The reach-avoid game theory is an ideal tool to handle the conflicts among intelligent agents and has been previously studied assuming full state information and no time limits on the players in the past decades. In this article, we extend the problem by requiring the defender to detect the attacker and adding maximum operation time constraints to the attacker. The attacker aims to reach the target region without being captured or reaching its time limit. The defender can employ strategies (...) to intercept the attacker only when the attacker is detected. A geometric method is proposed to solve this game qualitatively. By analyzing the geometric property of the Apollonian circle and the detection range, we give the barrier under the condition that the attacker is initially detected and the attacker’s shortest route which guarantees its arrival at the target region when it is initially outside the detection range. Then, a barrier that separates the game space into two respective winning regions of the players is constructed based on the shortest route and the time limit of the attacker. The main contributions of this work are that this paper provides the first attempt to introduce the abovementioned two concepts simultaneously, which makes the game more practical, and we provide the complete solution of the game in all possible situations. (shrink)

Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and (...) Deadlock appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory. (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy (...) between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy (...) between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation. (shrink)

In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent (...) books on which sure- win is impossible. Our main results provide geometric characterizations of the space of all books which are jointly coherent with a xed one. As a consequence we will also show that joint coherence is decidable. (shrink)

Johnson and Hudecki argue that Bernard Suits fails to refute Wittgenstein’s ‘family resemblance’ view of games because Suits’s account of how games begin, how they are played, and the ends they involve, fails to match basic facts of player experience. In reply, the current paper describes three keys to interpreting The Grasshopper: (1) distinguishing the four perspectives from which Suits describes games, (2) recognizing Suits' dispositional view of rule following, and (3) understanding the geometrical metaphor Suits uses to describe rules. (...) In light of these, this paper argues that Johnson and Hudecki’s critiques are either mistaken or are actually affirmations of Suits' position. (shrink)

The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λμ-calculus, which can be seen as an extension of system F to classical logic, and for which we define a categorical framework: control hyperdoctrines.Our game model of λμ-calculus is based on polymorphic arenas which evolve during the play. We show that type isomorphisms coincide with the “equality” on (...) arenas associated with types. Finally we deduce the equational characterization of type isomorphisms from this equality. We also recover from the same model Roberto Di Cosmo’s characterization of type isomorphisms for system F.This approach leads to a geometrical comprehension on the question of second-order type isomorphisms, which can be easily extended to some other polymorphic calculi including additional programming features. (shrink)

Through a phenomenological study of horse-human relations, this article explores the ways in which, as embodied beings, we live relationally, rather than as separate human identities. Conceptually this challenges oppositional logic and humanist assumptions, but where poststructuralist treatments of these issues tend to remain abstract, this article is concerned with an embodied demonstration of the ways in which we experience a relational or in-between logic in our everyday lives.

We argue that pedagogic authority relies on love, which is misunderstood if seen as a matter of actions and subjects. Love is based not on finite subjects and objects existing in Euclidean space and linear time, but, rather, on the non-finite ontology, space and time of relations. Loving authority is a matter of calling and vocation, arising from the spontaneous and simultaneous call-and-response of a lively relation. We make this argument through a reading of Buber’s I–You relation and Murdoch’ s (...) account of the responsiveness of ascetic discipline. In presenting this analysis, we draw upon a case study from a research project on Australian teachers and students. (shrink)

Prior research suggests brokers do not always act in the best interests of clients, although morally obligated to do so. We empirically investigated this issue focusing on trades executed at best execution price, before and after the introduction of electronic limit-order trading, on the London Stock Exchange. As a result of limit-order trading, the proportion of trades executed at the best execution price for the customer significantly increased. We attribute this to a sustained increase in the liquidity of stocks as (...) a result of limit-order trading, regardless of market capitalisation. We discuss the ethical implications of our findings and conclude that market structures that enhance market competitiveness may help reconcile broker and client interests. (shrink)

