We prove that the unification type of Łukasiewicz logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background (...) to such diverse tools. In particular, we offer a detailed proof of the duality theorem for finitely presented MV-algebras and rational polyhedra—a fundamental result that, albeit known to specialists, seems to appear in print here for the first time. (shrink)

We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. (...) Our treatment is aimed at showing exactly which parts of the basic theory of MV-algebras are needed in order to establish these results, with an eye towards future generalisations. (shrink)

Qu’elles soient d’Église ou d’État, les archives italiennes recèlent une documentation rapportant des cas de violences perpétrées par des clercs sur des pueri, c’est-à-dire des enfants ou des préadolescents. Bien que ce crime n’ait pas été inhérent au milieu clérical, de nombreux membres du clergé furent impliqués dans des affaires de crimes « odieux », délits « énormes » et agissements violents à l’époque moderne. Dans les procès, c’est la formation des enfants et des jeunes et leur proximit...

The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficiently specified circumstances, a predication of “is red” receives a unique, exact number from the real unit interval [0, 1]. You should then be committed to explain what is it that determines that value, settling for instance that my coat is red to degree 0.322 rather than 0.321. In this note (...) I revisit the problem in the important case of Łukasiewicz infinite-valued propositional logic that brings to the foreground the rôle of maximally consistent theories. I argue that the problem of artificial precision, as commonly conceived of in the literature, actually conflates two distinct problems of a very different nature. (shrink)

To believe that every single scientist ought to be individually engaged in ethical thinking in order for science to be responsible at a collective level may be too demanding, if not plainly unrealistic. In fact, ethical labor is typically distributed across different kinds of scientists within the scientific community. Based on the empirical data collected within the Horizon 2020 ‘RRI-Practice’ project, we propose a classification of the members of the scientific community depending on their engagement in this collective activity. Our (...) classification offers, on the one hand, a model of how the ethical aspects of science are taken into consideration by scientists and, on the other, some indications on how to institutionalize ethics in science. (shrink)

In his late years, Thomas Kuhn became interested in the process of scientific specialization, which does not seem to possess the destructive element that is characteristic of scientific revolutions. It therefore makes sense to investigate whether and how Kuhn’s insights about specialization are consistent with, and actually fit, his model of scientific progress through revolutions. In this paper, I argue that the transition toward a new specialty corresponds to a revolutionary change for the group of scientists involved in such a (...) transition. I will clarify the role of the scientific community in revolutionary changes and characterize the incommensurability across specialties as possessing both semantic and methodological aspects. The discussion of the discovery of the structure of DNA will serve both as an illustration of my main argument and as reply to one criticism raised against Kuhn—namely, that his model cannot capture cases of revolutionary yet non-disruptive episodes of scientific progress. Revisiting Kuhn’s ideas on specialization will shed new light on some often overlooked features of scientific change. (shrink)

In his mature works, Kuhn abandons the concept of a paradigm and becomes more interested in the analysis of the conceptual structure of scientific theories. These changes are interpreted as resulting from a ‘linguistic turn’ that Kuhn underwent sometimes around the 1980s. Much of the philosophical discussions about Kuhn’s post-‘linguistic turn’ philosophy revolves around his views on taxonomic concepts. Apart from taxonomy, however, the mature Kuhn introduces other concepts, such as conceptual networks and lexicons. This article distinguishes these three concepts (...) and shows that adopting each one of them has different impacts on Kuhn’s model of science. After distinguishing and assessing the concepts of taxonomy, network, and lexicon, it will be argued that the latter not only fits the Kuhnian model of science better, but it also helps capture the wide sense of Kuhn’s early concept of a paradigm. (shrink)

In his mature writings, Kuhn describes the process of specialisation as driven by a form of incommensurability, defined as a conceptual/linguistic barrier which promotes and guarantees the insularity of specialties. In this paper, we reject the idea that the incommensurability among scientific specialties is a linguistic barrier. We argue that the problem with Kuhn’s characterisation of the incommensurability among specialties is that he presupposes a rather abstract theory of semantic incommensurability, which he then tries to apply to his description of (...) the process of specialisation. By contrast, this paper follows a different strategy: after criticising Kuhn’s view, it takes a further look at how new scientific specialties emerge. As a result, a different way of understanding incommensurability among specialties will be proposed. (shrink)

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.

