Game theory is usually considered applied mathematics, but a few game‐theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e., the existence of a winning strategy in games that involve two players and two outcomes saying who wins. In a multi‐outcome setting, the notion of winning strategy is irrelevant yet usually replaced faithfully with the notion of (pure) Nash equilibrium. This article shows that every determinacy result over an (...) arbitrary game structure, e.g., a tree, is transferable into existence of multi‐outcome (pure) Nash equilibrium over the same game structure. The equilibrium‐transfer theorem requires cardinal or order‐theoretic conditions on the strategy sets and the preferences, respectively, whereas counter‐examples show that every requirement is relevant, albeit possibly improvable. When the outcomes are finitely many, the proof provides an algorithm computing a Nash equilibrium without significant complexity loss compared to the two‐outcome case. As examples of application, this article generalises Borel determinacy, positional determinacy of parity games, and finite‐memory determinacy of Muller games. (shrink)

According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. This grand narrative began with the exhibition of quantitative laws that these heroes, Galileo and Newton for example, had disclosed: the law of falling bodies, according to which the speed of a falling body is proportional to the square of the time that has elapsed since the beginning of its fall; the (...) law of gravitation, according to which two bodies are attracted to one another in proportion to the sum of their masses and in inverse proportion to the square of the distance separating them -- according to his own preferences, each narrator added one or two quantitative laws of this kind. The essential feature was not so much the examples that were chosen, but, rather, the more or less explicit theses that accompanied them. First, mathematization would be taken as the criterion for distinguishing between a qualitative Aristotelian philosophy and the new quantitative physics. Secondly, mathematization was founded on the metaphysical conviction that the world was created pondere, numero et mensura, or that the ultimate components of natural things are triangles, circles, and other geometrical objects. This metaphysical conviction had two immediate consequences: that all the phenomena of nature can be in principle submitted to mathematics and that mathematical language is transparent; it is the language of nature itself and has simply to be picked up at the surface of phenomena. Finally, it goes without saying that, from a social point of view, the evolution of the sciences was apprehended through what has been aptly called the "relay runner model," according to which science progresses as a result of individual discoveries. Grand narratives such as this are perhaps simply fictions doomed to ruin as soon as they are clearly expressed. In any case, the very assumption on which this grand narrative relies can be brought into question: even in the canonical domain of mechanics, the relevant epistemological units crucial to understanding the dynamics of the Scientific Revolution are perhaps not a few laws of motion, but a complex set of problems embodied in mundane objects. Moreover, each of the theses just mentioned was actually challenged during the long period of historiographical reappraisal, out of which we have probably not yet stepped. Against the sharp distinction between a qualitative Aristotelian philosophy and the new quantitative physics, numerous studies insist that Rome wasn't built in a day, so to speak. Since Antiquity, there have always been mixed sciences; the emergence of pre-classical mechanics depends on both medieval treatises and the practical challenges met by Renaissance engineers. It is indeed true that, for Aristotle, mathematics merely captures the superficial properties of things, but the Aristotelianisms were many during the Renaissance and the Early Modern period, with some of them being compatible with the introduction of mathematics in natural philosophy. In addition, the gap between the alleged program of mathematizing nature and its effective realization was underlined as most natural phenomena actually escaped mathematization; at best they were enrolled in what Thomas Kuhn began to rehabilitate under the appellation of the "Baconian sciences," i.e., empirical investigations aiming at establishing isolated facts, without relating them to any overarching theory. Hence, mathematization of nature cannot pretend to capture a historical fact: at most, it expresses an indeterminate task for generations to come. On top of these first two considerations, and against the thesis of the neutrality of the mathematical language, it was urged that mathematics is not "only a language" and that, exactly as other symbolic means or cognitive tools, it has its own constraints. For example, it has been thoroughly explained that the Euclidean theory of proportions both guides and frustrates the Galilean analysis of motion; its shortages were particularly clear with respect to the expression of continuity, which is crucial in the case of motion. Consequently, when calculus was invented and applied to the analysis of motion, it was not a transposition that left things as they stood. Even more clearly than in the case of a translation from one natural language to another, the shift from one symbolic language to another entails that certain possibilities are opened while others are closed. The cognitive constraints imposed by established mathematical theories, as seen in the theory of proportions or calculus, were not the only ones to be studied in relation to mathematization. Certain schemes dependent on the grammar of natural languages, e.g., the scheme of contrariety, or certain symbolic means of representation, e.g. geometrical diagrams and numerical tables, were also subject to such scrutiny. Lastly, it was insisted that, even if we concede the existence of scientific geniuses, mathematics is largely produced by intellectual communities and embedded within social practices. More attention was consequently paid to the forms of communication in given mathematical networks, or to the teaching of the discipline in, for example, Jesuit colleges and universities. The set of mathematical practices specific to specialized craftsmen, highly-qualified experts and engineers began to be studied in its own right. All these reflections may have helped us change our perspectives on the question of mathematization. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, and because of a shift in our interests. The more obscure and idiosyncratic they are, an alchemist, a patron of the sciences or a lunatic collector is nowadays honored in journals of the history of sciences. As for the general issues involved in the question of mathematization, they are rejected as obsolete, or reserved for specialized journals in the history of mathematics. Consequently, before presenting the essays of this fascicle, I would like to say a few words in favor of a renewed study of the forms of mathematization in the history of the early sciences. (shrink)