This study examined the link between employees’ adult attachment orientations and perceptions of line managers’ interpersonal justice behaviors, and the moderating effect of national culture. Participants from countries categorized as low collectivistic and high collectivistic completed an online survey. Attachment anxiety and avoidance were negatively related to interpersonal justice perceptions. Cultural differences did not moderate the effects of avoidance. However, the relationship between attachment anxiety and interpersonal justice was non-significant in the Southern Asia cultural cluster. Our findings indicate the importance (...) of ‘fit’ between cultural relational values and individual attachment orientations in shaping interpersonal justice perceptions, and highlight the need for more non-western organizational justice research. (shrink)

Abstract In this article we develop a relational understanding of sociality, that is, an account of social life that takes relation as primary. This stands in contrast to the common assumption that relations arise when subjects interact, an account that gives logical priority to separation. We will develop this relational understanding through a reading of the work of Martin Buber, a social philosopher primarily interested in dialogue, meeting, relationship, and the irreducibility and incomparability of reality. In particular, the article contrasts (...) Buber’s work with that of poststructuralist theorists who take as their starting point the deconstruction of the Hegelian logic of binary oppositions. Deconstruction understands difference as the excess that undoes the binary, but Buber, we argue, shows how difference derives from the primacy and ontological undefinability of relation. Relational logic does not exclude the logic of separations and oppositions: relation is the primal ground that makes separations possible. Content Type Journal Article Pages 1-13 DOI 10.1007/s11841-011-0278-9 Authors Andrew Metcalfe, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Ann Game, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Journal Sophia Online ISSN 1873-930X Print ISSN 0038-1527. (shrink)

The mechanisms responsible for the fine tuning of development, where the wildtype phenotype is reproduced with high fidelity, are not well understood. The difficulty in approaching this problem is the identification of mutant phenotypes indicative of a defect in these fine‐tuning control mechanisms. Evolutionary biologists have used asymmetry as a measure of developmental homeostasis. The rationale for this was that, since the same genome controls the development of the left and right sides of a bilaterally symmetrical organism, departures from symmetry (...) can be used to measure genetic or environmental perturbations. This paper examines the relationship between asymmtry and resistance to organophosphorous insecticides in the Australian sheep blowfly, Lucilia cuprina. A resistance gene, Rop‐1, which encodes a carboxylesterase enzyme, also confers a significant increase in asymmetry. Continued exposure of resistant populations to insecticide has selected a dominant suppressor of the asymmetry phenotype. Genetic evidence indicates that the modifier is the L. cuprina Notch homologue. (shrink)

Fix 2 < n < ω. Let CA n denote the class of cylindric algebras of dimension n, and let RCA n denote the variety of representable CA n ’s. Let L n denote first-order logic restricted to the first n variables. Roughly, CA n, an instance of Boolean algebras with operators, is the algebraic counterpart of the syntax of L n, namely, its proof theory, while RCA n algebraically and geometrically represents the Tarskian semantics of L n. Unlike Boolean (...) algebras having a Stone representation theorem, RCA n ⊊ CA n. Using combinatorial game theory, we show that the existence of certain finite relation algebras RA, which are algebras whose domain consists of binary relations, implies that the celebrated Henkin omitting types theorem fails in a very strong sense for L n. Using special cases of such finite RA ’s, we recover the classical nonfinite axiomatizability results of Monk, Maddux, and Biro on RCA n and we re-prove Hirsch and Hodkinson’s result that the class of completely representable CA n ’s is not first-order definable. We show that if T is an L n countable theory that admits elimination of quantifiers, λ is a cardinal < 2 ℵ 0, and F = 〈 Γ i : i < λ 〉 is a family of complete nonprincipal types, then F can be omitted in an ordinary countable model of T. (shrink)

In this paper, we study dialogue as a game, but not only in the sense in which there would exist winning strategies and a priori rules. Dialogue is not governed by game rules like for chess or other games, since even if we start from a priori rules, it is always possible to play with them, provided that some invariant properties are preserved. An important discovery of Ludics is that such properties may be expressed in geometrical terms. The (...) main feature of a dialogue is “convergence”. Intuitively, a dialogue “diverges” when it stops prematurely by some disruption, or a violation of the tacit agreed upon conditions of the discourse. It converges when the two speakers go together towards a situation where they agree at least on some points. As we shall see, convergence may be thought of through the geometrical concept of orthogonality . Utterances in a dialogue have as their content, not only the processes (similar to proofs) which lead to them from a monologic view, but also their interactions with other utterances. Finally, any utterance must be seen as co-constructed in an interaction between two processes. That is to say that it not only contains one speaker’s intentions but also his or her expectations from the other interlocutor. From our viewpoint, discursive strategies like narration , elaboration , topicalization may derive from such interactions, as well as speech acts like assertion, question and denegation. (shrink)

