We formulate a restriction of Hindman’s Finite Sums Theorem in which monochromaticity is required only for sums corresponding to rooted finite paths in the full binary tree. We show that the resulting principle is equivalent to \-induction over \. The proof uses the equivalence of this Hindman-type theorem with the Pigeonhole Principle for trees \ with an extra condition on the solution tree.

Résumé La plupart des œuvres de Sophie Calle – reproduites dans des livres ou présentées aux cimaises des musées – s’offre comme le dépôt d’expériences vécues qui se trouvent précisément réglées par des contraintes arbitraires, ostensiblement formulées. La gratuité même des protocoles élus rapproche la démarche de l’artiste française du jeu. Le recours à la contrainte a pour conséquence effective de réintroduire la surprise et l’imprévu au sein de la vie quotidienne ; il induit une attention accrue au concours des (...) circonstances – comme à son impact sur la suite des événements, dès lors que celle-ci s’inscrit dans une forme de narrativité potentielle. (shrink)

Bacterial lipopolysaccharide (LPS) and its active component, lipid A, have been used either alone or as adjuvant in therapeutic anticancer vaccines. Lipid A induces various transcription factors via intracellular signaling cascades initiated by their receptor CD14-TLR4. These events lead to the synthesis of cytokines, which either have direct cytotoxic effect or stimulate the immune system. Their antitumoral effect has been demonstrated in animal models as well as clinical trials. Studies in animal models showed that their antitumoral effect relies mostly on (...) the generation of an effective immune response. In humans, the antitumoral effect was correlated with an antibody response and cell-mediated cytotoxicity. So far, some encouraging results have been achieved in phase I and II clinical trials with regards to response and stabilization of the disease, but an expansion of the studies and trials is needed to find the best conditions for their clinical application. BioEssays 24:284–289, 2002. © 2002 Wiley Periodicals, Inc.; DOI 10.1002/bies.10053. (shrink)

Cosmopolitics, the concept of a world politics based on shared democratic values, is in an increasingly fragile state.

In view of the concern with the insertion of critical environmental education in school, we seek theoretical-methodological contributions in critical historical pedagogy. In this sense, this article will address theoretical reflections that are born within the “Grupo de Pesquisa em Educação Ambiental” - Unesp-Bauru and that were issued during the 1st Symposium on Dialectical Historical Materialism and Research on Science Education and Environmental Education. Thus, we approach the question of the content of critical environmental education from the curriculum design of (...) critical historical pedagogy. Despite the question of the content and form of Environmental Education being present since its origins, we understand that the indepth debate on what should be its content in the school context is still absent. In this sense, assuming the school insertion of critical Environmental Education as the core of the curriculum is a way to overcome its limitations in theory and practice for the human formation necessary for social transformation. (shrink)

Type II DNA topoisomerases (Topo II) are essential enzymes implicated in key nuclear processes. The recent discovery of a novel kind of Topo II (DNA topoisomerase VI) in Archaea led to a division of these enzymes into two non‐homologous families, (Topo IIA and Topo IIB) and to the identification of the eukaryotic protein that initiates meiotic recombination, Spo11. In the present report, we have updated the distribution of all Topo II in the three domains of life by a phylogenomic approach. (...) Both families exhibit an atypical distribution by comparison with other informational proteins, with predominance of Topo IIA in Bacteria, Eukarya and viruses, and Topo IIB in Archaea. However, plants and some Archaea contain Topo II from both families. We confront this atypical distribution with current hypotheses on the evolution of the three domains of life and origin of DNA genomes. BioEssays 25:232–242, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...) From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle. (shrink)

ABSTRACTThis paper offers an opportunity to ponder the way the Catholic Church and its methods of information control reshaped, and paradoxically even enabled, the dissemination and practice of science in early modern Italy. Focusing on the activities of Newtonian scholars operating in Rome in the First half of the eighteenth century – especially the Celestine monk Celestino Galiani and prelate Francesco Bianchini – I will argue that major contributions to the spread of Newtonianism in Italy came from individuals operating within (...) the Church, acting more-or-less independently from the Church’s oversight. These scholars realized they were witnessing an inexorable transition and that the medieval scholastic cosmology and physics could not survive. In order to rescue the Church – and to avoid further embarrassment, especially after the Galileo Affair – renewal was needed. Counterintuitively, the dissemination of Italian Newtonianism was largely a Catholic effort. (shrink)