Réponse à G. Roux ( BCH, 104 [1980], p. 127-149). Le spairistèrion dont l'existence est attestée dans certains gymnases grecs n'est pas un espace hypèthre destiné à la pratique jeux de balle. Ni l'étude architecturale des gymnases de Delphes et de Délos, ni celle des épigraphiques qui s'y rapportent, ni plus généralement nos connaissances sur les jeux ne permettent cette interprétation. L'auteur maintient son point de vue que le spairistèrion était une salle où les athlètes s'entraînaient à la boxe.

47. Le « linteau » inscrit du « Dioscourion ». Examen de la thèse de G. Roux selon lequel le linteau inscrit ID 2548 est à restituer à la porte du temple A du sanctuaire GD 123. Cette solution s'accorde mal soit aux données du terrain, soit au texte de l'inscription. Autres restitutions possibles. 48. Les portes du Létôon, le péribole du Dôdékathéon et le prétendu débarquement à Skardhana. Chronologie respective de la construction et de la destruction du péribole (...) du Dôdékathéon, des deux portes du Létôon (on envisage l'hypothèse que celle du Sud ait toujours existé) et des étapes successives de la construction de l'Agora des Italiens. Rejet de l'hypothèse d'un débarquement archaïque à Skardhana. 49. Les propylées et autres accès de l'Agora des Italiens. Rien ne permet de prétendre, comme le font ceux qui veulent y voir un marché aux esclaves, que l'Agora des Italiens n'avait pas les larges accès habituels à ce genre d'édifices. 50. Encore les pressoirs. Présentation d'un pressoir aménagé tardivement dans l'Agora des Italiens et le Létôon. Graffite chrétien associable au pressoir de la Maison de Cléopâtre. 51. Sur Vorigine supposée détienne des bronzes du Pirée. Il est gratuit de supposer avec G. Dontas que les grands bronzes du Pirée proviennent d'un pillage de Délos. (shrink)

La niche en conglomérat SD 108 est proche de l’entrée du sanctuaire delphique d’Apollon. Depuis sa découverte, on a beaucoup écrit au sujet de son architecture, de sa datation et surtout de sa destination première, mais la connaissance des réalités du terrain égalait rarement celle des textes. Au bout de près de soixante-dix ans, G. Roux a démontré, contre l’opinion commune, qu’elle ne pouvait pas avoir contenu les statues des «Navarques » érigées en mémoire de la victoire lacédémonienne d’Aigos-Potamoi, (...) mais il s’est trompé sur le reste. Le dossier archéologique constitué à partir de 1966 a permis d’établir que SD 108 était d’époque classique et comportait une colonnade prostyle irrégulière de douze colonnes doriques dressées sur un podium. Cette forme insolite se doublait d’un aménagement intérieur extraordinaire. Enfin l’orientation, différente de celle des autres niches, semble avoir correspondu à celle du monument des «Navarques » et découlé d’un remaniement de tout le secteur Sud-Est. (shrink)