Mathematics, as Eugene Wigner noted, is unreasonably effective in physics. The argument of this paper is that the disproportionate attention that philosophers have paid to discrete structures such as the natural numbers, for which a nominalist construction may be possible, has deprived us of the best argument for Platonism, which lies in continuous structures—in fields and their derived algebras, such as Clifford algebras. The argument that Wigner was making is best made with respect to such structures—in a loose sense, with (...) respect to geometry rather than arithmetic. The purpose of the present paper is to make this connection between mathematical realism and geometrical entities. It thus constitutes an argument against formalism, for which mathematics is merely a game with humanly set rules; and nominalism, in which whatever mathematics is used is eliminable in the final analysis, by often insufficiently specified means. The hope is that light may be cast on the stubborn mysteries of the nature of quantum mechanics and its mathematical formulation, with particular reference to spinor representations—as they have been developed by Andrej Trautman. Thus, according to our argument, quantum mechanics (QM) may appear more natural, as we have better reasons to take spinor structures as irreducibly real, a view consonant with the work of Trautman and Penrose in particular. (shrink)

Even simple geometric shapes are seen as animate and goal-directed when they move in certain ways. Previous research has revealed a great deal about the cues that elicit such percepts, but much less about the consequences for other aspects of perception and cognition. Here we explored whether simple shapes that are perceived as animate and goal-directed are prioritized in memory. We investigated this by asking whether subjects better remember the locations of displays that are seen as animate vs. inanimate, (...) con- trolling for lower-level factors. We exploited the ‘Wolfpack effect’: moving darts (or discs with ‘eyes’) that stay oriented toward a particular target are seen to be actively pursuing that target, even when they actually move randomly. (In contrast, shapes that stay oriented perpendicular to a target are correctly perceived to be drifting randomly.) Subjects played a ‘matching game’ – clicking on pairs of panels to reveal animations with moving shapes. Across four experiments, the locations of Wolfpack animations (compared to control animations equated on lower-level visual factors) were better remembered, in terms of more efficient matching. Thus perceiving animacy influences subsequent visual memory, perhaps due to the adaptive significance of such stimuli. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

This book is a timely new interpretation of the moral and political philosophy of Thomas Hobbes. Staying close to Hobbes's text and working from a careful examination of the actual substance of the account of natural law, R.E. Ewin argues that Hobbes well understood the importance of moral behavior to civilized society. This interpretation stands as a much-needed corrective to readings of Hobbes that emphasize the rationally calculated, self-interested nature of human behavior. It poses a significant challenge to currently fashionable (...) game theoretic reconstructions of Hobbesian logic. It is generally agreed that Hobbes applied what he took to be a geometrical method to political theory. But, as Ewin forcefully argues, modern readers have misconstrued Hobbes's geometric method, and this has led to a series of misunderstandings of Hobbes's view of the relationship between politics and morality. Important implications of Ewin's reading are that Hobbes never thought that "the war of each against all" was an empirical possibility for citizens; that his political theory actually presupposes moral agency; and that Hobbes's account of natural law forces us to the conclusion that Hobbes was a virtue theorist. This major contribution to Hobbes studies will be praised and criticized, welcomed and challenged, but it cannot be ignored. All philosophers, political theorists, and historians of ideas dealing with Hobbes will need to take account of it. (shrink)

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric (...) sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth. (shrink)

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment (...) for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. (shrink)

