The EU Artificial Intelligence Act (AIA) defines four risk categories for AI systems: unacceptable, high, limited, and minimal. However, it lacks a clear methodology for the assessment of these risks in concrete situations. Risks are broadly categorized based on the application areas of AI systems and ambiguous risk factors. This paper suggests a methodology for assessing AI risk magnitudes, focusing on the construction of real-world risk scenarios. To this scope, we propose to integrate the AIA with a framework developed by (...) the Intergovernmental Panel on Climate Change (IPCC) reports and related literature. This approach enables a nuanced analysis of AI risk by exploring the interplay between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We further refine the proposed methodology by applying a proportionality test to balance the competing values involved in AI risk assessment. Finally, we present three uses of this approach under the AIA: to implement the Regulation, to assess the significance of risks, and to develop internal risk management systems for AI deployers. (shrink)

The EU proposal for the Artificial Intelligence Act (AIA) defines four risk categories: unacceptable, high, limited, and minimal. However, as these categories statically depend on broad fields of application of AI, the risk magnitude may be wrongly estimated, and the AIA may not be enforced effectively. This problem is particularly challenging when it comes to regulating general-purpose AI (GPAI), which has versatile and often unpredictable applications. Recent amendments to the compromise text, though introducing context-specific assessments, remain insufficient. To address this, (...) we propose applying the risk categories to specific AI scenarios, rather than solely to fields of application, using a risk assessment model that integrates the AIA with the risk approach arising from the Intergovernmental Panel on Climate Change (IPCC) and related literature. This model enables the estimation of the magnitude of AI risk by considering the interaction between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We use large language models (LLMs) as an example. (shrink)

In this paper I take it for granted that legal institutions are artifacts. In general, this can very well be considered a trivial thesis in legal philosophy. As trivial as this thesis may be, however, to my knowledge no legal philosopher has attempted an analysis of the peculiar reality of legal phenomena in terms of the reality of artifacts, and this is particularly striking because there has been much discussion about artifacts in general philosophy (specifically analytic metaphysics) over the last (...) twenty years. In particular, the concepts of intention, function, plan of action, and history are in competition to explain the ontology of artifacts, and a similar competition can be found at the core of legal theory. Such a striking parallelism between the domain of artifacts and that of legal institutions is a clue for legal ontology that deserves further attention: I will offer my own interpretation of this parallelism in the first part of this paper (Sections 2 and 3). In providing a theory of legal institutions as artifacts, one could be led to the conclusion that law is essentially an artificial phenomenon, something which does not bear any significant relationship to the natural domain. However, I think that such a conclusion would be mistaken. In fact, this is the second thesis I want to explore in this paper: not only that legal institutions are artifacts, but also that they can be artifacts which in some sense "mirror," or imitate, some descriptions of the natural, pre-social reality we live in. What I would like to show is not that legal institutions are "natural" in the sense that they have some feature which is not human-dependent, as some natural law theorists would say, but rather that their conceptual content can depend on our conceptualization of the natural domain despite being entirely artifactual. This is what I will call the "institutional mimesis" behind several important instances of legal artifacts, and I will deal with it in the second part of this paper (Sections 4 and 5). (shrink)

There is at least one immediate sense in which legal discourse is perspectival: it qualifies acts and facts in the world on the basis of rules. Legal concepts are for the most part constituted by rules, both in the sense that rules define these concepts’ semantic content and that, in order to engage with legal practice, we must act according to those rules, not necessarily complying with them but at least having them in mind. This is the distinctive perspective of (...) law: however, it would be misleading to think that this is the only perspective we can have in legal discourse. That of rule-constituted legal concepts is the fundamental perspective -- the inevitable presupposition of most legal assertions -- but other perspectives are possible on top of this fundamental background: perspectives on law, stemming from the basic perspective of law. -/- In this paper, I will try to argue that some different perspectives regarding law can be accounted for by analyzing different kinds of concepts that emerge in connection with legal institutions. My argument will consist of three steps as follows. First, I will explain how legal concepts are constituted by rules, referring in this regard to John Searle’s analysis of institutional concepts as it emerges in his Making the Social World, of 2010, and amending this analysis according to some criticisms that in 1986 Neil MacCormick had raised against Searle with specific reference to the legal domain. -/- Second, I will show that there are some kinds of concepts relevant for an institution which are not captured by Searle’s analysis in terms of constitutive rules, even if this is amended according to MacCormick’s criticisms. This I will do by considering the game of chess as a simple system of rule-constituted concepts (concepts such as 'checkmate,' 'bishop,' 'king'). I will consider four examples of perfectly legitimate assertions regarding a match of chess -- these being (1) ‘I won’; (2) 'you made a good attack'; (3) 'you are cheating'; (4) 'you made good use of the first-move advantage,' and I will show that, while the first three assertions can be analyzed in terms of concepts (those of 'victory,' 'attack,' and 'cheating') which are not constituted by the rules of chess but are rather common to several different competitive games, being typical of the broader practice of competitive game-playing of which chess is an instance, the fourth assertion includes a concept (that of 'first-move advantage') which is peculiar to chess, just like a rule-constituted element, but is not constituted by the rules of chess. This analysis will lead to a new categorization of institutional concepts. Apart from rule-constituted institutional concepts, which are the only ones recognized by Searle, in order to account for cases (1), (2), and (3) I will distinguish between three kinds of meta-institutional concepts, namely, goal-oriented, mode-oriented, and value-oriented meta-institutional concepts, and then I will introduce the category of para-institutional concepts to account for case (4). -/- Finally -- and this is the third step of my argument -- I will explain how these different kinds of institutional concepts appear when we adopt different perspectives on the institutional frameworks we deal with. This will lead us to a categorization of possible perspectives regarding law that corresponds to the previous one regarding concepts. There is first a structural perspective regarding the instantiation of institutional elements which clearly involves rule-constituted institutional concepts -- as when we say 'I am making a will.' There is then a teleological perspective regarding the goal of our institutional acts which calls into question goal-oriented meta-institutional concepts -- as when we say 'I wrote that will in order for you to have a distinctive right to my property.' Then, we can adopt a strategical perspective regarding some peculiar ways in which institutional acts can be performed, and this has often to do with mode-oriented meta-institutional concepts -- as when we say 'the Labour Party is making parliamentary obstructionism so that the Government will fall before the enactment of the labour reform,' or 'workers start today a work-to-rule action.' Clearly, we can also adopt an evaluative perspective over institutional facts or acts, and here typically value oriented meta-institutional concepts emerge -- as when we say 'that rule is clearly unjust' or 'that contract is unfair.' Finally, we can limit ourselves to a descriptive perspective on phenomena which are peculiar to a given institutional setting, and here para-institutional concepts are often useful -- as when we say 'the Italian electoral system before 1990 led to a sort of reform paralysis' or 'a strict use of the criterion requiring proof beyond any reasonable doubt can be expected to entail a low conviction rate.'. (shrink)