Under what conditions does the killing of a nonhuman animal qualify as euthanasia? In this paper, I elaborate an original nonprescriptive definition of nonhuman animal euthanasia which avoids the conceptual confusions surrounding the use of this expression. Such a definition imposes strict limitations on the notion of nonhuman animal euthanasia. On the one hand, the nonhuman animal whose life is ended through an act that legitimately qualifies as euthanasia is normally a sentient domestic animal. On the other, the painless and (...) merciful nature of the termination of a nonhuman animal’s life is a necessary but not sufficient condition for it to count as a genuine instance of nonhuman animal euthanasia. (shrink)

Graham Priest proposed an argument for the conclusion that ‘nothing’ occurs as a singular term and not as a quantifier in a sentence like (1) ‘The cosmos came into existence out of nothing’. Priest's point is that, intuitively, (1) entails (C) ‘The cosmos came into existence at some time’, but this entailment relation is left unexplained if ‘nothing’ is treated as a quantifier. If Priest is right, the paradoxical notion of an object that is nothing plays a role in our (...) very understanding of reality. In this note, we argue that Priest's argument is unsound: the intuitive entailment relation between (1) and (C) does not offer convincing evidence that ‘nothing’ occurs as a term in (1). Moreover, we provide an explanation of why (1) is naturally taken to entail (C), which is both plausible and consistent with the standard, quantificational treatment of ‘nothing’. (shrink)

Not only the vertical direction of images – perceptually subject to the law of gravity and its consequences – plays an important role in their interpretation; the horizontal direction left-right too seems to foster different interpretations from its converse. For this reason there are subjects and genres of painting, such as the Annunciation or the portrait, revealing some constants from this point of view, in their representation conventions. And for this same reason there are languages​​, like comics, where the left-right (...) direction is critical not only for the succession of panels – clearly bound to the direction of verbal writing – but also for the panel’s internal organization. These reflections suggest a cultural explanation of the differences in horizontal organization in pictures, linking it to the habits of writing, while ruling out the explanations making reference to the physiology of brain. (shrink)

© The Authors [2018]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...In his Moby Dick, Herman Melville writes that “to produce a mighty book you must choose a mighty theme”. Marc Lange’s Because Without Cause is definitely an impressive book that deals with a mighty theme, that of non-causal explanations in the empirical sciences and in mathematics. Blending a (...) variety of insights originating within the philosophy of science and the philosophy of mathematics, the book has an ambitious goal: capturing what features, in the many examples of putative explanations offered by mathematicians and scientists, make them genuinely explanatory.The architecture of Because Without Cause reflects its mighty character. The book is divided into four parts and eleven chapters, preceded by... (shrink)

Le présent travail se concentre sur les propriétés sémantico-syntaxiques du nom fait à l’exclusion, par conséquent, de ses usages énonciatifs, qui devraient constituer un volet complémentaire de la présente étude. La première partie du texte refait un bref historique de la définition des NSS et ajoute un nouvel argument à ceux de Adler pour appuyer l’idée que ces noms ne participent d’aucune « hiérarchie-être ». La seconde propose une répartition des NSS en trois sous-classes sur la base de critères syntaxiques, (...) qui font apparaître que toutes les structures spécificationnelles ne sont pas identiques, en dépit des apparences. Fait et les noms de « faits qualifiés » constituent une de ces sous-classes. Mais il est montré dans la troisième partie que fait occupe même dans sa propre sous-classe une position tout à fait unique. (shrink)

In this paper, we present a number of problems for intellectualism about knowledge-how, and in particular for the version of the view developed by Stanley & Williamson 2001. Their argument draws on the alleged uniformity of 'know how'-and 'know wh'-ascriptions. We offer a series of considerations to the effect that this assimilation is problematic. Firstly, in contrast to 'know wh'-ascriptions, 'know how'-ascriptions with known negative answers are false. Secondly, knowledge-how obeys closure principles whose counterparts fail for knowledge-wh and knowledge-that. Thirdly, (...) as opposed to knowledge-wh and knowledge-that, knowledge-how is inferentially isolated from further knowledge-that. We close by providing some evidence against the further reduction of knowledge-wh to knowledge-that, which is presupposed by the intellectualist theory under discussion. (shrink)