Mathematics is an important foundation for the development of science education. In the past, when instructors taught mathematical concepts of geometry shapes, they usually used traditional textbooks and aids to conduct teaching activities, which resulted in students not being able to understand the principles completely. Nowadays, it has become a trend to integrate emerging technologies into mathematics courses and to use digital instructional aids. Emerging technologies can effectively enhance students’ sensory experience while strengthening their impressions and understandings of subject concepts. (...) In this paper, we apply virtual reality immersive technologies to develop a “virtual reality immersive learning mathematics geometry system,” which is used to teach mathematical geometry concepts. Teachers use the system to develop three basic mathematical geometry learning materials: “Triangular pyramid volume = 1/3 prism volume,” “Cone volume calculation,” and “Triangle center of gravity derivation.” In the experimental activity, the teacher uses virtual reality teaching aids to guide students to learn mathematical geometry concepts in a fun way so that they can achieve the effectiveness of immersive learning. This study explores the impact of using the virtual reality immersive learning mathematics geometry system on students’ technology acceptance, learning motivations, and learning performance. The experimental result showed that using the virtual reality immersive learning mathematics geometry system can improve the learning motivation and learning performance of students. The findings indicated that the experimental group had better learning outcomes after completing the learning tasks of three geometric units. The experimental group used the virtual reality immersive learning mathematics geometry system which can lead to better learning outcomes. According to the ARCS questionnaire, students in the experimental group were confident to understand new subjects. At the same time, the mode of completing the game can effectively give students a sense of accomplishment. The use of emerging technologies in the classroom can be an attractive learning mode for students. (shrink)

Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general assumptions.

The Interface Theory of Perception, as stated by D. Hoffman, says that perceptual experiences do not to approximate properties of an “objective” world; instead, they have evolved to provide a simplified, species-specific, user interface to the world. Conscious Realism states that the objective world consists of ‘conscious agents’ and their experiences. Under these two theses, consciousness creates all objects and properties of the physical world: the problem of explaining this process reverses the mind-body problem. In support of the interface theory (...) I propose that our perceptions have evolved, not to report the truth, but to guide adaptive behaviors. Using evolutionary game theory, I state a theorem asserting that perceptual strategies that see the truth will, under natural selection, be driven to extinction by perceptual strategies of equal complexity but tuned instead to fitness. I then give a minimal mathematical definition of the essential elements of a “conscious agent.” Under the conscious realism thesis, this leads to a non-dualistic, dynamical theory of conscious process in which both observer and observed have the same mathematical structure. The dynamics raises the possibility of emergence of combinations of conscious agents, in whose experiences those of the component agents are entangled. In support of conscious realism, I discuss two more theorems showing that a conscious agent can consistently see geometric and probabilistic structures of space that are not necessarily in the world per se but are properties of the conscious agent itself. The world simply has to be amenable to such a construction on the part of the agent; and different agents may construct different structures as seeming to belong to the world. This again supports the idea that any true structure of the world is likely quite different from what we see. I conclude by observing that these theorems suggest the need for a new theory which resolves the reverse mind-body problem, a good candidate for which is conscious agent theory. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar (...) to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

One of the 20th century's most popular non-realistic genre is absurd. The root "absurd," connotes something that does not follow the roots of logic. Existence is fragmented, pointless. There is no truth so the search for truth is abandoned in Absurdist works. Language is reduced to a bantering game where words obfuscate rather elucidate the truth. Action moves outside of the realm of causality to chaos. Absurdists minimalize the sense of place. Characters are forced to move in an incomprehensible, (...) void-like realm. Danish philosopher Sїren Kierkegaard was the first to use the term "absurd" in its modern context. His application of the term related it to, what he considered, the incomprehensibility and unjustifiability of Christianity. Existentialist philosophers such as the Frenchman, Jean-Paul Sartre and the German, Martin Heidegger propagated use of the terms in their work. In the philosophical world of the novel, Albert Camus employed absurdism to portray the difference between man's intent and the resultant chaos he encounters. In modern civilization man is posited as the subject of knowledge in science and technology, animating the utopian projects of industrial civilization, and culminating in great urban conglomerates, as in the sealed universe of commodities which constitutes the omnipresent mall. Technique, defined as the ensemble of means, is the driving force of social development, moreimportant than the ends it is supposed to serve. Unfortunately, technique became an end in itself and the society is organized around it. Of course, we are all aware that we need a certain changes to subdue technique, but I think it is now too late to change the course of technique. However, technique is frequently pictured as the only hope for a better future and the only means of making the world more humane. And that is the sort of statement that French philosopher Jacques Ellul calls the technological bluff. Technology is a discourse on techniques: therefore, the bluff lies not in the failure of techniques as such but in presenting them in a falsely optimistic light. The author formulated in 1954 two laws of technical progress: first, it is irreversible: second, it advances by a geometric progression. Thus, a computer revolution changes nothing in the nature of technical progress, although products are new. This progress is hamperednot by internal mechanisms, but by maladaptation of the social body to it, since society is rooted in the past and constantly refers to it. On the other hand, technique is future oriented and discards as valueless everything that cannot be incorporated into the web of techniques. (shrink)

