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)

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)

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)

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 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)

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)

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)

I take advantage of two recent results: 1) the recognition of an alternative theoretical organization to the deductive-axiomatic one; it is characterized by a sequence of four logical steps belonging to intuitionist logic; 2) the recognition of the logical content of Cusanus’ philosophical works; also this content pertains to intuitionist logic, which Cusanus anticipated by even identifying some its logical laws. Many Cusanus’ books present the alternative theoretical organization; whose yet he did not apply in a clear way its last (...) two steps, the ad absurdum arguing and the application of the principle of sufficient reason. For this reason in the last books his thinking transcended to a metaphysical level. Hegel’s philosophy of logic shares Cusanus’ philosophical effort for exiting out classical logic. He seems to have assumed Cusanus’ anticipation of the new theoretical organization; all goes as if Hegel wanted to improve Cusanus’ poor method, by introducing a process of additions of two negations which however does not agree with the intuitionist logic. Moreover, Hegel presupposes, like Cusanus in his last years, the free application of the principle of sufficient reason to the entire subject of his philosophy of logic without awareness of the logical constraints to which is subject a correct application of this principle; hence, he introduced a metaphysical arguing which according to modern mathematical logic has no consistent content. Also Hegel’s supposed prolongation of Cusanus’ logical discoveries was an essentially metaphysical view. (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)

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)

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)

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)

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)

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)

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)

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 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 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)

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)

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 EU AI Act is the first step toward a comprehensive legal framework for AI. It introduces provisions for AI systems based on their risk levels in relation to fundamental rights. Providers of AI systems must conduct Conformity Assessments before market placement. Recent amendments added Fundamental Rights Impact Assessments for high-risk AI system users, focusing on compliance with EU and national laws, fundamental rights, and potential impacts on EU values. The paper suggests that automating business process compliance can help standardize (...) these assessments and outlines some methodological guidelines. (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)

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.

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.

Biological ontologies are used to organize, curate, and interpret the vast quantities of data arising from biological experiments. While this works well when using a single ontology, integrating multiple ontologies can be problematic, as they are developed independently, which can lead to incompatibilities. The Open Biological and Biomedical Ontologies Foundry was created to address this by facilitating the development, harmonization, application, and sharing of ontologies, guided by a set of overarching principles. One challenge in reaching these goals was that the (...) OBO principles were not originally encoded in a precise fashion, and interpretation was subjective. Here we show how we have addressed this by formally encoding the OBO principles as operational rules and implementing a suite of automated validation checks and a dashboard for objectively evaluating each ontology’s compliance with each principle. This entailed a substantial effort to curate metadata across all ontologies and to coordinate with individual stakeholders. We have applied these checks across the full OBO suite of ontologies, revealing areas where individual ontologies require changes to conform to our principles. Our work demonstrates how a sizable federated community can be organized and evaluated on objective criteria that help improve overall quality and interoperability, which is vital for the sustenance of the OBO project and towards the overall goals of making data FAIR. Competing Interest StatementThe authors have declared no competing interest. (shrink)

The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...) conception of evidence and the knowledge-first view of evidence. (shrink)

This article explores a concept of artistic transgression I call aesthetic disobedience that runs parallel to the political concept of civil disobedience. Acts of civil disobedience break some law in order to publicly draw attention to and recommend the reform of a conflict between the commitments of a legal system and some shared commitments of a community. Likewise, acts of aesthetic disobedience break some entrenched artworld norm in order to publicly draw attention to and recommend the reform of a conflict (...) between artworld commitments and some shared commitments of a community. Considering artistic transgressions under the concept of aesthetic disobedience highlights often-overlooked features of modern artworld practices. Most significantly, it draws attention to the deliberative participation of a wide variety of citizens of the artworld, including not just artists and performers but also members of audiences, in the transformation of the rules and boundaries of the artworld itself. (shrink)

