The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic to invariant-mass-spheres (...) imbedded in each other, since the signatures result steadily Lorentzian; starting from dimension four (Minkowski) up to dimension ten with Clifford algebra ℂℓ(1, 9), where the construction naturally ends. The equations of motion met in the construction are most of those traditionally postulated ad hoc: from Weyl equations for neutrinos (and Maxwell's) to Majorana ones, to those for the electroweak model and for the nucleons interacting with the pseudoscalar pion, up to those for the 3 baryon-lepton families, steadily progressing from the description of lower energy phenomena to that of higher ones. The 3 division algebras: complex numbers, quaternions and octonions appear to be strictly correlated with Clifford algebras and then with this spinor-geometrical approach, from which they appear to gradually emerge in the construction, where they play a basic role for the physical interpretation: at the third step complex numbers generate U(1), possible origin of the electric charge and of the existence of charged—neutral fermion pairs, explaining also easily the opposite charges of proton-electron. Another U(1) appears to generate the strong charge at the fourth step. Quaternions generate the signature of space-time at the first step, the SU(2) internal symmetry of isospin and, in the gauge term, the SU(2) L one, of the electroweak model at the third step; they are also at the origin of 3 families; in number equal to that of quaternion imaginary units. At the fifth and last step octonions generate the SU(3) internal symmetry of flavour, with SU(2) isospin subgroup and, in the gauge term, the one of color, correlated with SU(2) L of the electroweak model. These 3 division algebras seem then to be at the origin of charges, families and of the groups of the Standard model. In this approach there seems to be no need of higher dimensional (>4) space-time, here generated by the four Poincaré translations, and dimensional reduction from ℂℓ(1,9) to ℂℓ(1,3) is equivalent to decoupling of the equations of motion. This spinor-geometrical approach is compatible with that based on strings, since these may be expressed bilinearly (as integrals) in terms of Majorana–Weyl simple or pure spinors which are admitted by ℂℓ(1, 9) = R(32). (shrink)

A theoretical interpretation of the observed periodicity of large-scale (∼128 Mpc) correlations of galaxies is proposed as due to eigenvibrations of the closed expanding universe. Eigensolutions of the equations of motion for a scalar field in an inflationary model allow one to compute the energy density, interpreted as matter density. Isotropic eigensolution give rise to a matter density distribution having a periodic structure centered at the north pole of the closed Robertson-Walker universe represented by S3/Z2. It is able to reproduce (...) well the striking periodicity of the observational data, in the galactic north-south directions. The dipole and quadrupole eigensolutions and the location of the co-moving observer in a point of S3/Z2 different from the center of the vibrational structure would imply, in a theoretically well predictable way, a decrease of the observed periodicity in some other directions. (shrink)

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? (...) These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics. (shrink)

In Multi Agent Systems it is often the case that individual preferences are not compatible and coalitions compete to achieve a given result. The paper presents a language to talk about the conflict between coalitional choices and it expresses deontic notions to evaluate them. We will be specifically concerned with cases where the collective perspective is at odds with the individual perspective.

The study of evil and the different forms in which it manifests itself has long been the interest of a significant number of scholars, mainly philosophers and theologians. Yet, following the libera...

This article introduces a novel theoretical framework for addressing epistemic injustice—a phenomenon where certain groups or individuals are systematically excluded from knowledge creation and dissemination processes—by employing ontological relativity and conceptual analysis. “Ontological relativity” refers to a philosophical perspective that posits our understanding of reality as being shaped by our toolbox of concepts, categories, language, and social practices; “conceptual analysis” is a method of inquiry that involves the rigorous examination and deconstruction of a particular concept or set of concepts in (...) order to uncover their constituent elements, relationships, and underlying assumptions. To exemplify the effectiveness of the ontology‐based approach, two paradigmatic applications are explored: (a) educational practices and (b) clinical practice and access to health care. Through the presentation of these applications and the step‐by‐step illustration of the applied methodology, the aim of the article is to showcase the efficacy of ontology in tackling epistemic injustices, suggesting innovative paths for future research in this domain. (shrink)