For most people on our planet, spiritual values are vital in driving communitarian behaviour. It is becoming increasingly clear that a lasting and effective social commitment must consider cultural, sociological and religious dimensions. In particular, the current environmental crisis has demonstrated how effectively religious communities have mobilised to respond to climate change. With their emphasis on wisdom, social cohesion and interrelationships, religions can be a strategic player in ensuring effective integral human development. The ecological crisis is not just an ethical (...) dilemma but an ontological and theological matter that demands both a new way of thinking and a new way of being. Think differently and act differently! The United Nations (UN) and many governments are increasingly recognising the vital contribution of religious leaders and organisations in political processes, such as the 2030 Agenda for Sustainable Development, hypostasised in the Faith Plans for People and Planet programme, representing the most prominent and boldest environmental initiative to date by the global faith community. -/- Contribution: Today we realise that a combination of science and spirituality can engage and empower an array of stakeholders from different cultural and religious backgrounds. This article addresses the question of an integrated ecology by selecting appropriate and recent literature from mainstream religions and the subsequent interpretation and application. (shrink)

The literature on counterspeech has been debating how institutions and citizens should respond to offensive or dangerous communicative acts. This article identifies a gap in this debate, namely, the lack of attention paid to the individual vote in large-scale democratic elections as an effective act of distancing from candidates who use explicitly derogatory forms of expression to unify and mobilize supporters. In studying the place of voting in the ethics of counterspeech, this article investigates what counterspeakers can expect other counterspeakers (...) to do in large-scale democratic elections framed as a vote for or against hateful representatives. I argue that even in large-scale elections, the individual act of voting, understood as a contribution to increasing the clarity of the indicators of force of a collectivized speech act, can be an effective form of counterspeech. Voting is one of the first forms of counterspeech that must be taken so that other, and perhaps more controversial, actions can stand criticism on moral grounds. For this reason, I also argue that counterspeakers can expect other counterspeakers to contribute to an electoral outcome that, under certain circumstances, can be received as a vote against representatives who use explicit derogatory forms of expression to gain consensus. (shrink)

In this article, I argue that stability is one of the enabling conditions for epistocratic arrangements to function well and justify their claim right to rule. Against this backdrop, I demonstrate that advocates of strategies to allocate exclusive decision-making power to knowledgeable citizens fail to demonstrate that in a context marked by the fact of pluralism, liberal epistocracies will be stable. They could argue that liberal epistocracies will be stable because epistocratic arrangements are better equipped than democratic decision-making bodies to (...) produce outcomes that approximate the common good. They could argue that liberal epistocracies will be stable because there is a shared meritocratic set of values and ideas. Furthermore, they could opt for two standard liberal strategies, such as overlapping consensus and modus vivendi. Yet, in all cases, the argument for the stability of liberal epistocracies is not persuasive. (shrink)

While most of the literature has attempted to justify harsh and soft containment given some fundamental commitments of political liberalism, I focus on how justified forms of containment can in themselves be deemed effective. This article shows that a reading of Rawls allows for a comparison of different containment practices based on their capacity to protect the stability of liberal democracies under serious threat. And, in making it possible to compare harsh and soft containment, I evaluate immediate stability gains against (...) citizens’ judgements about their liberal democratic institutions. (shrink)