Quel rapport est-il possible de tracer entre l'ethique et la politique? Michel Foucault, Pierre Hadot et Stanley Cavell, a partir de trois positions philosophiques tres differentes, ont elabore des strategies de reponse a cette question que le present ouvrage se propose de rendre explicites et d'explorer. Ainsi, l'esthetique de l'existence, les exercices spirituels et le perfectionnisme moral y sont combines afin de construire un arriere-plan conceptuel et pratique permettant de saisir a la fois les enjeux politiques d'une ethique de soi (...) et l'incontournable dimension ethique d'une politique de nous-memes. Cet ouvrage entend contribuer a l'elaboration d'une philosophie analytique de la politique dont le but est de rendre visibles l'existence et le fonctionnement concret du pouvoir dans ses ramifications quotidiennes; une telle entreprise se noue de facon etroite avec une analyse des techniques de l'ordinaire, c'est-a-dire de ces pratiques que les individus utilisent pour donner une forme a leur vie et pour transformer leur rapport a eux-memes, aux autres et au monde. (shrink)

Expectations play a central role in understanding scientific and technological changes. Future-oriented representations are also central with regard to nanotechnologies as they can guide policy activities, provide structures and legitimation, attract different interests, focus policy-makers’ attention and foster investments for research. However, the emphasis on future scenarios tends to underrate the complexity of the challenges of the present market of nanotechnologies by flattening them under the needs and promises of scientific research. This is particularly apparent if we consider the viewpoint (...) of the regulator who faces two different ranges of problems with regard to the market and research and is expected, simultaneously, to manage two different types of regulatory instruments, pursuing at the same time the same goals. Instead, by favoring only the future scenarios, the regulator runs the risk of abruptly shifting from more flexible and elastic tools to forms of hard legislation, wasting, thus, the resources of the soft-regulation, in particular those of self-regulation. By referring primarily to the European context, human rights, also thanks to their normative structure of principles, can help in strengthening both the legislation needed for regulating the present market and the soft instruments needed for steering research and for fostering the stakeholders’ participation without sacrificing the coherence of the regulatory response. (shrink)

The investigation of condensed matter transformations hinges on the precision of free-energy calculations. This article charts the evolution of molecular simulations, tracing their development from the techniques of the early 1960s, through the emergence of free-energy calculations toward the end of the decade, and leading to the advent of umbrella sampling in 1977. The discussion explores the inherent challenges and limitations of early simulational endeavors, such as the struggle with accurate phase-space sampling and the need for innovative solutions like importance (...) sampling and multistage sampling methods. Taken together, the initial hurdles and subsequent adoption of advanced techniques exemplify the leap from analytical methods to effective computational strategies that enabled more reliable simulations. Further analysis of this narrative reveals the methodological breakthroughs as well as the setbacks that transformed the theoretical and practical understanding of condensed matter phenomena. A follow-up study will examine the shifts in free-energy calculations from the late 1970s into the 1980s. (shrink)

Anticipation is one of the main goals of new governance models, such as Responsible Research and Innovation. However, there is not a single mode of anticipation in this model. Two approaches can be addressed within the RRI framework: a socio-empirical one, which tends to underline the role of the democratic processes, aimed at identifying values on which governance needs to be anchored ; and a normative one, which stresses the role of EU goals as ‘normative anchor points’ in governance. These (...) two approaches also address two different models of anticipation: one based on the construction of shared pathways for reflexivity on the purposes of innovation, the other based on the progressive implementation of constitutional goals in risk assessment and management tools. However, both can be deemed partially unsatisfactory from the standpoint of human rights since one puts individual rights in the middle of the ‘values lottery’ where any participatory process ultimately leads; the other can be inadequate since fundamental rights are balanced alongside other goals and thus can be sacrificed, exposing the system to possible adverse court decisions. The normative framework of human rights can help to counterbalance both models aimed at maximising inclusion and those aimed at pursuing constitutional normative principles at the basis of technologically advanced societies, strengthening their dimension of anticipation according to a rights-based perspective. (shrink)

A groundbreaking examination of Michel Foucault's history of truth. Many blame Michel Foucault for our post-truth and conspiracy-laden society. In this provocative work, Daniele Lorenzini argues that such criticism fundamentally misunderstands the philosopher’s project. Foucault did not question truth itself but what Lorenzini calls “the force of truth,” or how some truth claims are given the power to govern our conduct while others are not. This interest, Lorenzini shows, drove Foucault to articulate a new ethics and politics of truth-telling (...) precisely in order to evade the threat of relativism. The Force of Truth explores this neglected dimension of Foucault’s project by putting his writings on regimes of truth and parrhesia in conversation with early analytic philosophy and by drawing out the “possibilizing” elements of Foucault’s genealogies that remain vital for practicing critique today. (shrink)

