Une approche biologique de la genèse de l'identité individuelle. Pour introduire notre discours biologique au niveau anthropologique, nous ferons le line entre un exposé purement ethnologique et un exposé d'analyse linguistique. Cette insertion est d'autant plus cruciale qu'il s'agit de présenter ici une approche de l'identité perpendiculaire à l'analyse structurale - comme le temps est orthogonal à l'espace. Plutôt donc que d'entrer immédiatement dans le vif du sujet, je vais user d'un langage qui peut paraître quelque peu paradoxal ou inadéquat, (...) en décrivant, parmi la mythologie prégnance, quelque chose qui soit symétrique, et non équivalent, de la mort du père: je vais commencer par évoquer les mythes qui concernent la mort de la progéniture. (shrink)

Traduire consiste à faire passer la teneur d’un message exprimé dans une langue, dans une autre, avec la plus grande fidélité. Pour que la traduction soit fidèle au texte de départ il est donc nécessaire de comprendre ledit texte. Lorsque ce dernier est de nature juridique, traduire sous-tend de comparer deux systèmes de droit (tradition civiliste et Common Law pour les textes qui nous intéressent) qui généralement ne coïncident que de manière partielle. On se propose d’analyser la traduction de concepts (...) qui posent problème sur le plan du signifiant et/ou sur celui du signifié, soit parce que la graphie des mots qui les désignent est identique ou très proche en anglais et en français—ce sont des faux amis, parmi lesquels on distinguera les vrais des faux -, soit parce que l’équivalence des mots généralement posés en miroir présente des subtilités qui interdisent parfois de traduire l’un par l’autre : parmi ces «vrais amis» , moins amicaux qu’il n’y paraît, on distinguera, là encore, les vrais, des faux. On tâchera de montrer que parfois, «bien» traduire ce peut être d’opter pour une traduction descriptive; d’autres fois, c’est choisir un équivalent fonctionnel, dès lors qu’on a identifié que l’on ne se trouve pas dans l’espace non partagé par les deux concepts juridiques; d’autres fois encore, mais de manière marginale, c’est décider de ne pas traduire. (shrink)

La déconstruction heideggérienne de l’animalité qui a lieu dans les Concepts fondamentaux de la métaphysique va jusqu’à faire disparaître l’idée même d’une vie animale , d’une vie propre aux animaux. La vie, comme le disait déjà Heidegger dans Être et temps , est « un mode d’être propre », ce qui veut dire, comme le confirmera le cours de 1929-1930, que la vie est « le mode d’être de l’animal et de la plante ». D’emblée conçus comme « organismes », (...) les animaux se retrouvent désormais privés de monde, plongés dans une torpeur végétative, dans une Benommenheit , du fond de laquelle ils ne font, comme les végétaux, « rien de plus que vivre ». La méthode de l’ontologie de la vie -- annoncée dans Sein und Zeit comme une « interprétation privative » -- se révèle être une réduction au biologique : la stratégie consiste à trouver des équivalences fonctionnelles pour tout ce qui a trait chez les animaux à quelque chose comme une vie, à quelque chose comme une existence biographique, pour ne leur laisser que la vie, au sens strictement biologique du terme. Du se-mouvoir jusqu’à la perception en passant par cette forme de désir irrationnel qu’est l’impulsion, les traditionnelles facultés animales seront instituées en propre de l’homme, ne laissant plus aux animaux qu’une forme de vie organique, hors sens, hors possible, hors monde. (shrink)

Résumé Cet article examine la formalisation sémiotique de la traduction, proposée par Alexandre Ljudskanov, à travers la confrontation de son modèle avec celui de l’École de Leipzig. Alors que les allemands Kade et Neubert ne quittent pas le champ de la Translationslinguistik, le traductologue bulgare s’applique à mettre en œuvre une sémiotique du processus traductif. En partant de la prémisse que toute information n’existe que sous forme de code, il définit la traduction comme un échange communicatif entre deux systèmes sémiotiques, (...) qui demande forcément une médiation sémiotique de nature cognitive. Le modèle de Ljudskanov implique le décodage et l’encodage. Ces deux phases supposent la transformation des signes d’un code à l’autre de sorte à préserver l’information portée par le message. L’information invariante est transmise par des équivalents fonctionnels dont la pertinence et le principe de fonctionnement seront illustrés par des exemples de proverbes, d’aphorismes, d’expressions idiomatiques et leur traduction en plusieurs langues. (shrink)