In this paper I discuss the ontological status of actants. Actants are argued as being the basic constituting entities of networks in the framework of Actor Network Theory (Latour, 2007). I introduce two problems concerning actants that have been pointed out by Collin (2010). The first problem concerns the explanatory role of actants. According to Collin, actants cannot play the role of explanans of networks and products of the same newtork at the same time, at pain of circularity. The second (...) problem is that if actants are, as suggested by Latour, fundamentally propertyless, then it is unclear how they combine into networks. This makes the nature of actants inexplicable. -/- I suggest that both problems rest on the assumption of a form of object ontology, i.e. the assumption that the ontological basis of reality consists in discrete individual entities that have intrinsic properties. I argue that the solution to this problem consists in the assumption of an ontology of relations, as suggested within the framework of Ontic Structural Realism (Ladyman & Ross, 2007). Ontic Structural Realism is a theory concerning the ontology of science that claims that scientific theories represent a reality consisting on only relation, and no individual entities. -/- Furthermore I argue that the employment of OSR can, at the price of little modification for both theories, solve both of the two problems identified by Collin concerning ANT. -/- Throughout the text I seek support for my claims by referring to examples of application of ANT to the context of networked learning. As I argue, the complexity of the phenomenon of networked learning gives us a convenient vantage point from which we can clearly understand many important aspects of both ANT and OSR. -/- While my proposal can be considered as an attempt to solve Collin's problems, it is also an experiment of reconciliation between analytic and constructivist philosophy of science. -/- In fact I point out that on the one hand Actor Network Theory and Ontic Structural Realism show an interesting number of points of agreement, such as the naturalistic character and the focus on relationality. On the other hand, I argue that all the intuitive discrepancies that originates from the Science and Technology Studies’ criticism against analytic philosophy of science are at a closer look only apparent. (shrink)

In the last times some scholars tried to characterize Einstein’s distinction between ‘constructive’ – i.e. deductive - theories and ‘principle’ theories, the latter ones being preferred by Einstein. Here this distinction is qualified by an accurate inspection on past physical theories. Some previous theories are surely non-deductive theories. By a mutual comparison of them a set of features - mainly the arguing according to non-classical logic - are extracted. They manifest a new ideal model of organising a theory. Einstein’s paper (...) of 1905 on quanta, qualified by him as a ‘principle theory’, is interpreted according to this model of theory. Some unprecedented characteristic features are manifested. At the beginning of the same paper Einstein declared one more dichotomy about the kind of mathematics in theoretical physics. These two dichotomies are recognised as representing the foundations of theoretical physics. With respect to these dichotomies the choices by Einstein in the paper on quanta are the alternative choices to Newton’s ones. This fact gives reason to the ‘revolutionary’ nature that Einstein attributed to his paper. (shrink)

In this article, I provide an argument against the idea that public hate-speech events are harmful because they cause a discrete, traceable and harmful change in one’s propositional attitudes. To do so, I identify the essential conceptual architecture of public hate-speech situations, I assess existing arguments for the direct and indirect harm of public hate speech and I propose a novel way to approach public hate-speech situations: a maieutic approach. On this perspective, public hate-speech events do not cause changes in (...) propositional attitudes, but rather, if successful, either such events bring a person’s latent propositional attitudes into clear consciousness, or they play with propositional attitudes speakers and their audience had prior to the public hate-speech situation. (shrink)

Starting from the observation that the deterioration of democratic communication is a political problem that requires individual and collective, private and public, actions, I first defend a baseline duty to avoid using expressions that conventionally show a disrespectful attitude toward targeted groups. Then, I develop a set of guidelines that can guide political theorists in distributing additional duties that respect the situated agency of different individuals. I propose two normative constraints (capacity-to-act and influence) that should influence how theorists assign duties. (...) Then, I present three criteria (pointless, antisocial, and lawfulness) to specify the content in a context-sensitive way. (shrink)

Since the 2008 financial crisis, the attempts to use Karl Polanyi's framework to make sense of current developments have multiplied, producing a noticeable and lively debate. This debate centres on the notion of double movement put forward by the Hungarian thinker in his masterpiece – The Great Transformation. The paper is a contribution to this debate. The first part addresses a series of questions that make the interpretations of the double movement advanced so far not very compelling. To this end, (...) a close reading of Polanyi's text, with the aim of dismantling and rearticulating its analytical structure, is carried out. The upshot is a dynamic and multistage picture of the double process as a recurrent and vortex-like attempt to progressively commodify natural and social resources against growing opposition. The second part employs this revised reading of the double movement to explain the collapse of the postwar consensus politics, the success of the neoliberal counterrevolution and the development of the knowledge economy. The claim put forward here is that, in addition to sustained efforts to deepen previous forms of commodification (land, labour and money), we are witnessing a fullblown attempt to turn knowledge into a new fictitious commodity. Building on the idea of digital Taylorism, the paper tries to show that information and computer technologies are being used to standardise and routinise a growing number of intellectual, professional and managerial activities which were able to escape previous attempts in this direction. Once again, at the forefront of this process there are powerful state actors, who are using New Public Management policies strategically to: support the enclosure of intangible cultural resources through the creation of intellectual property rights regimes, and undermine the counter-reaction of negatively affected societal actors by rising the collective action problems they face. (shrink)

Taking seriously the task of sustaining the democratic project requires debunking pessimism, thinking critically about what constitutes the distinctive character of democracy, and taking a future-oriented perspective on democratic transformations.