Whistleblowing is the public disclosure of information with the purpose of revealing wrongdoings and abuses of power that harm the public interest. This book presents a comprehensive theory of whistleblowing: it defines the concept, reconstructs its origins, discusses it within the current ethical debate, and elaborates a justification of unauthorized disclosures. Its normative proposal is based on three criteria of permissibility: the communicative constraints, the intent, and the public interest conditions. The book distinguishes between two forms of whistleblowing, civic and (...) political, showing how they apply in the contexts of corruption and government secrecy. The book articulates a conception of public interest as a claim concerning the presumptive interest of the public. It argues that public interest is defined in opposition to corporate powers and its core content identified by the rights that are all-purposive for the distribution of social benefits. A crucial part of the proposal is dedicated to the impact of security policies and government secrecy on civil liberties. It argues that unrestrained secrecy limits the epistemic entitlement of citizens to know under which conditions their rights are limited by security policies and corporate interests. When citizens are denied the right to assess when these policies are prejudicial to their freedoms, whistleblowing represents a legitimate form of political agency that safeguards the fundamental rights of citizens against the threat of unrestrained secrecy by government power. Finally, the book contributes to shifting the attention of democratic theory from the procedures of consent formation to the mechanisms that guarantee the expression of dissent. It argues that whistleblowing is a distinctive form of civil dissent that contributes to the demands of institutional transparency in constitutional democracies and explores the idea that the way institutions are responsive to dissent determines the robustness of democracy, and ultimately, its legitimacy. What place dissenters have within a society, whether they enjoy personal safety, legal protection, and safe channels for their disclosure, are hallmarks of a good democracy, and of its sense of justice. (shrink)

In this paper, I argue that the vindicatory/unmasking distinction has so far prevented scholars from grasping a third dimension of genealogical inquiry, one I call possibilising. This dimension has passed unnoticed even though it constitutes a crucial aspect of Foucault’s genealogical project starting from 1978 on. By focusing attention on it, I hope to provide a definitive rebuttal of one of the main criticisms that has been raised against genealogy in general, and Foucauldian genealogy in particular, namely the idea that (...) Foucault’s genealogical project lacks normative grounding and is therefore ultimately incapable of telling us why we should resist and fight against the mechanisms of power it nevertheless reveals in an empirically insightful way. This conclusion, I argue, is mistaken because it conceives of Foucauldian genealogy exclusively as an unmasking or problematising method, whereas I claim that Foucault’s genealogical project possesses a possibilising dimension that provides his work with sui generis normative force. (shrink)

In this article I try to solve an hermeneutical problem concerning some lines (2,7–24) of the Commentary to the Categories of John Philoponus. There, the commentator would seem committing an error, stating that Heraclitus was a disciple of Pyrrho by the expression «ὁ δὲ μαθητὴς αὐτοῦ Ἡράκλειτος (2,15)». I will present the edition of the text made by Busse with its translation and exegesis and, then, I will compare the passage in Philoponus with similar ones in other Neoplatonic commentators to (...) the Categories. Hence, I will show how the speech of Philoponus is, contrary to what was previously thought, complete and efficient and I will try to propose possible solutions for the text. (shrink)

It is commonly hypothesized that scientists are more likely to engage in data falsification and fabrication when they are subject to pressures to publish, when they are not restrained by forms of social control, when they work in countries lacking policies to tackle scientific misconduct, and when they are male. Evidence to test these hypotheses, however, is inconclusive due to the difficulties of obtaining unbiased data. Here we report a pre-registered test of these four hypotheses, conducted on papers that were (...) identified in a previous study as containing problematic image duplications through a systematic screening of the journal PLoS ONE. Image duplications were classified into three categories based on their complexity, with category 1 being most likely to reflect unintentional error and category 3 being most likely to reflect intentional fabrication. We tested multiple parameters connected to the hypotheses above with a matched-control paradigm, by collecting two controls for each paper containing duplications. Category 1 duplications were mostly not associated with any of the parameters tested, as was predicted based on the assumption that these duplications were mostly not due to misconduct. Categories 2 and 3, however, exhibited numerous statistically significant associations. Results of univariable and multivariable analyses support the hypotheses that academic culture, peer control, cash-based publication incentives and national misconduct policies might affect scientific integrity. No clear support was found for the “pressures to publish” hypothesis. Female authors were found to be equally likely to publish duplicated images compared to males. Country-level parameters generally exhibited stronger effects than individual-level parameters, because developing countries were significantly more likely to produce problematic image duplications. This suggests that promoting good research practices in all countries should be a priority for the international research integrity agenda. (shrink)