Thomas Kuhn (1922-1996) is widely considered as one of the most important philosophers of science of the 20th century, while his The Structure of Scientific Revolutions (SSR) is regarded as one of the most influential works in the philosophy ofscience. At the same time, however, his place within philosophy of science remains ambiguous. On the one hand, despite the popularity of SSR, there is no proper ‘Kuhnian school of thought’ in HPS. On the other hand, the interest towards Kuhn does (...) not seem to fade away and the number of publications about his work does not seem to decrease. We suggest that there are at least three different ways to go ‘beyond SSR’: (i) by scrutinising the development of Kuhn’s thought, from his pre- to his post-SSR writings; (ii) by contextualising Kuhn in the philosophical milieu of his time, thus interpreting his view as emerging from the intellectual exchanges he had with contemporary philosophers; (iii) by reinterpreting and developing some of his most known ideas, in ways that perhaps Kuhn himself was not able to contemplate. (shrink)

Incommensurability may be regarded as driving specialisation, on the one hand, and as posing some problems to interdisciplinarity, on the other hand. It may be argued, however, that incommensurability plays no role in either specialisation or interdisciplinarity. Scientific specialties could be defined as simply 'different' (that is, about different things), rather than 'incommensurable' (that is, competing for the explanation of the same phenomena). Interdisciplinarity could be viewed as the co- ordinated effort of scientists possessing complemetary and interlocking skills, and not (...) as the overcoming of some sort of incommensurable divide. This article provides a comprehensive evaluative examination of the relations between specialisation, interdisciplinarity, and incommensurability. Its aim is to defend the relevance of incommensurability to both specialisation and interdisciplinarity. At the same time, it aims at correcting the tendency, common among many philosophers, to regard incommensurability in a restrictive manner - such as, for example, as an almost purely semantic issue. (shrink)

Designing a pension system is both a complex endeavor and a long lasting legacy. Complexity stems from the many trade-offs that conceiving a pension system entail and from how these initial decisions affect the social and economic behavioral responses of workers and retirees. Policy-makers planning a pension system have to evaluate its internal economic consistency, but also these feedbacks. Economic and demographic models that allow a quantitative evaluation of these costs and benefits are required. More than ever at the initial (...) stage of design, since pension systems are persistent. Yet, pension systems are not monolith, but living entities that change over time. Some of these modifications are produced by individuals’ reactions to incentives built in the system, and need to be foreseen during the initial planning. Other changes are induced by reform measures and constitute the policy responses to unpredicted exogenous shocks – such as population aging. Re-designing the pension system to cope with new demands, while being limited by existing constraints, is a difficult task. Recent reforms of the Italian pension system are discussed in detail to highlight the policy trade-offs and the economic motivations behind the decision of the reform policies. (shrink)

There is a growing concern for the proper role of science within democratic societies, which has led to the development of new science policies for the implementation of social responsibility in research. Although the very expression ‘social responsibility of science’ may be interpreted in different ways, many of these emerging policy frameworks define it, at least in part, as a form of anticipative reflection about the potential impacts of research in society. What remains a rather under-discussed issue is the definition (...) of the bearer of the social responsibility of science. In other words, it is not clear who is supposed to engage in such an anticipative reflection, whether individual researchers or research groups. In the past few years, philosophers of science have begun to use qualitative research methods to fill the gaps between normative models of the organisation of ideal scientific communities and the reality of actual scientific practices. In this article, I follow this approach to discuss the issue of the collective dimension of the social responsibility of science. I rely on a qualitative study conducted on an interdisciplinary research group and I describe how group dynamics position individuals and distribute duties and roles, including social responsibility. Qualitative descriptions of the distribution of duties within actual research groups should inform the formulation of general prescriptive theories on the collective responsibility of science. (shrink)

One of the challenges confronted by language learners is to master the interpretation of sentences with multiple logical operators, where different interpretations depend on different scope assignments. Five-year-old children have been found to access some readings of potentially ambiguous sentences much less than adults do :73–102, 2006; Musolino, Universal Grammar and the acquisition of semantic knowledge, 1998; Musolino and Lidz, Lang Acquis 11:277–291, 2003, among many others). Recently, Gualmini et al. have shown that, by careful contextual manipulation, it is possible (...) to evoke some of the putatively unavailable interpretations from young children. Their proposal is quite general, but the focus of their work was on sentences involving nominal quantifiers and negation. The present paper extends this investigation to sentences with modal expressions. The results of our two experimental studies reveal that, in potentially ambiguous sentences with modal expressions, the kinds of contextual manipulations introduced by Gualmini and colleagues do not suffice to explain children’s initial scope interpretations. In response to the recalcitrant data, we propose a new three-stage model of the acquisition of scope relations. Most importantly, at the initial stage, child grammars make available only one interpretation of negative sentences with modal expressions. We call this the Unique Scope Assignment stage. (shrink)

Both in the bibliography and in the citation in the text, Michelle Gibbons’ article below has been mistakenly attributed to “Gibson.” The proper reference to the article should be: Gibbons, M.. Reassessing discovery: Rosalind Franklin, scientific visualization, and the structure of DNA. _Philosophy of Science, 79_, 63–80.