The ways in which we exercise intentional agency are varied. I take the domain of intentional agency to include all that we intentionally do versus what merely happens to us. So the scope of our intentional agency is not limited to intentional action. One can also exercise some intentional agency in omitting to act and, importantly, in producing the intentional outcome of an intentional action. So, for instance, when an agent is dieting, there is an exercise of agency both with (...) respect to the agent’s actions and omissions that constitute her dieting behavior and in achieving the intended outcome of losing weight. In our mental lives we exercise intentional agency both in performing mental actions and when we intentionally produce certain outcomes at which our mental actions are aimed. The nature and scope of our intentional agency in our mental lives with respect to controlling the acquisition of mental states such as belief, desire, and intention is a topic that is of interest in its own right. In this essay, I will focus solely on our control over coming to believe. Understanding what sort of control we have our beliefs has far-reaching implications. For instance, theorizing about self-deception and wishful thinking is aided by theorizing about what if any intentional agency we can exercise with respect to acquiring beliefs. Another often mentioned concern that motivates thinking about doxastic agency comes from religion (when conversion requires a change of belief). We also hold persons morally and epistemically responsible for beliefs they have or fail to have. Finally, some deontological theories of epistemic justification require that agents be able to exercise a robust form of doxastic control. Fruitful work on any of these problems requires that we have an account of our intentional agency in acquiring beliefs. There are at least three loci of doxastic control. The first is over acquiring beliefs. The second is over maintaining beliefs. The third is over how we use our beliefs. I am chiefly concerned with the first locus of doxastic control in this essay, but I will say something about the second locus along the way. Also, I will only consider one way we might exercise control over acquiring beliefs. Specifically, I will present an argument against direct doxastic voluntarism (DDV). By “DDV” I mean to refer to the thesis that it is conceptually possible for agents to consciously exercise the same sort of direct voluntary control over coming to acquire a doxastic attitude—such as belief, suspension of belief, and disbelief—that they exercise over uncontroversial basic actions. If DDV is correct, then coming to believe can be a basic action-type. DDV, or something very close to it, was Bernard Williams’ target in his 1973 paper, “Deciding to Believe.” Williams’s argument is widely regarded as having been a failure. But I think that Williams was on to something in his paper. Hence, in this paper, while I do not attempt to resurrect Williams’s argument, I develop and defend a revised argument for a thesis that is quite close to Williams’s. I will proceed as follows. First, I will discuss Bernard Williams’ (1973) failed attempt at showing that DDV is conceptually impossible. This will be followed by a discussion of some constraints on our belief-forming activities. I will then clarify my target a bit more than Williams does in his original paper. Finally, I will present my own argument against the conceptual possibility of DDV. (shrink)

In men and women sexual arousal culminates in orgasm, with female orgasm solely from sexual intercourse often regarded as a unique feature of human sexuality. However, orgasm from sexual intercourse occurs more reliably in men than in women, likely reflecting the different types of physical stimulation men and women require for orgasm. In men, orgasms are under strong selective pressure as orgasms are coupled with ejaculation and thus contribute to male reproductive success. By contrast, women's orgasms in intercourse are highly (...) variable and are under little selective pressure as they are not a reproductive necessity. The proximal mechanisms producing variability in women's orgasms are little understood. In 1924 Marie Bonaparte proposed that a shorter distance between a woman's clitoris and her urethral meatus (CUMD) increased her likelihood of experiencing orgasm in intercourse. She based this on her published data that were never statistically analyzed. In 1940 Landis and colleagues published similar data suggesting the same relationship, but these data too were never fully analyzed. We analyzed raw data from these two studies and found that both demonstrate a strong inverse relationship between CUMD and orgasm during intercourse. Unresolved is whether this increased likelihood of orgasm with shorter CUMD reflects increased penile–clitoral contact during sexual intercourse or increased penile stimulation of internal aspects of the clitoris. CUMD likely reflects prenatal androgen exposure, with higher androgen levels producing larger distances. Thus these results suggest that women exposed to lower levels of prenatal androgens are more likely to experience orgasm during sexual intercourse. . (shrink)

Recent work in epistemology defends the unorthodox theses that belief is (1) an evidentially weak, and (2) question-sensitive attitude, and (3) that forming beliefs is sometimes a matter of guessing. What motivates these theses are examples of rationally permissible belief-ascriptions that exhibit these traits. The main aim of this paper is to outline a semantic account of categorical and conditional belief-ascriptions that captures the motivating data. We then survey some consequences of the proposed semantics, particularly with respect to the question (...) of whether closure under rules of inference is rationally required for weak, question-sensitive belief. (shrink)