There is a plurality of formal constraints for aggregating probabilities of a group of individuals. Different constraints characterise different families of aggregation rules. In this paper, we focus on the families of linear and geometric opinion pooling rules which consist in linear, respectively, geometric weighted averaging of the individuals’ probabilities. For these families, it is debated which weights exactly are to be chosen. By applying the results of the theory of meta-induction, we want to provide a general rationale, (...) namely, optimality, for choosing the weights in a success-based way by scoring rules. A major argument put forward against weighting by scoring is that these weights heavily depend on the chosen scoring rule. However, as we will show, the main condition for the optimality of meta-inductive weights is so general that it holds under most standard scoring rules, more precisely under all scoring rules that are based on a convex loss function. Therefore, whereas the exact choice of a scoring rule for weighted probability aggregation might depend on the respective purpose of such an aggregation, the epistemic rationale behind such a choice is generally valid. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:New Essays on the RationalistsSteven NadlerRocco J. Gennaro and Charles Huenemann, editors. New Essays on the Rationalists. Oxford: Oxford University Press, 1999. Pp. xvii + 391. Cloth, $60.00.Here is yet another collection of essays on early modern philosophy. The focus this time is on the Seventeenth century, in particular "the rationalists." What this apparently involves is, as the old-fashioned classification has it, Descartes, Spinoza, and Leibniz. But there (...) is no overall theme to the essays, nothing uniting them besides the fact that almost all are devoted to those three thinkers and the fact that the volume was inspired by a summer seminar run by Jonathan Bennett.What the editors mean by "the rationalists" (besides the extensional definition) is [End Page 437] thinkers "united in the belief that the intellect and human reason are powerful tools in our ability to know about the ultimate nature of mind and matter." What is supposed to separate "the rationalists" from "the empiricists" is "a belief in the power of human reason" (xv). This is a fairly weak claim; and I, for one, am skeptical that such categories are truly useful (or even valid—one would be hard-pressed to find a single issue on which Descartes, Spinoza, and Leibniz all agree and on which those who are usually called "empiricists" unanimously dissent). In the light of so much important and creative work done over the last twenty years in seventeenth-century philosophy, it would have been nice to see a volume devoted to "the rationalists" include at least one sophisticated discussion of the legitimacy and grounds of such a label.The essays in this book are divided into three categories: Matter and Substance; Freedom and Necessity; and Mind and Consciousness. The contributors are a broad mix of scholars: some established and accomplished, others new and up-and-coming. The quality of the work is consistently high. There is a lot of detailed and careful work here, both in the attention to the historical texts and in philosophical analyses. However, not all of the essays are of great scope or interest; in fact, most are not. There is a definite tendency toward the small-scale (but not brevity): a concern with micro-problems (for example, the chapter by Clarence Bonnen and Daniel Flage, "Distinctness," is devoted to the question of what the "distinctness" of an idea is for Descartes) and an emphasis on theses and arguments (such as Geoffrey Gorham's examination of the "similarity condition" for causation in Descartes, "Causation and Similarity in Descartes,"). If there is indeed an "analytical" way of doing history of philosophy, that school is well represented here.And then there are a couple of essays that stand out by transcending this narrowness of focus. The chapters by Catherine Wilson ("The Illusory Nature of Leibniz's System") and Don Garrett ("Teleology in Spinoza and Early Modern Rationalism") are, without question, the boldest and most interesting of the collection. Wilson argues that, in the light of Leibniz's changing and inconsistent views on substance, there really is no metaphysical "system" in his philosophy. Garrett, in what is, to my mind, the best essay in the book (although I think I disagree with him), defends an account of teleology in Spinoza's metaphysics, and then compares Spinoza's views on teleology with those of Aristotle, Descartes, and Leibniz; he concludes that Spinoza not only accepted teleological explanations of particular phenomena, but did so more strongly than anyone else in the modern period. Experts will, of course, disagree with the claims made by Wilson and Garrett; that is what this game is all about. But it is truly refreshing to see scholars such as these taking on large-scale issues.It is worth noting that there is also a nice, indirect dialogue between two of the essays: Charles Huenemann's interesting account of a consistent necessitarianism in Spinoza ("The Necessity of Finite Modes and Geometrical Containment in Spinoza's Metaphysics,") and Edwin Curley and Gregory Walski's argument (in "Spinoza's Necessitarianism Reconsidered,") that, when it comes to the finite modes, Spinoza is not a strong or absolute necessitarian. What is truly unfortunate about the collection, however... (shrink)