Ce terme, et son équivalent latin « prescription », signifient « texte dont le propos est de provoquer un comportement spécifique de la part de son récepteur ». Le comportement se dépolitise progressivement, pour devenir de plus en plus fonctionnel. Mais, dans cette série progressive, il y a rupture. Toutes les prescriptions, des Dix Commandements jusqu’au mode d’emploi, s’orientent vers l’Homme. Tout programme d’ordinateur, lui, indique une machine. Je proposerai dans cet essai l’idée que la rupture entre l’avant-dernier et le (...) dernier exemple de la série est ce qui nous caractérise. (shrink)

Le texte juridique est des plus marqués culturellement. Le langage du droit reflète la complexité de la société qui l'a produit, dont les institutions et leur vocabulaire recèlent une culture parfois multimillénaire. Le traducteur doit relever le double défi que posent la langue et le droit, et reproduire fidèlement dans le texte d'arrivée le message de départ. Le transfert d'un texte de droit est une opération délicate présentant de nombreux risques. Inhérents à la langue, ils en marquent les limites. Le (...) résultat auquel parviendra le traducteur n'est au mieux qu'un « compromis raisonnable » entre les impératifs du droit et les servitudes de la langue. En s'efforçant d'amener l'auteur au lecteur, il tend vers une forme d'équivalence, dite fonctionnelle.The legal text is the most culturally defined. The language of the law reflects the complexity of the society that produced it, the institutions and culture sometimes contain vocabulary multimillénaire. The translator must address the dual challenges posed by language and law, and faithfully reproduce the text of the original message arrived. The transfer of a legal text is a delicate operation with many risks. Inherent in the language, they mark the boundaries. The result which will succeed the translator is at best a "reasonable compromise" between the demands of the law and rights of the language. Striving to bring the author to the reader, it tends towards a form of equivalence, called functional. (shrink)

We study some representations of real numbers. We compare these representations, on the one hand from the viewpoint of recursive functionals, and of complexity on the other hand.The impossibility of obtaining some functions as recursive functionals is, in general, easy. This impossibility may often be explicited in terms of complexity: - existence of a sequence of low complexity whose image is not a recursive sequence, - existence of objects of low complexity but whose images have arbitrarily high time- complexity .Moreover, (...) some representations of real numbers that are equivalent from the viewpoint of recursive functionals, are very distinct from the viewpoint of complexity.We make a particular study of representations via continued fractions . We precise exactly what part of information available in the x's dfc is equivalent to the information available in its Dedekinds cut. We show that the sum of two reals whose dfcs are polynomial-time computable may be a real whose dfc has time complexity arbitrarily high.This work confirms that the unique representation of real numbers suitable for the ordinary calculus is via explicit Cauchy sequences of rationals.RésuméNous étudions différentes manières de présenter les nombres réels. Nous comparons ces présentations du point de vue des fonctionnelles récursives d'une part, et de celui des classes de complexité d'autre part.L'impossibilité d'obtenir certaines fonctions sous forme de fonctionnelles récursives est en général facile à établir. Cette impossiblité peut souvent être explicitée en termes de complexité: - il existe une suite de faible complexité dont l'image est une suite non récursive, - il existe des objets de faible complexité mais dont les images sont des objets de complexité arbitrairement grande .En outre, certaines présentations des réels équivalentes du point de vue des fonctionnelles récursives se distinguent nettement du point de vue de la complexité.Nous faisons une étude particulière concernant les développements en fraction continue . Nous précisions exactement quelle est la partie de l'information disponible dans le dfc d'un réel x qui équivaut à l'information disponible dans sa coupure de Dedekind. Nous montrons également que la somme de deux réels dont le dfc est calculable en temps polynomial peut être un réel dont le dfc est de complexité arbitrairement grande.Ce travail confirme que seule une présentation des réels via des suites de rationnels explicitement de Cauchy est adaptée aux calculs avec les réels. (shrink)

