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)

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)

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)

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)

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)

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)

Considerations related to randomness appear relatively late in European history, at the turn of the Middle Ages and the modern era. They initially concern to the chances of winning in various games or situations and later move on to introduce classical and geometric probabilities. From a mathematical point of view, the probability calculus is completed by Kolmogorov’s axiomatic theory. However, many open questions, problems and paradoxes remain in the way probability is perceived and interpreted. The four main directions in (...) the concept of probability (logical, frequentist, subjective and propensity) are closely related to the way of perceiving randomness (epistemological or ontological). Reflections on the evolution of the perception of randomness and the interpretation of probability bring the ability to navigate the basic principles and findings of science and contributes to a deeper understanding of the entire issue. (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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Children in the Visual Arts of Imperial RomeJenifer NeilsJeannine Diddle Uzzi. Children in the Visual Arts of Imperial Rome. Cambridge: Cambridge University Press, 2005. xiv + 252 pp. 75 black-and-white ills. Cloth, $80.As anyone who has looked at images of the Christ Child in early medieval art or Baroque portraits of young royalty knows, the imagery of children is highly constructed and a minefield of interpretive challenges. In (...) classical art, [End Page 289] representations of children are never as straightforward as they might at first seem. A girl on a swing painted on an Athenian vase, for instance, is not an innocent child at play but an expiation rite for Erigone, the daughter of Ikarios, who after her father's murder committed suicide by hanging herself. Except for funerary memorials, children are rare in classical art, and their presence usually connotes a special event or situation, often one with dire consequences. The earliest images of children in Greek art are those shown on Geometric funerary vases mourning a dead parent or the slaughter of the innocents at Troy. Likewise, in Roman art children appear not as principal players but as adjuncts to ceremonial events or military exploits.Although ancient Roman childhood has been thoroughly investigated of late, most notably by the social historian Beryl Rawson, studies of the depictions of children in Roman art are not numerous. By its title, Uzzi's book might seem to fill the void, but its contents are limited to children depicted on coins, historical reliefs, sarcophagi, and one silver vessel—some one hundred thirty in all. Chronologically it covers the reign of Augustus to the Severan dynasty, and it excludes as much it includes, namely, mythological children, slaves, camilli/ae, and, perhaps most surprisingly since the author claims to examine only official art, children who can be identified as members of the imperial family. A more apt title might be something like Narratives of Roman Identity: Roman and Non-Roman Children on Historical Reliefs.The basic premise of this book is the visual distinction between Roman and non-Roman children, which Uzzi relates to narratives of inclusion and exclusion—or, what it means to be Roman. In brief, Roman children are generally shown with their fathers in public rituals such as those of imperial largesse (congiarium, alimenta, liberalitas), adlocutiones, processions, games, and sacrifices. By contrast non-Roman children are depicted in rites of submission, as captives in triumphal processions, and in scenes of military activity often with their mothers (e.g., on the two helic columns in Rome). These distinctions are particularly evident on the Column of Trajan because it includes scenes of both Roman and non-Roman children. Scene XCI uniquely shows both together in a scene of sacrifice made upon the arrival of the emperor: three children in Roman dress are accompanied by male figures at the front, nearest to Trajan, while the three provincial children, in non-Roman attire, are farther back with women. While it is not surprising among the Dacians to find only mothers tending their children (all the able-bodied fathers presumably being actively engaged in combat), it is noteworthy that Roman children, both boys and girls, make public appearances with their fathers in Dacian territory. Are they simply led out to see the emperor (as we line up our children to see the presidential motorcade) or is there another agenda here, a process of Romanization, as Uzzi suggests?In the introductory chapter, Uzzi considers modern theories and definitions of nationhood, setting the background for her inquiry into Roman identity. In the next chapter, entitled "Primary Sources," she in fact surveys the secondary literature on Roman children and their imagery (Rawson, Currie, Kleiner), [End Page 290] various methodological approaches to Roman art (Zanker, Evans, Gregory, Hannestad, Brilliant, Beard), and definitions of childhood (Carp, Eyben, Pleket, Locke, Foucault). She then goes on to identify markers of ethnicity, namely, hairstyle and costume. For the purposes of this study she identifies children as "those figures who are approximately one-half to two-thirds the size of adults of the same gender (if known), with round faces and bodies (again, if possible to determine), and without... (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)