This article tries to show William James’s presence in the works of Eugenio d’Ors by offering key textual evidence. Both the agreement and disagreement between these two philosophers can help to understand the intellectual itinerary of the Spanish philosopher.

This article sheds light upon the role of the audience in the construction and amendment of populist representative claims that in themselves strengthen representative-represented relationships and simultaneously strengthen ties between the represented who belong to different constituencies. I argue that changes in populist representative claims can be explained by studying the discursive relationship between a populist representative and the audience as a conversation in which both poles give and receive something. From this perspective, populist representative claims, I also argue, can (...) be understood as acts of bonding with the intended effect of constituting ‘the people,’ and inputs from the audience can be seen as conversational exercitives. Populist appeals therefore may change when the audience enacts new permissibility facts and signals to populist representatives that there is another way to strengthen relationships between several individuals belonging to otherwise-different constituencies. (shrink)

Quel est le rôle de Galilée dans la naissance séculaire de la science moderne? Je réponds à la question ci-dessus à la lumière de deux nouveaux éléments. Dès le xvie siècle, Nicolas de Cues, quoiqu’il ne pratiquât pas la science expérimentale, a anticipé une partie substantielle de la révolution copernicienne et de la naissance de la méthodologie galiléenne. Le deuxième élément est l’introduction d’une nouvelle conception des fondements de la science ; ils sont définis comme constitués de trois dialectiques. Après (...) cette définition, la naissance de la science moderne correspond à un très long processus historique qui se conclut à notre époque. Sur cette longue période, Galilée ne fut pas seulement le premier à recourir à une méthodologie scientifique, mais aussi presque le seul à jamais avoir été conscient de l’ampleur des enjeux intellectuels de l’entreprise scientifique. (shrink)

When witnessing someone else's action people often take advantage of the same motor cognition that is crucial to successfully perform that action themselves. But how deeply is motor cognition involved in understanding another's action? Can it be selectively modulated by either the agent's or the witness's being actually in the position to act? If this is the case, what does such modulation imply for one's making sense of others? The paper aims to tackle these issues by introducing and discussing a (...) series of experimental studies showing how body and space may constrain one's own motor cognition reuse in understanding another's action. These findings, I shall argue, may shed new light on the mechanisms underlying the primary ways of identifying ourselves with other people and of being connected to them . (shrink)

Despite the importance of the requirement that all parties subject to a modus vivendi accept it, the philosophical basis of the all-subjected principle has been largely neglected in the realist literature on modus vivendi arrangements as responses to disagreements on issues of common concern. In this article, I argue that the inclusion of all-subjected parties should be understood as instrumental to justifying the presupposition that enough parties will have the motivation to comply with an arrangement that they grudgingly accept as (...) a modus vivendi. I also argue that without accepting the democratic commitments implicit in the acceptance of the standard reading of the all-subjected principle, realist modus vivendi theorists should demonstrate that all those parties who are subjected to a modus vivendi arrangement have the capacity to voice their objection and to be heard for such a claim. (shrink)

If a theory addressing problems that are global in scope aims to be convincing outside its own tradition, it should be robust-enough to deal with the simple observation that, around the world, there are multiple systems of norms, rules and institutionalized normative orders.

The change in the organization of science education over the past fifty years is quickly recalled. Being its cultural bound the lack of a conception of the foundation of science, the multiple innovations have resulted as temporary improvements without a clear direction, apart from the technocratic goal of an automation of learning processes. The discovery of two dichotomies as the foundations of science suggests a pluralist conception of science, and hence the need to entirely renew science education, in particular by (...) introducing the notions of incommensurability and radical variations in meaning of the basic notions. This change was already anticipated by several proposals within each subject-matter. (shrink)

MethodologyA new hypothesis on the basic features characterizing the Foundations of Mathematics is suggested.Application of the methodBy means of it, the several proposals, launched around the year 1900, for discovering the FoM are characterized. It is well known that the historical evolution of these proposals was marked by some notorious failures and conflicts. Particular attention is given to Cantor's programme and its improvements. Its merits and insufficiencies are characterized in the light of the new conception of the FoM. After the (...) failures of Frege's and Cantor's programmes owing to the discoveries of an antinomy and internal contradictions, respectively, the two remaining, more radical programmes, i.e. Hilbert's and Brouwer's, generated a great debate; the explanation given here is their mutual incommensurability, defined by means of the differences in their foundational features.ResultsThe ignorance of this phenomenon explains the inconclusiveness of a century-long debate between the advocates of these two proposals. Which however have been so greatly improved as to closely approach or even recognize some basic features of the FoM.Discussion on the resultsYet, no proposal has recognized the alternative basic feature to Hilbert's main one, the deductive organization of a theory, although already half a century before the births of all the programmes this alternative was substantially instantiated by Lobachevsky's theory on parallel lines. Some conclusive considerations of a historical and philosophical nature are offered. In particular, the conclusive birth of a pluralism in the FoM is stressed. (shrink)