We discuss the probabilistic analysis of explanatory power and prove a representation theorem for posterior ratio measures recently advocated by Schupbach and Sprenger. We then prove a representation theorem for an alternative class of measures that rely on the notion of relative probability distance. We end up endorsing the latter, as relative distance measures share the properties of posterior ratio measures that are genuinely appealing, while overcoming a feature that we consider undesirable. They also yield a telling result concerning formal (...) accounts of explanatory power versus inductive confirmation, thereby bridging our discussion to a so-called no-miracle argument. (shrink)

In the past few years, social epistemologists have developed several formal models of the social organisation of science. While their robustness and representational adequacy has been analysed at length, the function of these models has begun to be discussed in more general terms only recently. In this article, I will interpret many of the current formal models of the scientific community as representing the latest development of what I will call the ‘Kuhnian project’. These models share with Kuhn a number (...) of questions about the relation between individuals and communities. At the same time, they also inherit some of Kuhn’s problematic characterisations of the scientific community. In particular, current models of the social organisation of science represent the scientific community as essentially value-free. This may put into question both their representational adequacy and their normative ambitions. In the end, it will be shown that the discussion on the formal models of the scientific community may contribute in fruitful ways to the ongoing debates on value judgements in science. (shrink)

This paper deals with those time travels mostly considered by physics, namely those in the form of the so-called closed timelike curves. Some authoritative scholars have raised doubts about the status of these journeys as proper time travels. By using David Lewis’ famous definition of time travels proposed in 1976, we show that this proper status may actually be recovered, at least in some cosmological contexts containing spacetime regions, such as those concerning black holes described by the Kerr–Newman metric, that (...) allow the formation of local closed curves. But, the mathematical incompatibility between ordinary black hole solutions to Einstein field equations and the cosmological solutions induces us to take into consideration the more general issue pertaining to the slippery interplay between models related to local and global aspects of the world, highlighting, in particular, the different notions of time that these domains inevitably imply. This leads us to think that time is not a univocal entity of the world, but is a scale-related characteristic which claims the adoption, when investigating its ontological status, of a sort of regional approach. We also briefly dwell upon the most appropriate form of realism that such a kind of dispute between local and global models may involve. (shrink)

Excerpt from Considerazioni Sopra le Dottrine Religiose di Vittorio Cousin, per Servir di Appendice Alla Introduzione Allo Studio della Filosofia Le accuse ch 10 muovo contro le dottrine del sig. Cousin nella mia Introduzione allo studio della filosofia benchè bre vemente espresse essendo gravissime, ragion vuole che siano ben provate. Io mi reputo tanto più in obbligo di farlo che I' illustre Autore negli ultimi suoi scritti protesta altamente di non meritarle. Dichiarazione che ogni lettore assennato accet terebbe tanto più (...) volentieri quanto è più lodevole e degno di un animo generoso il ritrattar gli errori in cui la giovinezza, I' esempio el' indole dei tempi possono precipitare gl' ingegni più eminenti. Il panteismo e la miscredenza sono così fatali a chi segue un cattivo metodo nelle sue speculazioni, che una mente eziandio capacissima può esserne sedotta non ostante la loro falsità ed assurdità intrinseca. Quanti sono al dl d' oggi, a cui sia toccata la buona sorte di ricevere debitamente la fede cattolica, e di conservarla fra le tristi influenze del secolo? Quanti che nel dar opera agli studi speculativi siano provve duti di una buona metodologia? Certo pochissimi; e niuno sicuramente vorrà recare a colpa del sig. Cousin se pagò anch' egli il fio all' infelicissima età in cui a noi tutti è toccato di nascere. Imperocche, quando non si è ben ricevuto negli anni teneri, o si è scosso all' entrar nel mondo il giogo salutare della fede vi sottentra quello del senso e lo spirito dell' uomo ricade senza saperlo nella condizione del gentilesimo a cui(4) About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)