It has been widely believed that David Hilbert, a precursor of formalism, consid-ered mathematics an ordinary “game of signs”. In this paper, I try to show that Hilbert worked out and applied in his research a cohesive, holistic and organic, as well as universal picture of mathematics (as a supranational discipline) and a vision of its development. This scientific area was supposed to constitute a complex construction, and was perceived by him in an optimistic and humanistic way (it enabled (...) solution to any research problem and fulfilled diverse human needs). External experience (e.g. in the case of geometric pictures) and abstraction of its internal structures (a priori state, mathematical analysis of infinity) are particularly important for this exact science. Mathematics creates a bridge between theory and practice, between thinking and ob-servation. (shrink)

El escrito de la Ciencia Nueva es un texto cifrado. Pero quizá pueda descifrarse –él y la entera obra viquiana– mediante el juego conjugado de dos claves hermeneúticas inseparables: la una metafísica, semiótica la otra. Ambas se condicionan recíprocamente por la idea de “sintesis geométrica” cuya textualización descansa a su vez en un subtexto no escrito. Este subtexto posibilitador de la síntesis de semiótica en Vico no es otro que su modo de pensamiento transcendental, en nada kantiano, moderno en todo.The (...) writing of Scienza Nuova is an encoded text. It might perhaps be deciphered not only that very text but the whole Vico’s work as well by using the connected game of two distintics hermeneutic cleves: one is metaphysical, the other semiotic. Both maintein a mutual relationship and both also are conditioned by the "geometrical syntax", a textualiztion of which seems torest in a non-written text. This subtext which makes possible to carry a complete synthesis of both metaphysics and semiotic in Vico, is nothing but his particular way of transcendental thinking, which has little to do with the Kantian tradition and is fully rooted in the contemporay thinking. (shrink)

While “meaning negotiation” has become an ubiquitous term, its use is often confusing. A negotiation problem implies not only a convenience to agree, but also diverging interest on what to agree upon. It implies agreement but also the possibility of disagreement. In this chapter, we look at meaning negotiation as the process through which agents starting from different preferred conceptual representations of an object, an event or a more complex entity, converge to an agreement through some communication medium. We shortly (...) sketch the outline of a geometric view of meaning negotiation, based on conceptual spaces. We show that such view can inherit important structural elements from game theoretic models of bargaining – in particular, in the case when the protagonists have overlapping negotiation regions, we emphasize a parallel to the Nash solution in cooperative game theory. When acceptable solution regions of the protagonists are disjoint, we present several types of processes: changes in the salience of dimensions, dimensional projections and metaphorical space transformations. None of the latter processes are motivated by normative or rationality considerations, but presented as argumentation tools that we believe are used in actual situations of conceptual disagreement. (shrink)

ABSTRACT At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on ‘alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and (...) he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory. (shrink)