We are often told that public hate speech is something that deviates from what is standard in contemporary liberal democracies. So far, much of the literature has focused on the allegedly bad effects of such deviations as well as on measures to bring liberal democracies back to the normal course of events. Less has been said on the fundamental assumption that at a certain moment in time, and within that political context, hate speech is out of the ordinary. In this (...) paper, drawing upon pragmatics, I contend that often public hate speech responds to a supply-demand logic, where speakers fulfill expectations by attacking target groups. Within this scheme, hate speech would be an answer to what a certain audience is ready to listen. At that moment of time, and within that political context, therefore, I argue in this article, hate speech is ordinary. (shrink)

Nella storia della metafisica è stato un grande problema come chiarire l’idea della coincidentia oppositorum (la coincidenza degli opposti) di Cusano, il quale è riconosciuto comunque da Cassirer come il primo epistemologo del pensiero moderno, in particolare come colui che ha saputo conquistare l’infinito alla mente umana. Dopo alcuni secoli, ha avuto una grande importanza una idea simile a quella di Cusano, la dialettica di Hegel, la quale aggiunge una negazione ad una prima frase negata per ottenere una sintesi in (...) termini generali. Ma poi queste idee sono state sempre meno seguite, eccetto che nel XX secolo da un filosofo non accademico, Lanza del Vasto che ha criticato Hegel e si è ricondotto a Cusano. Nello scritto esamino questa tematica mediante gli strumenti recentemente forniti dalla logica matematica, già verificati sugli scritti di altri scienziati; essi sono capaci di distinguere con precisione che cosa, negli scritti di uno studioso, è un passaggio logico formale e che cosa è una semplice illazione, derivata dalla conoscenza comune o dalla sua creatività; e se è un passaggio logico, decidere di che tipo di logica è. Per mezzo di questo metodo formale, i) presento alcune caratteristiche del ragionare di Cusano; ii) critico il metodo di Hegel; il risultato si accorda con la analisi critica di Hegel che Lanza del Vasto ha compiuto in maniera intuitva; iii) dimostro che la relazione tra Cusano e Lanza del Vasto è più forte di quanto dichiara quest’ultimo; iv) suggerisco una spiegazione della coincidentia oppositorum, chiarendo che la novità di ragionare in logica non classica è stata così innovativa che il tentativo di Cusano di precisarne il metodo è risultato in una scorciatoia, non errata ma valida solo in alcune situazioni; mentre è stato deviante il tentativo di Hegel; Lanza del Vasto, che ha portato un contributo al metodo di Cusano, si è comunque reso conto che occorreva arrivare a formalizzare un nuovo tipo di logica, che oggi risulta essere quella non classica. In definitiva, occorre attribuire a Cusano il merito di aver suggerito una nuova maniera di razionalità logica, quella capace di ragionare in logica non classica e di averne dato, sia pure in maniera imprecisa ed oscura, una prima formalizzazione. (shrink)

I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.

A new hypothesis on the basic features characterising the Foundations of Mathematics is suggested. By means of them the entire historical development of Mathematics before the 20th Century is summarised through a table. Also the several programs, launched around the year 1900, on the Foundations of Mathematics are characterised by a corresponding table. The major difficulty that these programs met was to recognize an alternative to the basic feature of the deductive organization of a theory - more precisely, to Hilbert’s (...) main tenet. Ironically, already half a century before the births of these programs the alternative organization has been substantially represented by Lobachevsky's theory on parallel lines. Moreover, although each program’s founder recognised the basic features in a partial way only, all together these programs represented just the four possible foundational approaches. (shrink)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

The book is the proceeding of a conference in Pisa 12007 on the philosophy of Lanza del Vasto - the unique Western disciple of Gandhi - examined under the items: his thesis work in Philosophy (Fabris), his Greek and Christian methaphysics (Salmeri), his criticism of Hegel (Vigne), the relationship with Gandhi (Manara), Trinity (Vermorel) Indian philosophical traditioon (Trianni), his henologixcal thinking (Reale) his trinitarian metaphysics (Bertini), his mystical thinking (Vannini) a logicaL analysis of his thinking(Drago), his philosophy and theory of (...) non-violence(Cozzo) The relationship with Catholic Church (Tanzarella), Pedagogy (Butturini), sojourn in Pisa (Lanza). (shrink)