L'étude des piliers érigés au Sud de la terrasse d'Attale Ier à Delphes a amené les auteurs à s'interroger sur une partie des restitutions de la publication de G. Roux (FD II, La Terrasse d'Attale /). D'autres restitutions sont donc proposées et justifiées notamment par des dessins montrant les superpositions de blocs et les coïncidences de scellements. Après une première partie consacrée à l'étude architecturale, est proposée une interprétation de la consécration attalide comme téménos de Néoptolème, le père de (...) l'éponyme Pergamos, réaménagé par le roi de Pergame en manifestation d'évergétisme envers Delphes, l'Amphictionie et ses alliés éto- liens. L'article aborde enfin les modifications apportées par la construction du second pilier et les transformations de l'ensemble à l'époque paléochrétienne. (shrink)

Un examen attentif des sources montre que la théorie la plus largement répandue fixant la session d'Automne de l'Amphictionie de Delphes au mois delphique Boukatios (mois des Pythia tous les quatre ans) et la session de Printemps en Bysios (mois privilégié pour la consultation de l'oracle) ne peut se fonder que sur la seule vraisemblance. Les seuls mois attestés dans les Actes Amphictioniques sont Héraios/Boathoos pour l'Automne et Endyspoïtropios pour le Printemps. En réalité, ces noms importent peu : les membres (...) de l'Amphictionie, dans le désordre causé par la diversité de leurs calendriers respectifs, ne pouvaient sans doute s'entendre que sur un rendez-vous fixé par des repères astronomiques. προγόνων» είναι πιθανόν οι ημερομηνίες ενός ημερολογίου «κατά θεόν» κοινού σε όλους. Είναι λοιπόν περιττό να ζητάμε την καταχρηστική συστηματοποίηση χρονολογικών αναφορών που είναι πολύ σπάνιες και συχνά αντιφατικές. Με αυτό το δεδομένο, η διάκριση του G. Roux μεταξύ Πυλαίας-συνεδρίασης και Πυλαίας-λογαριασμών, δεν επιβεβαιώνεται από τα επιγραφικά δεδομένα, καθώς επίσης και η υπόθεση για την ύπαρξη μιας «μόνιμης αντιπροσωπείας» απαρτιζόμενης από μερικούς ιερομνήμονες. (shrink)

The Onchestos passage in the Homeric Hymn to Apollo (229-38) has been discussed extensively, most usefully by A. Schachter (BICS 23 (1976)102-14) and G. Roux (REG 77 (1964) 1-22). Further consideration of the disputed verbal forms in lines 235 and 236 and the plurals of 233-6 suggests that the plurals do indeed indicate a two-horse chariot team but that the presence of a team is not incompatible with the test of a single colt, and that if a chariot is (...) wrecked by the unguided horses, it is righted and left in situ (with the horses removed) while prayers of supplication are made to Poseidon. The events referred to are interpreted as elements of a religious ritual with explicit military implications, dating from the Mycenaean period. It is, however, noted that a Babylonian ritual parallel might suggest a Near Eastern (and possibly non-military) origin. (shrink)