What I call theoretical abduction (sentential and model-based) certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanations occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action (...) provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I call epistemic mediators, which are illustrated in the last part of the paper, together with an analysis of the related notion of external representation . Finally, some examples of computational programs that simulate geometrical reasoning are illustrated. The computational embodiment generates a kind of squared epistemic mediator: geometrical construction, as an example of epistemic mediator, is further mediated. (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)

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)

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)

Many weaknesses of game theory are cured by new models that embody simple cognitive principles, while maintaining the formalism and generality that makes game theory useful. Social preference models can generate team reasoning by combining reciprocation and correlated equilibrium. Models of limited iterated thinking explain data better than equilibrium models do; and they self-repair problems of implausibility and multiplicity of equilibria.

The aim of this communication is to consider morphological processes in sociology, mainly through the study of the stability of forms of sociality. At the same time, it aims to study the regulation of constraints, related to an increasingly conflictual environment, through political organization. We use a specific theoretical framework: the catastrophe theory developed by René Thom in topology, further developed by Claude Bruter from a physics point of view, and reworked by Jacques Viret in biology. The idea is to (...) show the existence of archetypal processes organizing social forms. (shrink)

We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as (...) the operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

A threat to humanity portending the end of our species lurks in the cold recesses of space. Our only hope is an eleven-year-old boy. Celebrating the long-awaited release of the movie adaptation of Orson Scott Card’s novel about highly trained child geniuses fighting a race of invading aliens, this collection of original essays probes key philosophical questions raised in the narrative, including the ethics of child soldiers, politics on the internet, and the morality of war and genocide. Original essays dissect (...) the diverse philosophical questions raised in Card’s best-selling sci-fi classic, winner of the Nebula and Hugo Awards and which has been translated in 29 languages Publication coincides with planned release of major motion picture adaptation of _Ender’s Game_ starring Asa Butterfield and Harrison Ford Treats a wealth of core contemporary issues in morality and ethics, including child soldiers, the best kind of education and the use and misuse of global communications for political purposes A stand-out addition to the Blackwell Philosophy and Pop Culture series. (shrink)

This project assesses the ability of a game tutorial, “Goblin Threat” to increase university students’ ability to recognize plagiarized passages. The game tutorial covers information about how to cite properly, types and consequences of plagiarism, and the differences between paraphrasing and plagiarism. The game involves finding and clicking on “goblins” who ask questions about various aspects of plagiarism. Sound effects and entertaining visuals work to keep students’ attention. One group of 177 students enrolled in an online Psychology (...) of Adolescence course answered four multiple choice plagiarism recognition questions in the months after completing the online game tutorial while another group of over 400 students in the same online psychology course did not have access to the game tutorial, but answered the same multiple choice plagiarism recognition questions over the same period of time. The group who played the game tutorial showed an 11% improvement in recognizing plagiarized passages over the comparison group, a statistically significant difference. Results suggest the ability to keep students focused may be an important ingredient for plagiarism interventions. (shrink)

Trustful and trustworthy behaviors have important externalities for the society. But what exactly drives people to behave in a trustful and trustworthy manner? Building on research suggesting that individuals’ social preferences might be a common factor informing both behaviors, we study the impact of a set of different motives on individuals’ choices in a dual-role Trust Game (TG). We employ data from a large-scale representative experiment ( N = 774), where all subjects played both roles of a binary TG (...) with real monetary incentives. Subjects’ social motives were inferred using their decisions in a Dictator Game and a dual-role Ultimatum Game. Next to self-interest and strategic motives we consider preferences for altruism, spitefulness, egalitarianism, and efficiency. We demonstrate that there exists considerable heterogeneity in motives in the TG. Most importantly, among individuals who choose to trust as trustors, social motives can differ dramatically as there is a non-negligible proportion of them who seem to act out of (strategic) self-interest whereas others are driven more by efficiency considerations. Subjects’ elicited trustworthiness, however, can be used to infer such motivations: while the former are not trustworthy as trustees, the latter are. We discuss that research on trust can benefit from adding the second player’s choice in TG designs. (shrink)