The main subject of Cusanus’ investigations was the name of God. He claimed to have achieved the best possible one, Not-Other. Since Cusanus stressed that these two words do not mean the corresponding affirmative word, i.e. the same, they represent the failure of the double negation law and there￾fore belong to non-classical, and above all, intuitionist logic. Some of his books implicitly applied intuitionist reasoning and the corresponding organization of a theory which is governed by intuitionist logic. A comparison of (...) two of Cusanus’ short writings shows that throughout his life he substantially improved his use of this kind of logic and ultimately was able to reason consistently within such a logic and recognize some of its basic laws. One important idea developed by him was that of a proposition composed of a triple repetition of “not-other” expressing “the Tri-unity of concordance” i.e. the “best name for the Trinity”. I complete his application of intuitionist logic to theological subjects by charac￾terizing the inner relationships within the Trinity in such a way that there are no longer contradictions in the notion. Generally speaking, the notion of the Trin￾ity implies a translation from intuitionist to classical logic, to which Cusanus closely approximated. Moreover, I show that the main aspects of Christian rev￾elation, including Christ’s teachings, are represented both by this translation and by some doubly negated propositions of intuitionist logic. Hence, intuition￾ist logic was introduced into the history of Western theological thinking with Christian revelation, as only Cusanus partly recognized. Appendix 1 summa￾rizes a detailed analysis of Cusanus’ second short writing. Appendix 2 shows that the Athanasian creed regarding the Christian Trinity is a consistent se￾quence of intuitionist propositions provided that some verbal emendations are added, showing that ancient trinitarian thinking was also close to intuitionist reasoning. (shrink)

Double negations are easily recognised in both the so-called “negative literature” and the original texts of some important scientific theories. Often they are not equivalent to the corresponding affirmative propositions. In the case the law of double negation fails they belong to non-classical logic, as first, intuitionist logic. Through a comparative analysis of the theories including them the main features of a new kind of theoretical organization governed by intuitionist logic are obtained. Its arguing proceeds through doubly negated propositions and (...) ad absurdum arguments. Then, the final doubly negated predicate is translated in the corresponding affirmative one, from which all the consequences are deduced in order to test them against reality. According to this model the true formalization of intuitionist logic is Kolmogorov’s 1932 paper. The above analysis also shows that modal words play an auxiliary or substitutive role to intuitionist propositions. In addition, it is shown that Vasiliev’s paraconsistent logic is represented through doubly negated propositions. By means of these three kinds of logic one can attribute a specific kind of logic to each of the three distinct steps of the process of building a scientific theory from the experimental data to its final theoretical system. It is also shown that the definition of negation is of a structural kind, rather than of an objective kind or a subjective kind: it has to be referred to the organization of the theory to which it belongs. (shrink)

Whereas “Science does not think" (Heidegger), the "new historiography of science" - mainly Koyré's and Kuhn's ones - has addressed our minds to think about science in a new way. Recently Heelan suggested taking this new viewpoint for conceiving hermeneutic method in a more adequate way to present scientific practice. By an interpretative analysis of the categories of the above two historians, the present paper suggests a new way to conceive the foundations of science. Two basic dichotomies result: on the (...) kind of logic and on the kind of mathematics. They generate four models of scientific theory, sharply severed by the radical differences in their respective choices; that offers an accurate definition of incommensurability and even of an alternative scientific theory to a dominant one, which can be properly called a paradigm. In the past hermeneutic scholars gave negative appraisals on Western science; according to the new viewpoint recognising pluralism in the foundations of science, these appraisals concern the dominant paradigm only. In the light of the basic dichotomies a new way to define hermeneutics is suggested; it can be qualified in short by the following words: ‘The understanding of science is the science of understanding’. (shrink)

The obscure and punctuated history of symmetry is compared with the history of the celebrated and exalting notion of infinitesimal; some considerations about them are derived. A long list of odd and hidden events concerning symmetry in theoretical physics is offered. The last event is the discovery of the nature of the same word “symmetry” which pertains to non-classical logic, and it is linked to the principle of sufficient reason. A comparison of the roles played by the two mathematical techniques (...) within a classical physical theory is performed. It leads to recognize the different roles played by the two mathematical tools as a manifestation of an incommensurability phenomenon caused by two foundational dichotomies. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

In the light of a study of the di erence between political actors and ordinary citizens as language users, and based on three moral arguments (consequence-based, recognition-based, and complicity-based), we propose that democratic representatives have an imperfect duty to use gender-fair-language in their public communication. In the case of members of the executive, such as ministries, prime ministries, and presidents, such an imperfect duty could also be justi ed on democratic grounds. Their choice of using a gender-unfair language, we argue, (...) can cast doubts on the fundamental democratic commitment to respect the agency of all present and future citizens as potential participants in the law-making process. (shrink)

In previous papers I have characterized four ways of reasoning in Peirce’s philosophy, and four ways of reasoning in Computability Theory. I have established their correspondence on the basis of the four pairs of choices regarding two dichotomies, respectively the dichotomy between two kinds of Mathematics and the dichotomy between two kinds of Logic. In the present paper I introduce four principles of reasoning in theoretical Physics and I interpret also them by means of the four pairs of choices regarding (...) the above two dichotomies. I show that there exists a meaningful correspondence among the previous three fourfold sets of elements. This convergence of the characteristic ways of reasoning within three very different fields of research - Peirce’s philosophy, Computability theory and physical theories - suggests that there exists a general-purpose structure of four ways of reasoning. This structure is recognized as applied by Mendeleev when he built his periodic table. Moreover, it is shown that a chemist-, applies all the above ways of reasoning at the same time. Peirce’s professional practice as a chemist applying at the same time this variety of reasoning explains his stubborn research into the variety of the possible inferences. (shrink)