In this book William G. Lycan offers an epistemology of philosophy itself, a partial method for philosophical inquiry. The epistemology features three ultimate sources of justified philosophical belief. First, common sense, in a carefully restricted sense of the term-the sorts of contingentpropositions Moore defended against idealists and skeptics. Second, the deliverances of well confirmed science. Third and more fundamentally, intuitions about cases in a carefully specified sense of that term. The first half of On Evidence in Philosophy expounds a version (...) of Moore's method and applies it to each of several issues. This version is shown to resist all the standard objections to Moore; most of them do not even apply. It is argued, in Chapters 5 and 6, that philosophical method is far lesspowerful than most have taken it to be. In particular, deductive argument can accomplish very little, and hardly ever is an opposing position refuted except by common sense or by science. The final two chapters defend the evidential status of intuitions and the Goodmanian method of reflectiveequilibrium; it is argued that philosophy always and everywhere depends on them. The method is then set within a more general explanatory-coherentist epistemology, which is shown to resist standard forms of skepticism.In sum, William G. Lycan advocates a picture of philosophy as a very wide explanatory reflective equilibrium incorporating common sense, science, and our firmest intuitions on any topic-and nothing more, not ever. (shrink)

A partire dalla seconda metà del Novecento la questione della mostruosità è stata oggetto – insieme a quella del prodigio, da cui si differenzia soltanto parzialmente – di un crescente interesse accademico. Gli studi riguardanti la funzione antropologica, cosmologica, estetica e naturalistica dei mostri, sono oramai tanto numerosi e tanto vari nell'approccio da renderne ardua anche solo una parziale enumerazione. Difficilmente potremmo esimerci dal menzionare un autore come Jurgis Baltrušaitis, che così acutamente ha posto il tema della funzione estetica del (...) mostruoso e del deforme, e allo stesso modo non potremmo dimenticare gli ormai classici studi storici e interpretativi di Claude-Claire Kappler, Jean Céard, Jacques Le Goff, Leslie Fiedler o David Williams, la cui scelta di prender parte alla nostra rassegna ci ha sinceramente onorati. Così facendo, tuttavia, trascureremmo lavori davvero pregevoli, come (solo per dirne alcuni) il poderoso tomo prodotto da Lorraine J. Daston e Katharine Park, il prezioso volumetto di José Gil, la ricca raccolta a cura di Charles T. Wolfe, la voluminosa storia della teratologia di Olivier Roux e le profonde riflessioni di Richard Kearney. Sarebbe possibile proseguire con un elenco di molte pagine, che includerebbe senz'altro i molti e altrettanto degni di nota lavori di alcuni degli autori di questa raccolta, che, con gli altri, ringraziamo: Albrecht Classen, Peter G. Platt, Maddalena Mazzocut-Mis, David Gilmore... (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

More than twenty-five years after the first signs of potential harm, the US remains locked in the grip of an opioid epidemic, with more Americans dying from overdoses than ever before.1 Diversion of prescription opioids plays an important role in opioid-related harms. Much of the scientific and public health focus on diversion has been on end-users, given how commonly non-medical prescription opioid use occurs, as well as the proportion of individuals who report that their source of non-medical opioids was friends (...) or family. However, diversion of opioids, as well as their rampant oversupply, can be discerned higher up the supply chain, including among wholesalers, pharmacies and rogue prescribers whose behavior may trigger well-described “flags” warranting further evaluation and action. (shrink)

Resumen:Junto con Rebeldes académicos de Iván Jaksić (SUNY 1989; UDP 2013) y Una disciplina de la distancia de Cecilia Sánchez (CESOC 1992), este libro ya forma parte del canon bibliográfico selecto y escaso que propone investigaciones de largo aliento sobre la historia de la filosofía en el Chile republicano. No se trata de una reseña de nombres y obras, ni de una historia interna del desarrollo de problemas puros o escuelas. Más bien, su foco, en afinidad con las obras mencionadas, (...) son “las distintas relaciones históricas entre las fuerzas del poder y las razones de la filosofía […] las distintas inscripciones en los también múltiples quiasmos entre saberes y poderes” (14-15), asumiendo, de modo más sustantivo, que “el bloque histórico dominante en Chile rara vez ha logrado establecer un relato coherente de la dominación, justamente porque es poco lo que le importan las razones en nombre de las cuales ejerce la fuerza” (41). (shrink)

