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)

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)

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.

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)

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)

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)

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)

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)

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)

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)

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. Buridan also moves on (...) from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

According to the prevailing sentiment, changing the past is logically impossible. The prevailing sentiment is wrong. In this paper, I argue that the claim that changing the past entails a contradiction ultimately rests upon an empirical assumption, and so the conclusion that changing the past is logically impossible is to be resisted. I then present and discuss a model of time which drops the empirical assumption and coherently models changing the past. Finally, I defend the model, and changing the past, (...) against objections. (shrink)

This original and lively book uses texts from ancient medicine, epic, lyric, tragedy, historiography, philosophy, and religion to explore the influence of Greek ideas on health and disease on Greek thought. Fundamental issues are deeply implicated: causation and responsibility, purification and pollution, the mind-body relationship and gender differences, authority and the expert, reality and appearances, good government, and good and evil themselves.

Dealing with the nature of historical knowledge, this book is concerned with both philosophical and historical questions. It involves considerations as various as statistical hypothesis testing, componential analysis and the problem of the Synoptic Gospels. --.

The purpose of this note is to acknowledge a gap in a previous paper, "The complexity of revision," and to provide a corrected version of the argument.

"This book represents a continuation of the research project in philosophy of language and semantics represented in the journal "Protosociology" at the J. W. ...

Classical temples in ancient Greece show two deterministic illusionistic principles of architecture, which govern their functional design: geometric proportionalism and a set of illusion-strengthening rules in the proportionalism's stochastic margin. Animal morphology, in its mechanistic-deductive revival, applies just one architectural principle, which is not always satisfactory. Whether a Greek Classical situation occurs in the architecture of living structure is to be investigated by extreme testing with deductive methods.Three deductive methods for explanation of living structure in animal morphology are proposed: the (...) parts, the compromise, and the transformation deduction. The methods are based upon the systems concept for an organism, the flow chart for a functionalistic picture, and the network chart for a structuralistic picture, whereas the optimal design serves as the architectural principle for living structure. These methods show clearly the high explanatory power of deductive methods in morphology, but they also make one open end most explicit: neutral issues do exist. (shrink)

It has become a truism that we live in so‐called information societies where new information technologies have made information abundant. At the same time, information science has made us aware of many phenomena tied to the way we process information. This article explores a series of socio‐epistemic information phenomena resulting from processes that track truth imperfectly: pluralistic ignorance, informational cascades, and belief polarization. It then couples these phenomena with the hypothesis that modern information technologies may lead to their amplification so (...) as to give rise to what are called “infostorms.” This points to the need for studying further the exact relations between information technologies and such infostorms, as well as the ways we may design technologies to avoid being misled away from what we have good reasons to believe. (shrink)

In contrast to symbolic or associationist representations, I advocate a third form of representing information that employs geometrical structures. I argue that this form is appropriate for modelling concept learning. By using the geometrical structures of what I call conceptual spaces, I define properties and concepts. A learning model that shows how properties and concepts can be learned in a simple but naturalistic way is then presented. I also discuss the advantages of the geometric approach over the symbolic and associationist (...) traditions. (shrink)