This book is a timely interpretation of the moral and political philosophy of Thomas Hobbes. Staying close to Hobbes's text and working from a careful examination of the actual substance of the account of natural law, R. E. Ewin argues that Hobbes well understood the importance of moral behavior to civilized society. This interpretation stands as a much-needed corrective to readings of Hobbes that emphasize the rationally calculated, self-interested nature of human behavior. It poses a significant challenge to currently fashionable (...) game theoretic reconstructions of Hobbesian logic. It is generally agreed that Hobbes applied what he took to be a geometrical method to political theory. But, as Ewin forcefully argues, modem readers have misconstrued Hobbes's geometric method, and this has led to a series of misunderstandings of Hobbes's view of the relationship between politics and morality. Important implications of Ewin's reading are that Hobbes never thought that "the war of each against all" was an empirical possibility for citizens; that his political theory actually presupposes moral agency; and that Hobbes's account of natural law forces us to the conclusion that Hobbes was a virtue theorist. This major contribution to Hobbes studies will be praised and criticized, welcomed and challenged, but it cannot be ignored. All philosophers, political theorists, and historians of ideas dealing with Hobbes will need to take account of it. (shrink)

Is it ever morally wrong to enjoy fantasizing about immoral things? Many video games allow players to commit numerous violent and immoral acts. But, should players worry about the morality of their virtual actions? A common argument is that games offer merely the virtual representation of violence. No one is actually harmed by committing a violent act in a game. So, it cannot be morally wrong to perform such acts. While this is an intuitive argument, it does not resolve (...) the issue. -/- Focusing on why individual players are motivated to entertain immoral and violent fantasies, Video Games, Violence, and the Ethics of Fantasy advances debates about the ethical criticism of art, not only by shining light on the interesting and under-examined case of virtual fantasies, but also by its novel application of a virtue ethical account. Video games are works of fiction that enable players to entertain a fantasy. So, a full understanding of the ethical criticism of video games must focus attention on why individual players are motivated to entertain immoral and violent fantasies. -/- Video Games, Violence, and the Ethics of Fantasy engages with debates and critical discussions of games in both the popular media and recent work in philosophy, psychology, media studies, and game studies. (shrink)

The paper argues that Roger Bacon adhered to a unique form of geometrical atomism, according to which elemental matter can be analysed into cubic (when at rest) or pyramidal (when in motion) portions. Bacon addressed geometrical atomism from the perspective of the Aristotelian review, using his interpretation of Aristotelian principles to render the theory plausible. He was mostly concerned with solving the contradiction between the angular shapes of the portions and the shape of the elemental spheres. His motivation for doing (...) so, I argue, was his conviction in the applicability of geometry onto natural philosophy, and his goal was to render matter capable of geometrical analysis. In this way, he was convinced, geometrical properties can be considered efficient causes of matter’s spatial formation and motion. (shrink)

Games occupy a unique and valuable place in our lives. Game designers do not simply create worlds; they design temporary selves. Game designers set what our motivations are in the game and what our abilities will be. Thus: games are the art form of agency. By working in the artistic medium of agency, games can offer a distinctive aesthetic value. They support aesthetic experiences of deciding and doing. -/- And the fact that we play games shows something (...) remarkable about us. Our agency is more fluid than we might have thought. In playing a game, we take on temporary ends; we submerge ourselves temporarily in an alternate agency. Games turn out to be a vessel for communicating different modes of agency, for writing them down and storing them. Games create an archive of agencies. And playing games is how we familiarize ourselves with different modes of agency, which helps us develop our capacity to fluidly change our own style of agency. (shrink)

Games may seem like a waste of time, where we struggle under artificial rules for arbitrary goals. The author suggests that the rules and goals of games are not arbitrary at all. They are a way of specifying particular modes of agency. This is what make games a distinctive art form. Game designers designate goals and abilities for the player; they shape the agential skeleton which the player will inhabit during the game. Game designers work in the (...) medium of agency. Game-playing, then, illuminates a distinctive human capacity. We can take on ends temporarily for the sake of the experience of pursuing them. Game play shows that our agency is significantly more modular and more fluid than we might have thought. It also demonstrates our capacity to take on an inverted motivational structure. Sometimes we can take on an end for the sake of the activity of pursuing that end. (shrink)

Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested (...) in laws of nature, modal notions, or more general issues in ontology. (shrink)