The current definition of Constructive mathematics as “mathematics within intuitionist logic” ignores two fundamental issues. First, the kind of organization of the theory at issue. I show that intuitionist logic governs a problem-based organization, whose model is alternative to that of the deductive-axiomatic organization, governed by classical logic. Moreover, this dichotomy is independent of that of the kind of infinity, either potential or actual, to which respectively correspond constructive mathematical and classical mathematical tools. According to this view a mathematical theory (...) is based on the choices regarding these two dichotomies. As an example of this kind of foundation, arithmetic is rationally re-founded on constructive mathematical tools and the model of the problem-based organization. In conclusion, constructive mathematics is not only mathematics making use of constructive tools in intuitionist logic but also organized according to around a basic problem, solved by a method discovered using intuitionist logic. (shrink)

At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it is like many (...) other scientific theories, in particular the first theories of both mechanical machines and heat machines. A more accurate examination of Theory of Computation shows a difference from the above mentioned theories in its essentially including an odd notion, “thesis”, to which no theorem corresponds. On the other hand, arguments of each of the other theories conclude a doubly negative predicate which then, by applying the inverse translation of the ‘negative one’, is translated into the corresponding affirmative predicate. By also taking into account three criticisms to the current Theory of Computation a rational re-formulation of it is sketched out; to Turing-Church thesis of the usual theory corresponds a similar proposition, yet connecting physical total computation functions with constructive mathematical total computation functions. -/- . (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of (...) logic). This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

The primary aim of this chapter is to show that several missteps made by others in in their thinking about law as an artefact are due to misconceptions about the role of intentions in understanding law as an artefact. I first briefly recap my own contention that law is a genre of institutionalized abstract artefacts (put forth in The Functions of Law (OUP 2016) and subsequent papers), mostly following Searle’s understanding of institutions and Thomasson’s understanding of public artefacts. I highlight (...) the central place that this theory affords law’s functions, without requiring the theorist to say that possession or performance of the function is either necessary or sufficient for inclusion in the class of law. Some of the most common misunderstandings are exemplified in Brian Leiter’s paper ‘Legal Positivism about the Artifact Law’. He thinks that holding an intentionalist view of artefacts commits the theorist to privileging drafters’ intentions when interpreting law. (It doesn’t.) He also has confusions about the differences between artefact tokens and artefact types leading him to a problematically broad understanding of artefacts. Another problem can be seen in thinking that functional understandings of artefacts are vulnerable to the same problems that arise in functional explanations for biological systems. I go on to consider the work of Luka Burazin and Corrado Roversi, addressing worries that making intentionality central to artefacts implies too much conscious thought is required to make one, noting that several theories of intentionality do not require conscious thought in the execution of intentional action. While those who think a central place for intentionality threatens to leave us unable to explain customary law, this can be dealt with by noting the important distinction between customary rules and customary laws (where the latter requires a decision to enlist public aid in redressing violations). I claim that authors’ intentions are communicated requests for the artefacts’ audiences to see the artefacts as members of their putative kinds. Finally, I address the question of whether or not legal systems are themselves artefacts and institutions, given that they may or may not have been intentionally created. An early lawgiver might have created a legal system by accident in the process of handing down the first laws. I raise the possibility that we might want to impute intentionality to necessary by-products of artefact creation, seeing those by-products as artefacts as well. (shrink)

One of the most frequently voiced criticisms of free will skepticism is that it is unable to adequately deal with criminal behavior and that the responses it would permit as justified are insufficient for acceptable social policy. This concern is fueled by two factors. The first is that one of the most prominent justifications for punishing criminals, retributivism, is incompatible with free will skepticism. The second concern is that alternative justifications that are not ruled out by the skeptical view per (...) se face significant independent moral objections (Pereboom 2014: 153). Despite these concerns, I maintain that free will skepticism leaves intact other ways to respond to criminal behavior—in particular incapacitation, rehabilitation, and alteration of relevant social conditions—and that these methods are both morally justifiable and sufficient for good social policy. The position I defend is similar to Derk Pereboom’s (2001, 2013, 2014), taking as its starting point his quarantine analogy, but it sets out to develop the quarantine model within a broader justificatory framework drawn from public health ethics. The resulting model—which I call the public health-quarantine model (Caruso 2016, 2017a)—provides a framework for justifying quarantine and criminal sanctions that is more humane than retributivism and preferable to other non-retributive alternatives. It also provides a broader approach to criminal behavior than Pereboom’s quarantine analogy does on its own since it prioritizes prevention and social justice. -/- In Section 1, I begin by (very) briefly summarizing my arguments against free will and basic desert moral responsibility. In Section 2, I then introduce and defend my public health-quarantine model, which is a non-retributive alternative to criminal punishment that prioritizes prevention and social justice. In Sections 3 and 4, I take up and respond to two general objections to the public health-quarantine model. Since objections by Michael Corrado (2016), John Lemos (2016), Saul Smilanksy (2011, 2017), and Victor Tadros (2017) have been addressed in detail elsewhere (see Pereboom 2017a; Pereboom and Caruso 2018), I will here focus on objections that have not yet been addressed. In particular, I will respond to concerns about proportionality, human dignity, and victims’ rights. I will argue that each of these concerns can be met and that in the end the public health-quarantine model offers a superior alternative to retributive punishment and other non-retributive accounts. (shrink)