Numerous instruments have been developed to elicit numerical values that represent the strength of preference for different health states. However, relatively few studies have attempted to analyse the reasoning processes that people employ when they are asked to answer questions based on these elicitation methods. The lottery equivalents method is a preference elicitation instrument that has recently received some attention in the literature. This study attempts a qualitative analysis of the use of this instrument on a group of 25 relatively (...) highly educated respondents. For each of three health states considered in the study, a substantial number of respondents refused to trade the chance of survival for a possible improvement in the health state. Therefore, many respondents violated an assumption that is necessary for the lottery equivalents instrument to generate cardinal health state values. These findings place a question mark against the usefulness of the lottery equivalents method, and add weight to the suspicion that ‘preferences’ are constructed according to how questions are framed. (Published Online July 31 2007). (shrink)

When compared with the Pāli versions of the Nanda tale—the story of the ordainment and liberation of the Buddha’s half-brother—some of the peculiar features of Aśvaghoṣa’s telling in the Saundarananda come to the fore. These include the enticing love games that Nanda plays with his wife Sundarī before he follows Buddha out of the house, and the powerful, troubling scene in which Buddha forces Nanda to ordain. While the Pāli versions are aware of fantastic elements such as the flight to (...) the Himālayas, and while each adds its own unique emphases that re-shape the events, none raise such deep ambivalence as done by Aśvaghoṣa. The Comparison of the different tellings then raises a more general theoretical point in relation to Buddhist literature—that genre defines the special features of each adaptation of the story, rather than any historical conditions regarding transmission; the versions each conform to the specific intellectual context of the text that appropriates them. This understanding allows an advancement of the idea of genre in Buddhist canonical and semi-canonical texts. (shrink)

I. L’unité fonctionnelle se définit par une synergie s’étendant à des corrélations de plus en plus complexes : elle dépend soit des mécanismes du système nerveux, soit des sécrétions internes, soit de la corrélation des organes.II. L’unité mentale est la systématisation consciente et réfléchie des représentations ; ‘dans bien des cas, elle dépend de processus sensori-moteurs ; dans le cas des idées, elle en est indépendante, et elle se manifeste par le langage conceptuel.III. Les structures sensori-motrices et mnémiques opèrent le (...) lien entre unité fonctionnelle et unité mentale. (shrink)

Felsefe metinlerinde kavramların erek kültüre aktarılmasıyla ilgili gerçekleştirilen farklı yorum ve yanlışlıklar, ahlak ve hukuk alanlarında küçük hataların büyük anlaşılmazlıklara yol açabilmesi sebebiyle, dikkat edilmesi gereken önemli bir husustur. Felsefe metinlerinin güçlüğü ve açık uçluluğundan dolayı yaşanan aktarım sorunlarını en aza indirgeyebilmek için hem kavramsal ilişkiler hem de kültürel perspektifler dikkate alınmalıdır. Bu amaçla disiplinlerarası nitelikteki çalışmamızda, felsefe metinlerinin nitelikleri ortaya konularak diğer metin türlerinden farkları vurgulanmıştır. Akabinde felsefe alanındaki çeviri faaliyetleri sürecinde, felsefî kavramların erek kültüre işlevsel bir biçimde aktarılabilmesinin (...) imkânları ve yolları ayrıca irdelenmiştir. Bu çerçevede, Aristoteles’in “adalet” kavramı örneğinde, felsefe alanında kaynak kültürdeki kavramların erek kültürde karşılık bulması açısından ortaya çıkan sorunlara işaret edilmiş ve okurun yazara götürülmesini esas alan bakış açısı doğrultusunda felsefe metinlerinin işlevsel çevrisinin imkânı üzerinde durulmuştur. (shrink)

Kim attribue aux émergentistes un modèle de « réduction logique » dans lequel la prédiction ou l’explication d’une occurrence de la propriété réduite ne requiert, outre des informations sur le niveau réducteur, que des principes logiques et mathématiques. Sur la base de cette interprétation, je conteste deux thèses de Kim. La première concerne la légitimité du modèle émergentiste de réduction. J’essaie de montrer, à l’aide de l’exemple de l’addition des masses, que l’adoption de la réduction logique rendrait irréductibles certaines propriétés (...) qui sont clairement réductibles. La deuxième est la thèse selon laquelle la réduction fonctionnelle correspond aux exigences émergentistes sur la réduction. Telle que Kim la caractérise, la réduction fonctionnelle comporte, outre une définition fonctionnelle de la propriété à réduire, l’indication des propriétés réalisatrices. Or cette information, qui correspond à la découverte d’une loi de correspondance , est empirique et non seulement logique.I read Kim as attributing to the emergentists a model of “logical reduction” in which the prediction or explanation of an occurrence of the reduced property requires, beyond information on the reducing level, only logical and mathematical principles. On the basis of this interpretation, I argue against two theses of Kim's. The first concerns the legitimacy of the emergentist model of reduction. I try to show by the example of the addition of masses that according to logical reduction certain properties which are clearly reducible come out as irreducible. The second is the thesis that functional reduction as construed by Kim satisfies the emergentist constraints on reduction. Functional reduction implies, over and above a functional definition of the reduced property, the indication of its realizers. But this information corresponding to the discovery of a bridge law is empirical and not only logical. (shrink)