Can taxation and the redistribution of wealth through the welfare state be conceived as a modern system of circulation of the gift? But once such a gift is institutionalized, regulated and sanctioned through legal mechanisms, does it not risk being perverted or corrupted, and/or not leaving room for genuinely altruistic motives? What is more: if the market’s utilitarian logic can corrupt or ‘crowd out’ altruistic feelings or motivations, what makes us think that the welfare state cannot also be a source (...) of corruption? To explain the standard answers to the abovementioned questions as well as their implications I will first re-examine two opposing positions assumed here as paradigmatic examples of other similar positions: on the one hand, Titmuss’s work and the never-ending debate about it; on the other, Godbout’s position, in-so-far as it shows how Titmuss’s arguments can easily be turned upside down. I will then introduce and reinterpret Einaudi’s “critical point” theory as a more complex and richer anthropological explanation of the problems and answers considered herein. Through the analysis of these paradigmatic positions I will develop two interrelated arguments. 1) The way these problems are posed as well as the standard answers to them are: a) subject to fallacies: the dichotomy fallacy and the fallacy of composition; b) too reductive and simplistic: we should at least try to clarify what kind of ‘gift’ or ‘corruption’ we are thinking about, and who or what the ‘giver’, the ‘corrupter’, the ‘receiver’ and/or the ‘corrupted’ party are. 2) The answers to these problems cannot be found by merely following a theoretical approach, nor can they be merely based on empirical evidence; instead, they need to take into account the forever troublesome, ambiguous and unpredictable matter of human freedom. (shrink)

The rise of XVIIthcentury natural philosophy determines a significant break with the tradition and enthe idea of a new beginning of scientific investigation grounded on mathematics and experiment; at the same time, the diffusion of printed books represents an essential factor for the dissemination of the new philosophy. The ideal of the book, as an expression for this new philosophy, results from the speculation about the correspondence between the language and structure of the philosophical book and the “book of nature” (...) written by God. At the same time, the pursuit of this ideal requires the critical knowledge of the book tradition and the awareness of the imperfection that characterizes any given accomplishment of the ideal. This inner tension finds an exemplary solution in Newton’s Principia mathematica, where the incompleteness of the book of natural philosophy is recognized as an intrinsic feature, which directs Newton’s own selection and ordering of the material in the process of editing his work. After Newton, several attempts have been made to recover the systematic unity of natural philosophy in a single book, in a system of books or in encyclopaedies. In late XIXthcentury, as the specialization and multiplication of scientific disciplines establishes the impossibility to master natural philosophy as a whole, the intrinsic historicity of natural philosophy is recognized as a crucial factor of scientific thought itself. This significant change of perspective, compared to early modern philosophy, produces the need for different ways of understanding the unity of science and the role of books in scientific practice. Nowadays several distinguished scholars in the history and philosophy of science underscore the need to restore the historical awareness of late XIXth-early XXthcentury science among scientists, in order to promote the development of new scientific ideas. (shrink)

This volume brings together the papers published in Historiographia Linguistica 9:3 (1982), which was devoted to the history of linguistics in Italy, with Marazzini's paper first published in Historiographia Linguistica 10:1/2 (1983), and an original article by Franco Lo Piparo expressly written for this volume. The present volume provides in addition an index of subjects, as well as an index of names, which supplies bio-bibliographical references to authors discussed.