Robert Brandom’s normative-pragmatic theory is intended to represent the minimal set of practical abilities whose exhibition qualifies creatures as speaking a language. His model of a minimally discursive practice (MDP) is one in which participants, devoid of logical vocabulary, are only capable of making assertions and drawing inferences. This paper argues that Brandom’s purely assertional practices are not MDPs and that speech acts of asking questions (queries) must be included in any practice that counts as an MDP. The upshot of (...) the argument is support for the claim that the normative pragmatic analysis of assertions requires a corresponding analysis of queries and vice versa. (shrink)

For the greater part of the last 50 years, it has been common for philosophers of mind and cognitive scientists to invoke the notion of realization in discussing the relationship between the mind and the brain. In traditional philosophy of mind, mental states are said to be realized, instantiated, or implemented in brain states. Artificial intelligence is sometimes described as the attempt either to model or to actually construct systems that realize some of the same psychological abilities that we and (...) other living creatures possess. The claim that specific psychological. (shrink)

We study active set methods for optimization problems in Block Angular Form (BAF). We begin by reviewing some standard basis factorizations, including Saunders' orthogonal factorization and updates for the simplex method that do not impose any restriction on the pivot sequence and maintain the basis factorization structured in BAF throughout the algorithm. We then suggest orthogonal factorization and updating procedures that allow coarse grain parallelization, pivot updates local to the affected blocks, and independent block reinversion. A simple parallel environment appropriate (...) to the description and complexity analysis of test procedures is defined in Section 5. The factorization and updating procedures are presented in Sections 6 and 7. Our update procedure outperforms conventional Updating procedures even in a purely sequential environment. (shrink)

In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...) logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic. (shrink)

A heuristic is a rule of thumb. In psychology, heuristics are relatively simple rules for making judgments. A fast heuristic is easy to use and allows one to make judgments quickly. A frugal heuristic relies on a small fraction of the available evidence in making judgments. Typically, fast and frugal heuristics (FFHs) have, or are claimed to have, a further property: They are very reliable, yielding judgments that are about as accurate in the long run as ideal non-fast, non-frugal rules. (...) This paper introduces some well-known examples of FFHs, raises some objections to the FFH program, and looks at the implications of those parts of the FFH program about which we can have some reasonable degree of confidence. (shrink)

Using a model of cognition as extended and enactive, we examine the role of materiality in making minds as exemplified by lithics and writing, forms associated with conceptual thought and meta-awareness of conceptual domains. We address ways in which brain functions may change in response to interactions with material forms, the attributes of material forms that may cause such change, and the spans of time required for neurofunctional reorganization. We also offer three hypotheses for investigating co-influence and change in cognition (...) and material culture. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793. (shrink)

Consumers often buy products not because of their attributes per se but rather because of the ultimate benefits that these attributes provide, in turn leading to the satisfaction of ultimate values. And Apple is a type of company which understand their customers & future aspects of innovation in a way that no other companies do. That’s the reason that apple is at No. 1 place in Top 50 Most innovative companies. This article endeavors to recognize the consumer perception towards the (...) Apple products and what is Apple’s ideology. In this article the researcher has listed down 12 variables which affect the consumer behavior most while purchasing Apple products. (shrink)

The National Center for Biomedical Ontology is now in its seventh year. The goals of this National Center for Biomedical Computing are to: create and maintain a repository of biomedical ontologies and terminologies; build tools and web services to enable the use of ontologies and terminologies in clinical and translational research; educate their trainees and the scientific community broadly about biomedical ontology and ontology-based technology and best practices; and collaborate with a variety of groups who develop and use ontologies and (...) terminologies in biomedicine. The centerpiece of the National Center for Biomedical Ontology is a web-based resource known as BioPortal. BioPortal makes available for research in computationally useful forms more than 270 of the world's biomedical ontologies and terminologies, and supports a wide range of web services that enable investigators to use the ontologies to annotate and retrieve data, to generate value sets and special-purpose lexicons, and to perform advanced analytics on a wide range of biomedical data. (shrink)