Cet article est une réponse directe à certains critiques du projet de démocratie cosmopolitique, qui insistent sur l’absence de détails sur les acteurs politiques, économiques et sociaux susceptibles d’avoir un intérêt à soutenir ce programme. Nous montrons qu’il existe différentes manières de développer la gouvernance démocratique au niveau mondial, qui sont associées à divers acteurs politiques, économiques et sociaux trouvant leur intérêt dans un projet de ce genre. La démocratie cosmopolitique est donc un projet ouvert dont le but est de (...) rendre la gouvernance mondiale plus responsable, plus transparente et plus légitime. La palette des acteurs et des mesures présentée ici met en avant l’orientation et les choix politiques nécessaires pour faire de ce projet une réalité. (shrink)

We describe a decidable class of formulas in a first order timed logic that covers a good amount of properties of real-time distributed systems. Earlier we described a decidable class based on some finiteness properties, and sketched a decidable class in a weaker logic that captures periodicity properties, though without complete proof. The new feature of the decidable class presented here is to be able to treat parametric properties, in particular, properties that concern an arbitrary number of processes as compared (...) to the just mentioned class that could express only properties for a fixed, explicitly given number of processes. As before the properties may use non-trivial arithmetics. We also state another important feature of the class: if a verification formula is not true then our algorithm gives a quantifier-free description of all its counter-models of the complexity involved in the definition of the decidable class and that is quite representative. In conclusion we discuss theoretical and practical issues of the complexity and some open questions. (shrink)

Les avancées rapides dans les technologies numériques ont considérablement changé et amélioré la façon dont les données, informations et outils peuvent être diffusés, gérés, utilisés et réutilisés dans la recherche, et ont créé de nouvelles opportunités pour accélérer le progrès dans la science et l’innovation. Ces développements sont principalement dus au large mouvement formel ou informel de la peer production et à la diffusion globale de l’information mobilisant la coopération de communautés distribuées œuvrant dans des environnements en réseaux. Les initiatives (...) comme celle de Science Commons s’appuient sur un modèle économique de la science évoluant dans un environnement numérique et plus précisément sur un socle de partage et d’échange entre communautés de pairs comme modalité de production. Beaucoup d’autres initiatives de ce type sont en cours . Nous avons choisi Science Commons, dont l’objectif, au-delà de la communication scientifique, vise à accélérer la traduction des données en découverte – en débloquant tous les verrous y compris juridiques qui empêchent que la société bénéficie plus rapidement des résultats scientifiques. La philosophie et les outils pratiques de Science Commons seront décrits comme constitutifs d’une approche résolument ouverte de la connaissance scientifique, dans la lignée de la déclaration de Berlin .Rapid advances in the digital technologies have profoundly changed and improved the way in which data, information and tools can be disseminated, managed, used and re-used in research, and have created new opportunities to speed up progress in science and innovation. These developments are mainly due to an emerging broader movement in support of formal and informal « peer production » and global dissemination of information drawing on the cooperation of distributed science and knowledge communities working in open networked environments. Initiatives like the Science Commons rely on an economic model where science evolves in a digital environment, and more specifically on sharing and exchanges between peer communities as a basis for production. Many other initiatives of this kind are under way . We have chosen the Science Commons, whose objective, over and above scientific communication, is to speed up the translation of data into discovery by removing all barriers, including legal obstacles, that prevent society from enjoying the benefits of scientific results as quickly as possible. The philosophy and practical tools of the Science Commons are described as making up a resolutely open approach to scientific knowledge, as recommended by the Berlin Declaration. (shrink)

Autour et avec le cas exemplaire qu’est Marcel Raymond, l’article présente ce qu’il en est du voyage d’un sujet, de sa reprise dans un récit et de l’établissement qui en résulte d’une critique affinitaire. La part du sujet, celle d’une existence et de sa formation intellectuelle dans ses années d’apprentissage et la part de l’objet, en l’occurrence des œuvres littéraires, y trouvent un équilibre dialectique entre expérience et connaissance, existence et interprétation, singularité d’un sentiment et intelligibilité.