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

The publication of Guido Calabresi’s book “The Future of Law and Economics” has drawn a substantial amount of attention among law and economics scholars. We thought that the best way to devote special attention to this book was to devote a Special issue to it. This article situates Calabresi’s book among other reflections on the future of the discipline, introduces and explains the reasons behind this Special issue and discuss the organization and content of it. -/- We emphasize how Calabresi’s (...) historical-conceptual standpoint allows him to isolate the stakes of different future developments around the question of how could further appreciation of legal institutions that defy the standard economic assumptions help the field develop theoretically. Overall, the contributors all shared Calabresi’s attempt to restore the balance between Law and Economics and the need to better account for the “whole unanalysed experience of human race”, often neglected by the Economic Analysis of Law approach. Most disagreements are about the ‘how’. In any case, the search for the Law and Economics ‘not (yet) taken’ or for other “Law and … ” approaches is always open to the Future. (shrink)

This introduction explains the reasons behind this Special issue and discuss the organization and content of it. The difficulty of a genuine dialogue and understanding between economics, law and humanities, seems to be due not only to the fragmentation of reflections on man, but to a real ‘conflict of anthropologies’. What kind of conceptions of man and human values are presupposed by and / or privileged by economics, law, economic approaches to law and social sciences? How and when do these (...) conceptions come into conflict within and between disciplines? How do these conceptions of man and his values influence the conceptions of economics, law and institutions, and vice versa, how do these last conceptions influence the former? What are the normative, regulatory and practical implications of assuming an anthropological and / or axiological perspective instead of another? This Special issue aims at exploring the possibility of finding a common ground for discussion between economics, law and humanities, through the analysis and comparison of both the conceptions of man, human action and values assumed by economics, law and humanities, and their normative implications. The contributions to this Special issue and its organization are outlined at the end of this introduction. (shrink)

The paper aims to address the following two questions: what kind of discourse is that which attempt to found or defend the autonomy or the boundaries of a discipline? Why do such discourses tend to turn into normative, dogmatic-excommunicating discourses between disciplines, schools or scholars? I will argue that an adequate answer may be found if we conceive disciplines as dogmatics, where such discourses often take the form of a discourse on the foundation of a discipline, a foundation in the (...) name of which the scholar speaks and with which he/she entertains an identity relationship. To this purpose I will re-examine the methodological discourses of (and debates between) Pareto, Croce and Einaudi on the demarcation issue between philosophy, economics and value-judgments as highly instructive to understand such issues. (shrink)

Bringing together contributors from philosophy, international relations, security studies, and strategic studies, New Wars and New Soldiers offers a truly interdisciplinary analysis reflective of the nature of modern warfare. This comprehensive approach allows the reader to see the broad scope of modern military ethics, and to understand the numerous questions about modern conflict that require critical scrutiny. Aimed at both military and academic audiences, this paperback will be of significant interest to researchers and students in philosophy, sociology, military and strategic (...) studies, international relations, politics, and security studies, acting as an ideal course text or as supplementary reading. (shrink)

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals and (...) conditionals. (shrink)

Il libro ricostruisce la vita e il pensiero di Jean Guitton (1901-1999), il grande amico di Paolo VI, a quasi ventʼanni dalla sua morte. La vicenda umana di questo scrittore e filosofo cristiano ha attraversato quasi integralmente il XX secolo quale testimone diretto di eventi epocali: i primi tentativi ecumenici, le due guerre mondiali, le radicalizzazioni ideologiche del secondo dopoguerra, lʼera atomica e il Concilio Vaticano II. Il primo capitolo del volume è dedicato alla ricostruzione della vita di Guitton (...) e alle sue prime sintesi accademiche; ed esso fanno seguito altri due capitoli che trattano della sua antropologia (il tempo, il pudore, l'amore umano) e della sua cristologia filosofica (le condizioni di possibilità della rivelazione, la filosofia della risurrezione, la sua innovativa mariologia). Ne viene il ritratto di un pensiero di impronta umanista, ben radicato nella tradizione francese e che forse, come già lamentava Yves Congar nel 1963, non ha avuto, fino ad oggi, quellʼattenzione e quellʼaccoglienza che sembra meritare. (shrink)