This treatise on aesthetics begins by showing that the word "art" is used as a name not only for "art proper" but also for certain things which are "art falsely so called." These are craft or skill, magic, and amusement, each of which, by confusion with art proper, generates a false aesthetic theory. In the course of attacking these theories the author criticizes various psychological theories of art, offers a new theory of magic, and reinterprets Plato's so-called "attack on art," (...) showing that it has been entirely misunderstood. Finally, he draws important inferences concerning the position of art in human society. (shrink)

The AGI alignment problem has a bimodal distribution of outcomes with most outcomes clustering around the poles of total success and existential, catastrophic failure. Consequently, attempts to solve AGI alignment should, all else equal, prefer false negatives (ignoring research programs that would have been successful) to false positives (pursuing research programs that will unexpectedly fail). Thus, we propose adopting a policy of responding to points of philosophical and practical uncertainty associated with the alignment problem by limiting and choosing necessary assumptions (...) to reduce the risk of false positives. Herein we explore in detail two relevant points of uncertainty that AGI alignment research hinges on---meta-ethical uncertainty and uncertainty about mental phenomena---and show how to reduce false positives in response to them. (shrink)

Fichte assigns ‘intellectual intuition’ a new meaning after Kant. But in 1799, his doctrine of intellectual intuition is publicly deemed indefensible by Kant and nihilistic by Jacobi. I propose to defend Fichte’s doctrine against these charges, leaving aside whether it captures what he calls the ‘spirit’ of transcendental idealism. I do so by articulating three problems that motivate Fichte’s redirection of intellectual intuition from being to acting: (1) the regress problem, which states that reflecting on empirical facts of consciousness leads (...) only to further facts and so cannot yield a first principle; (2) the rhapsody problem, which states that the categories form a haphazard set and so lack necessity unless they derive from a first principle; and (3) the nihilism problem, which states that a first principle cannot lie outside our cognition of it, lest it be the cause of our cognition and, being first, the cause of all our actions, reducing us to machines. Crucially, Fichte’s three motivating problems are in fact aspects of a single problem. Leaving any aspect unsolved spoils putative solutions to the other two. Consequently, Fichte requires a single unified solution to all three, which his doctrine of intellectual intuition provides. (shrink)

There is growing interest in the use of neurointerventions to reduce the risk that criminal offenders will reoffend. Commentators have raised several ethical concerns regarding this practice. One prominent concern is that, when imposed without the offender’s valid consent, neurointerventions might infringe offenders’ right to bodily integrity. While it is commonly held that we possess a moral right to bodily integrity, the extent to which this right would protect against such neurointerventions is as-yet unclear. In this paper, we will assess (...) whether, why, and how severely three forms of neurointervention might infringe the right to bodily integrity. We show that the severity of the infringement of the right to bodily integrity differs across different forms of neurointervention. Moreover, we argue that mental and behavioral effects of neurointerventions could in some cases be relevant to determining the severity of infringements of the right to bodily integrity. (shrink)

A central theme in the scholarly literature on Enlightenment Europe concerns the increased focus on the role of reason in the development of European thought, especially in the development of the new science by the natural philosophers. As a consequence, there is a tendency in both philosophical scholarship and teaching to bind philosophy and science tightly together. While there is certainly much that is correct in this approach, one motivation for pluralizing philosophy’s past is that this story leaves out a (...) great deal that is important in Enlightenment views of reason. We argue, using as an example the work of figures like Margaret Cavendish, that reason was significantly broader in scope—and that developments in science were paralleled by equally important advances in music, art, literature, medicine, philosophy, and other areas. In recognizing the lack of a sharp boundary between these areas, an inclusive canon of Enlightenment philosophy gives us this richer notion of reason. Integrating figures such as Cavendish into the canon helps us to see that the narrow focus on the scientific version of reason within Enlightenment scholarship creates a false distinction between science and the humanities and misses out on the humanistic ends for which we engage in philosophy. (shrink)