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate (...) discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force. (shrink)

In 1991 Larry Laudan and Jarret Leplin proposed a solution for the problem of empirical equivalence and the empirical underdetermination that is often thought to result from it. In this paper we argue that, even though Laudan and Leplin’s reasoning is essentially correct, their solution should be accurately assessed in order to appreciate its nature and scope. Indeed, Laudan and Leplin’s analysis does not succeed in completely removing the problem or, as they put it, in refuting the thesis of underdetermination (...) as a consequence of empirical equivalence. Instead, what they show is merely that science possesses tools that may eventually lead out of an underdetermination impasse. We apply their argument to a real case of two empirically equivalent theories: Lorentz’s ether theory and Einstein’s special relativity. This example illustrates the validity of Laudan and Leplin’s reasoning, but also shows the importance of the reassessment we argue for. (shrink)

We introduce the notion of -determinacy for Γ a pointclass and E an equivalence relation on a Polish space X. A case of particular interest is the case when E = EG is the shift-action o...

We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an extra condition (...) such as continuity. (shrink)

As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive `equivalence' of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories provides a sense in which they are isomorphic, and mutually and canonically definable through an analog of `common definitional extension'.

Given a Polish groupG, let$E(G)$be the right coset equivalence relation$G^{\omega }/c(G)$, where$c(G)$is the group of all convergent sequences inG. The connected component of the identity of a Polish groupGis denoted by$G_0$.Let$G,H$be locally compact abelian Polish groups. If$E(G)\leq _B E(H)$, then there is a continuous homomorphism$S:G_0\rightarrow H_0$such that$\ker (S)$is non-archimedean. The converse is also true whenGis connected and compact.For$n\in {\mathbb {N}}^+$, the partially ordered set$P(\omega )/\mbox {Fin}$can be embedded into Borel equivalence relations between$E({\mathbb {R}}^n)$and$E({\mathbb {T}}^n)$.

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding (...) of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The proofs (...) use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models. (shrink)

In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...) so easily removed. Thus we correct some claims from Hintikka [8], Caicedo & Krynicki [3] and Hodges [11]. We refine definitions, in particular the notion of equivalence, and sharpen preconditions, allowing us to restore those claims, including the prenex form theorem of Caicedo & Krynicki [3], and, as a side result, we obtain an application to Skolem forms of classical formulas. It is a known fact that a complete calculus for IF-logic is impossible, but with our results we establish several quantifier rules that form a partial calculus of equivalence for a general version of IF-logic reflecting general properties of information flow in games. (shrink)

I argue that two competing accounts of persistence, three and four dimensionalism, are in fact metaphysically equivalent. I begin by clearly defining three and four dimensionalism, and then I show that the two theories are intertranslatable and equally simple. Through consideration of a number of different cases where intuitions about persistence are contradictory, I then go on to show that both theories describe these cases in the same manner. Further consideration of some empirical issues arising from the theory of special (...) relativity lead me to conclude that the two theories are equally explanatory, and thus finally that they are metaphysically equivalent. (shrink)

Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.