We consider the global structure of momentum space Π3, 1 in a field theory which is covariant with respect to the action of global conformal group G. We show that Π3, 1 is a homogeneous space for G which coincides with (S3×S1)/Z2 compact space. The radius of momentum space determines the natural invariant ultraviolet cutoff which may take the form of a Pauli-Vilars form factor in perturbation theory. We demonstrate in the case of the massless λφ4 theory how the conventional (...) ultraviolet divergences which appear in the flat momentum space are regularized in Π3, 1 global momentum space. (shrink)

Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical eigenfunctions: n, l, (...) m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured. (shrink)

Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z 2 and correlated by (...) conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

The aim of this article is to shed light on an understudied aspect of Giordano Bruno's intellectual biography, namely, his career as a mathematical practitioner. Early interpreters, especially, have criticized Bruno's mathematics for being “outdated” or too “concrete”. However, thanks to developments in the study of early modern mathematics and the rediscovery of Bruno's first mathematical writings (four dialogues on Fabrizio's Mordente proportional compass), we are in a position to better understand Bruno's mathematics. In particular, this article aims to reopen (...) the question of whether Bruno anticipated the concept of infinitesimal quantity. It does so by providing an analysis of the dialogues on Mordente's compass and of the historical circumstances under which those dialogues were written. (shrink)

This book offers new critical perspectives on the relationship between the notions of speculation, logic and reality in Hegel's thought as basis for his philosophical account of nature, history, spirit and human experience. The systematic functions of logic and pure thought are explored in their concrete forms and processual progression from subjective spirit to philosophy of right, society, the notion of habit, the idea of work, art, religion and science. Engaging the relation between the Logic and its realisations, this book (...) shows the internal tension that inhabits Hegel's philosophy at the intersection of logical speculation and concrete analysis. The investigation of this tension allows for a hermeneutical approach that demystifies the common view of Hegel's idealism as a form of abstract thought, while allowing for a new assessment of the importance of speculation for a concrete understanding of the world. (shrink)

The aim of my paper will be to provide a commentary on the introduction to the French edition of Ethics and the Limits of Philosophy (1985) by Bernard Williams (1929–2003) and to show the Nietzschean legacy that is made explicit there. In this introduction, called “L'éthique, question de style?” and published in 1990, Williams reflects on some of the problems of style that his book poses to French readers, to whom he feels his work is less familiar. Furthermore, Williams recalls (...) some moments of the Royaumont colloquium (which he attended in 1958) and dwells on some peculiarities that distinguish him from analytic philosophy, “French” philosophy, Wittgenstein and Heidegger. Finally, the text closes with a description of the image of the philosopher to whom Williams feels closest—that of Nietzsche—and illustrates the reasons that distance him from other models of philosophical writing. (shrink)

The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the implications of global compactified space-times for (...) cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

According to McDowell, in Empiricism and the Philosophy of Mind the myth of Jones has the purpose of completing the account of experience that Sellars needs to argue against traditional empiricism. In particular, on McDowell's view the myth of Jones should explain how to conceive of non-inferentially knowable experiences as containing propositional claims. This article argues that the myth of Jones does not succeed in providing such an account, especially on McDowell's own terms: assuming McDowell's epistemological distinction between inferential and (...) non-inferential knowledge, it turns out that in Sellars' thought experiment perceptual experiences can contain propositional claims only at the price of being known inferentially rather than non-inferentially. Therefore McDowell's Sellars' attack fails against traditional empiricism. (shrink)

This article begins by examining the status of “difference” in representations of perspectivist cosmologies, which are themselves often represented as radically different to Euro-American cosmologi...

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

Aristote attribue à la poésie la faculté de représenter la réalité par l'intermédiaire du récit: on comprend le monde en le racontant. Cette doctrine a été reçue, modifiée, pliée à de nouvelles exigences au cours des siècles. Comment les préoccupations de l'Antiquité ont-elles survécu à l'âge moderne?