This full-length study of Plato's dialogue Phaedrus, now in paperback, is written in the belief that such concerted scrutiny of a single dialogue is an important part of the project of understanding Plato so far as possible 'from the inside' - of gaining a feel for the man's philosophy. The focus of this account is on how the resources both of persuasive myth and of formal argument, for all that Plato sets them in strong contrast, nevertheless complement and reinforce each (...) other in his philosophy. Not only is the dialogue in its formal structure a dovetail of myth and argument, but the philosophic life that it praises is also shaped by an acknowledgement of the limitations of argument and the importance of mythical understanding. By means of this correlation of form and content Plato invites his readers, through the very act of reading, to take a first step along the path of the philosophical life. (shrink)

In the burgeoning literature on thought experiments (e.g., Cohen 2005; Freese 1995; Gendler 2000; Häggqvist 1996, 2009; Ierodiakonou and Roux 2011; Sorensen 1992), examples are drawn from almost all areas of philosophy. One exception, however, is aesthetics. There are good reasons why this is so: there are very few interesting theory‐ oriented thought experiments in aesthetics, which is unsurprising since there are few well‐developed theories to test in this field (see Chapter 34, Applied Aesthetics). We argue in this chapter, (...) however, that theory‐centered thought experiments are not the only kinds of thought experiments, and that the practical and productive thought experiments that are prevalent in aesthetics are also worthy of some attention. The outline of this chapter is as follows. First we describe in some detail the single most influential theoretical thought experiment in aesthetics. We assess this experiment in epistemic terms, and with this case in view discuss the distinction between theoretical and practical or productive thought experiments. Examples of the latter are introduced so as to illustrate the importance of that distinction. (shrink)

This chapter contains section titled: I II III IV V VI VII VIII IX X XI XII Coda Appendix Acknowledgements.

Philosophers and logicians have long debated how best to understand conditional or hypothetical sentences. William G. Lycan has a distinctive approach to this debate, attending not just to the semantics of such sentences, but equally to their syntax. He shows how insights from linguistic theory help to illuminate problems about the meaning and function of conditionals. For instance, philosophers and logicians have had problems analysing the locutions 'only if', 'unless', and 'even if'. Lycan sets out a general semantic theory of (...) conditionals which works for all such sentences; he assigns meanings to them in a way that explains how and why those meanings depend upon features of utterance context. According to Lycan's theory the 'if'-clauses refer to items called 'events', 'circumstances', or 'conditions'.Real Conditionals gives at last the definitive presentation of this original approach to a topic at the intersection of philosophy, logic, and linguistics. Lycan's characteristically lively and witty expository style ensures that it can be enjoyed by readers from all three disciplines. (shrink)

Throughout his career, Schelling assigns knowledge of the absolute first principle of philosophy to intellectual intuition. Schelling's doctrine of intellectual intuition raises two important questions for interpreters. First, given that his doctrine undergoes several changes before and after his identity philosophy, to what extent can he be said to “hold onto” the same “sense” of it by the 1830s, as he claims? Second, given that his doctrine of intellectual intuition restricts absolute idealism to what he calls a “science of reason”, (...) which he says cannot prove the absolute’s existence, what other doctrine does he require in order to prove this? I will answer these questions by tracing the shifts in Schelling’s doctrine of intellectual intuition from the 1790s to the 1830s and drawing out its evolving methodological role within his science of intelligibility. (shrink)

To incorporate medical ethics into clinical practice, it must first be understood and valued by health care professionals. The recognition of this principle led to an expanding and continuing educational effort by the ethics committee of the Vancouver General Hospital. This paper reviews this venture, including some pitfalls and failures, as well as successes. Although we began with consultants, it quickly became apparent that education in medical ethics must reach all health care professionals—and medical students as well. Our greatest successes (...) came in the formative years of a medical career (ie, in medical school and residency training programmes), but other efforts were not wasted, particularly among nurses and other health care professionals.Although this is a personal review of the experience in one institution, the lessons learnt in Vancouver are applicable to the further development of medical ethics in the UK. (shrink)