(1994). Identity and autonomy of psychology in cognitive sciences: Some remarks from language processing and knowledge representation. World Futures: Vol. 42, No. 1-2, pp. 71-78.

In this paper, I focus on Luigi Pareyson’s interpretation of Schelling, arguing that it must be read in continuity with Pareyson’s early engagement with the philosophies of Heidegger and Jaspers. Firstly, I argue that Pareyson shapes his existentialism on Jaspers’s and Heidegger’s thoughts, and particularly in relation to that which he considers the fundamental question of philosophy, namely ‘why is there Being rather than nothingness?’ Secondly, I demonstrate how Pareyson reads Schelling’s philosophy in light of his interpretations of Jaspers and (...) Heidegger, i.e., in relation to the ‘fundamental question of philosophy’. Finally, I show how Pareyson’s reading of Schelling is centered on the notion of ‘awe of reason’, and how he defines Schelling as a ‘post-Heideggerian thinker’, since Heidegger’s philosophy allows us to innovatively reinterpret Schelling’s philosophy in an existentialist way. (shrink)

In the context of the crisis of the European culture of the XVI century with the displacement of its cultural evidence towards modernity and its questioning of authority, the Conciliate of Trento, that has profoundly marked the profile of roman Catholicism is analyzed. The complexity of the prop..

This essay traces the history of early molecular dynamics simulations, specifically exploring the development of SHAKE, a constraint-based technique devised in 1976 by Jean-Paul Ryckaert, Giovanni Ciccotti and the late Herman Berendsen at CECAM (Centre Européen de Calcul Atomique et Moléculaire). The work of the three scientists proved to be instrumental in giving impetus to the MD simulation of complex polymer systems and it currently underpins the work of thousands of researchers worldwide who are engaged in computational physics, chemistry and (...) biology. Despite its impact and its role in bringing different scientific fields together, accurate historical studies on the birth of SHAKE are virtually absent. By collecting and elaborating on the accounts of Ryckaert and Ciccotti, this essay aims to fill this gap, while also commenting on the conceptual and computational difficulties faced by its developers. (shrink)

While the problem of the applicability of mathematics in science has been the object of much philosophical discussion, the converse issue of accounting for the successful application of science in mathematics is still in its exploratory stages. In this paper I focus on the latter issue and I discuss it in connection with the mapping view of applied mathematics, which is currently the most influential approach adopted by philosophers to account for the applicability of mathematics in the empirical sciences. More (...) specifically, I address the question of whether the mapping view works for cases of converse applications (i.e., successful applications of the empirical sciences in mathematics). By focusing on some case studies, I argue that the answer to this question is negative and the mapping account of applied mathematics, as it is usually presented in the literature on the applicability of mathematics, does not have the resources to handle the converse applicability issue. To make my point, I will proceed in the following way: first, I will maintain that we can distinguish two types of converse applications, which I name _in-argument_ and _in-result_ converse applications; next, I will assess the mapping account on these types of converse applications and I will point to the reasons why such view cannot accommodate converse applications within its framework. (shrink)

Syntax and semantics in Łukasiewicz infinite-valued sentential logic Ł are harmonized by revising the Bolzano-Tarski paradigm of “semantic consequence,” according to which, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} follows from Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} iff every valuation v that satisfies all formulas in Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} also satisfies θ.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta.$$\end{document} For θ\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} to be a consequence of Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document}, we also require that any infinitesimal perturbation of v that preserves the truth of all formulas of Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} also preserves the truth of θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document}. An elementary characterization of Łukasiewicz implication shows that the Łukasiewicz axiom →Y)→→X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \rightarrow Y ) \rightarrow \rightarrow X )$$\end{document} guarantees the continuity and the piecewise linearity of the implication operation →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}, an appropriate fault-tolerance property of any logic of [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{[0,1]}\,}}$$\end{document}-valued observables. The directional derivability of the functions coded by all ψ∈Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi \in \Theta $$\end{document} and by θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} then provides a quantitative formulation of our refinement of Bolzano-Tarski consequence, which turns out to coincide with the time-honored syntactic Ł-consequence. (shrink)