related theoretical artificiality in relation to the system of infinitesimals he invokes, viz. in relation to the hyperreal infinitesimals of nonstandard analysis. After arguing that any solution to the paradox must satisfy certain theoretical requirements, I examine White’s solution alongside two nilpotent solutions. One of these solutions is inspired by F.W. Lawvere’s Smooth Infinitesimal Analysis and the other is inspired by Paolo Giordano’s ring of Fermat Reals. I argue that Giordano’s nilpotents supply the best answer to Zeno’s paradox. (shrink)

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].

With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem of (...) the paper (Theorem 2.2) is analogous to the Wroski's result for equational classes of algebras [13]. It reads that for a large class of logics the conjunction of (AP) and (FEP) is equivalent to (IT) and that the latter property is equivalent to (MIP). (shrink)

The theory of general relativity has produced some great insights into the nature of space and time. Unfortunately, its relevance to the problem of the direction of time has been overestimated. This paper points out that the problem of the direction of time can be formulated in purely local ways, and that in this kind of formulation considerations of general relativity are of little or no importance. On the basis of this, positions which assume that relativistic considerations are always relevant (...) are criticised. (shrink)

Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have (...) taken it seriously have propounded solutions with which they profess themselves to be perfectly satisfied. So my question is: will Zeno's Arrow survive into the millennium just begun? (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the (...) distant ''future''), the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's version or in Bohm's version, (...) does not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, (...) TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models. (shrink)

DIVA new look at Kenneth Arrow’s classic study of the economics of health care: is his formulation still relevant 40 years later?/div.

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time’s arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory’s ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine’s version or in Bohm’s version, (...) does not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

A review of Huw Price's Time's Arrow and Archimedes' Point.

This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ is proposed. An approximate idea of obtaining $$\textsf{G}(\textbf{C}+\textbf{J})$$ is adding rules for classical implication on top of the intuitionistic multi-succedent sequent calculus by Maehara (Nagoya Math J 7:45–64, 1954). However, in the semantic treatment, some formulas do not (...) satisfy heredity, which leads to the necessity of a restriction on the right rule for intuitionistic implication to keep the soundness of the calculus. The calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ enjoys cut elimination and Craig interpolation, whose detailed proofs are described in this paper. Cut elimination enables us to show the decidability of this combination both directly and syntactically. This paper also employs a canonical model argument to establish the strong completeness of Hilbert system $$\mathbf {C+J}$$ proposed by del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996). (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions (...) of the connectives in question. (shrink)