The ji 己self is a site, storehouse, or depot of individuated allotment associated with the possession of things and qualities: wholesome and unwholesome desires (yu 欲) and aversions, emotions such as anxiety, and positive values such as humaneness and reverence. Each person's allotment is unique, and its "contents" are collected, measured, reflected on, and then distributed to others. The Analects, Mencius, Xunzi, Daodejing, and Zhuangzi each have their own vision for negotiating the space between self and other. Works as seemingly (...) dissimilar as the Analects and Daodejing both agree that positive qualities located within the self should be shared with others, and that the self can be optimized rather than maximized through sharing, emptying, or clearing. Sommer compares the ji self with other terms for body and person current in classical times. This self is strongly individuated, but it exists primarily in relation to other human beings (ren 人 ). These "others" are almost never one's own kind and are usually people who fall outside one's ascribed familial and social relationships. Negotiations between self and other often reflect apprehension regarding degrees of distance, intimacy, worth, recognition, or understanding (zhi 知) between people. (shrink)

A computational theory is developed that explains how line drawings of polyhedral objects can be interpreted rapidly and in parallel at early levels of human vision. The key idea is that a time-limited process can correctly recover much of the three-dimensional structure of these objects when split into concurrent streams, each concerned with a single aspect of scene structure.

ESPAÑOL: Similar a Baehr v. Miike en Hawaii (1993), Goodridge fue la primera decisión de un tribunal supremo estatal en Estados Unidos que concluyó que las parejas del mismo sexo tienen derecho al matrimonio. La traducción contiene los segmentos más importantes de Goodridge. ENGLISH: Similar to Baehr v. Miike in Hawaii (1993), Goodridge was the first time a state Supreme Court in the United States ruled that same-sex couples have the right to marry. The translation (English to Spanish) contains Goodridge’s (...) key passages. (shrink)

The present paper aims to validate our research on human–humanoid interaction (HHI) using the minimalist humanoid robot Telenoid. We conducted the human–robot interaction test with 142 young people who had no prior interaction experience with this robot. The main goal is the analysis of the two social dimensions (‘‘Perception’’ and ‘‘Believability’’) useful for increasing the natural behaviour between users and Telenoid.Weadministered our custom questionnaire to human subjects in association with a well defined experimental setting (‘‘ordinary and goal-guided task’’). A thorough (...) analysis of the questionnaires has been carried out and reliability and internal consistency in correlation between the multiple items has been calculated. Our experimental results show that the perceptual behaviour and believability, as implicit social competences, could improve the meaningfulness and the natural-like sense of human–humanoid interaction in everyday life task-driven activities. Telenoid is perceived as an autonomous cooperative agent for a shared environment by human beings. (shrink)

I explore the possibility that the feminine, like art, can be thought in terms of Jean-Luc Nancy’s concept of the singular plural. In Les Muses, Nancy claims that art provides for the rethinking of a technë not ruled by instrumentality. Specifically, in rethinking aesthetics in terms of the debates laid out by Kant, Hegel and Heidegger, he resituates the ontological in terms of the specificity of the techniques of each particular artwork; each artwork establishes relations particular to its world or (...) worlds. What is at stake in the singular plural is the multiplicity of relations that are lost in the unifying gestures that arise out of radical oppositions. I rethink the singular plural through a phenomenological encounter with Barb Hunt’s artwork, Antipersonnel, a collection of hand-knitted replicas of antipersonnel landmines. (shrink)

We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass (...) ratios suggest some further foundational interpretations of quantum electrodynamics. (shrink)

A knowledge argument is offered that presents unique difficulties for Christians who wish to assert that God is essentially omniscient. The difficulties arise from the doctrine of the incarnation. Assuming that God the Son did not necessarily have to become incarnate, then God cannot necessarily have knowledge de se of the content of a non-divine mind. If this is right, then God’s epistemic powers are not fixed across possible worlds and God is not essentially omniscient. Some options for Christian theists (...) are discussed, including rejecting traditional theism in favour of some version of pantheism or panentheism. (shrink)