This paper introduces the special issue on the Concept of God of the Journal of Applied Logics (College Publications). The issue contains the following articles: Logic and the Concept of God, by Stanisław Krajewski and Ricardo Silvestre; Mathematical Models in Theology. A Buber-inspired Model of God and its Application to “Shema Israel”, by Stanisław Krajewski; Gödel’s God-like Essence, by Talia Leven; A Logical Solution to the Paradox of the Stone, by Héctor Hernández Ortiz and Victor Cantero; No New Solutions to (...) the Logical Problem of the Trinity, by Beau Branson; What Means ‘Tri-’ in ‘Trinity’ ? An Eastern Patristic Approach to the ‘Quasi-Ordinals’, by Basil Lourié; The Éminence Grise of Christology: Porphyry’s Logical Teaching as a Cornerstone of Argumentation in Christological Debates of the Fifth and Sixth Centruies, by Anna Zhyrkova; The Problem of Universals in Late Patristic Theology, by Dirk Krasmüller; Intuitionist Reasoning in the Tri-unitrian Theology of Nicolas of Cues, by Antonino Drago. (shrink)

As philosophical and scientific arguments for free will skepticism continue to gain traction, we are likely to see a fundamental shift in the way people think about free will and moral responsibility. Such shifts raise important practical and existential concerns: What if we came to disbelieve in free will? What would this mean for our interpersonal relationships, society, morality, meaning, and the law? What would it do to our standing as human beings? Would it cause nihilism and despair as some (...) maintain or would it rather have a humanizing effect on our practices and policies, freeing us from the negative effects of belief in free will? In this chapter we consider the practical implications of free will skepticism and argue that life without free will and basic desert moral responsibility would not be as destructive as many people believe. We argue that prospects of finding meaning in life or of sustaining good interpersonal relationships, for example, would not be threatened. On treatment of criminals, we argue that although retributivism and severe punishment, such as the death penalty, would be ruled out, preventive detention and rehabilitation programs would still be justified. While we will touch on all these issues below, our focus will be primarily on this last issue. -/- We begin in section I by considering two different routes to free will skepticism. The first denies the causal efficacy of the types of willing required for free will and receives its contemporary impetus from pioneering work in neuroscience by Benjamin Libet, Daniel Wegner, and John-Dylan Haynes. The second, which is more common in the philosophical literature, does not deny the causal efficacy of the will but instead claims that whether this causal efficacy is deterministic or indeterministic, it does not achieve the level of control to count as free will by the standards of the historical debate. We argue that while there are compelling objections to the first route—e.g., Al Mele (2009), Eddy Nahmias (2002, 2011), and Neil Levy (2005)—the second route to free will skepticism remains intact. In section II we argue that free will skepticism allows for a workable morality, and, rather than negatively impacting our personal relationships and meaning in life, may well improve our well-being and our relationships to others since it would tend to eradicate an often destructive form of moral anger. In section III we argue that free will skepticism allows for adequate ways of responding to criminal behavior—in particular, incapacitation, rehabilitation, and alternation of relevant social conditions—and that these methods are both morally justified and sufficient for good social policy. We present and defend our own preferred model for dealing with dangerous criminals, an incapacitation account built on the right to self-protection analogous to the justification for quarantine (see Pereboom 2001, 2013, 2014a; Caruso 2016a), and we respond to recent objections to it by Michael Corrado and John Lemos. (shrink)

VAN PRAAG (Paul), Introduction : le Père Henri Bosmans, histo­rien des mathématiques (pp. 7-16). SAUVAGE (Pierre), Notice biographique du Père Henri Bosmans (pp. 17-25). HERMANS (Michel), Henri Bosmans : sa formation et ses réseaux de rela­tions (pp. 27-72). DELANGHE (Richard), Quelques aspects de la vie et de l’œuvre de Paul Mansion (1844-1919) (pp. 73-82). BRIGAGLIA (Aldo), Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique / traduit de l’italien par Bruna GAINO et Patricia RADELET-DE (...) GRAVE (pp. 83-104). MAWHIN (Jean), La tentative belge d’édition des œuvres complètes d’Euler vue par Henri Bos­mans (pp. 105-133). GOLVERS (Noël), Henri Bosmans, s.j., et la mission jésuite en Chine / traduit du néerlandais par Anne-Sophie MEURICE (pp. 135-152). ROMANO (Antonella), Henri Bosmans, jésuite et historien des mathéma­tiques dans la Belgique du premier XXe siècle (pp. 153-168). SAUVAGE (Pierre), Le Père Henri Bosmans et l’historiographie au tournant du XXe siècle (pp. 169-187). RADELET-DE GRAVE (Patricia), Le fonds Henri Bos­mans / avec un ajout de Michel HERMANS (pp. 189-215). MANSION (Paul), Correspondance de Paul Mansion adres­sée à Henri Bosmans / introduction, trans­cription et annotation par Michel HERMANS (pp. 217-251). HEEFFER (Albrecht) – HERMANS (Michel) – STOFFEL (Jean-François), Bibliographie d’Henri Bosmans (pp. 253-298). (shrink)