Clinical guidelines summarise available evidence on medical treatment, and provide recommendations about the most effective and cost-effective options for patients with a given condition. However, sometimes patients do not desire the best available treatment. Should doctors in a publicly-funded healthcare system ever provide sub-optimal medical treatment? On one view, it would be wrong to do so, since this would violate the ethical principle of beneficence, and predictably lead to harm for patients. It would also, potentially, be a misuse of finite (...) health resources. In this paper, we argue in favour of permitting sub-optimal choices on the basis of value pluralism, uncertainty, patient autonomy and responsibility. There are diverse views about how to evaluate treatment options, and patients’ right to self-determination and taking responsibility for their own lives should be respected. We introduce the concept of cost-equivalence, as a way of defining the boundaries of permissible pluralism in publicly-funded healthcare systems. As well as providing the most effective, available treatment for a given condition, publicly-funded healthcare systems should provide reasonable suboptimal medical treatments that are equivalent in cost to the optimal treatment. We identify four forms of cost-equivalence, and assess the implications of CE for decision-making. We evaluate and reject counterarguments to CE. Finally, we assess the relevance of CE for other treatment decisions including requests for potentially superior treatment. (shrink)

To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like (...) mental representations. Simon (1972, 1978) hoped to solve this debate by thoroughly reducing the differences between forms of mental representations (e.g., between images and sentences) to differences in computational efficiency; to carry out this reduction, he borrowed from computer science the concepts of data type and of data structure. I argue that, in the end, his account amounted to nothing more than characterizing representations by the fast operations on them. This analysis then allows me to assess what Simon’s approach actually achieves when transported from psychology to the study of scientific representations, as in Larkin and Simon (1987): it allows comparing, not representations in and of themselves, but rather the computational roles they play in particular problem-solving processes—that is, representations together with a particular way of using them. (shrink)

There is an ergodic, measure preserving, countable Borel equivalence relation E on a standard Borel probability space (X, µ) such that E\c is not essentially free on any conull C ⊂ X.

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley (...) and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

The problem of theoretical equivalence is traditionally understood as the problem of specifying when superficially dissimilar accounts of the world are reformulations of a single underlying theory. One important strategy for answering this question has been to appeal to formal relations between theoretical structures. This article presents two reasons to think that such an approach will be unsuccessful and suggests an alternative account of theoretical equivalence, based on the notion of interpretive equivalence, in which the problem is merely an instance (...) of a broader problem in the philosophy of physics. I thus conclude that there is no distinctive problem of theoretical equivalence at all. Two difficulties my approach raises for realist replies to the threat of underdetermination are then discussed, with particular emphasis on a recent reply by Norton. 1 Introduction2 Methodological Confusion3 Asymmetrical Equivalence3.1 Maxwell’s field equations3.2 Classical Lagrangian dynamics4 Formal Approaches: Quine and Glymour5 Theoretical Equivalence as Interpretive Equivalence6 Theoretical Equivalence without Interpretive Judgement?7 Lessons for Underdetermination. (shrink)

Dans cet article nous étudions trois notes de M. Fréchet sur les opérations linéaires et leur rôle dans l’émergence de l’analyse fonctionnelle au début du XXème siècle. Dans un premier temps nous mettons en évidence les processus de sélection, d’extraction et de réinterprétation mis en oeuvre par Fréchet à partir de matériaux publiés antérieurement. A partir de cette analyse nous nous attachons à montrer comment la progression vers une vision plus générale met en jeu des éléments structurels fondamentaux dans la (...) constitution d’un champ nouveau des mathématiques. Notre étude permet finalement de préciser le concept de structure dans son rôle central dans l’émergence de l’analyse fonctionnelle. (shrink)

Over the past years, a number of probabilistic measures of coherence have been proposed. As shown in the paper, however, many of them do not conform to the intuitition that equivalent testimonies are highly coherent, regardless of their prior probability.

Peter Spirtes and Thomas Verma. Equivalence of Causal Models with Latent Variables.

We characterize, in terms of determinacy, the existence of 0 ♯♯ as well as the existence of each of the following: 0 ♯♯♯ , 0 ♯♯♯♯ ,0 ♯♯♯♯♯ , .... For k ∈ ω, we define two classes of sets, (k * Σ 0 1 ) * and (k * Σ 0 1 ) * + , which lie strictly between $\bigcup_{\beta and Δ(ω 2 -Π 1 1 ). We also define 0 1♯ as 0 ♯ and in general, 0 (...) (k + 1)♯ as (0 k♯) ♯ . We then show that the existence of 0 (k + 1)♯ is equivalent to the determinacy of ((k + 1) * Σ 0 1 ) * as well as the determinacy of (k * Σ 0 1 ) * +. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

In this article I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality i...

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)