This biography sheds new light on the life and work of physicist Ettore Majorana (including unpublished contributions), as well as on his mysterious disappearance in March 1938. Majorana is held by many, including Nobel Laureate, Enrico Fermi, to have been a genius of the rank of Galilei and Newton. In this intriguing story, the author, himself a leading expert on the work of Majorana, supplements the existing literature with new insights, anecdotes and personal accounts of contemporaries (...) of Majorana. (shrink)

Il s’agit d’affronter la « figure » d’Ettore Majorana et d’en proposer un premier « profil philosophique ». La question des « fictions » apparaît alors centrale chez Majorana. On établit ensuite la dimension surrationaliste et européenne de ses affinités électives avec Giovanni Gentile Junior. Les deux oeuvres sont restituées dans le cadre d’un mathématisme constructif et inductif (Gaston Bachelard, puis Robert Blanché) qui s’oppose au géométrisme classique (Emile Meyerson) et au pythagorisme spiritualiste (Arthur Eddington).

Cet article retrace la carrière des publications d’Ettore Majorana en analysant les citations dont elles ont fait l’objet depuis le début des années 1930. Cette approche met en évidence la redécouverte, au milieu des années 1960, de l’article de 1937 portant sur les particules de spin quelconque et permet d’identifier les personnes à l’origine du travail de promotion de l‘œuvre de Majorana, dont la visibilité s’est accrue depuis le milieu des années 1970. L’étude des co-citations fait voir (...) le réseau conceptuel dans lequel les travaux de Majorana s’insèrent. (shrink)

We give an accurate historical and scientific account of a practically unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in English translation. It is likely related to an invited talk for a conference at Leningrad (or Kharkov) in 1933 (or 1934) which, however, Majorana never attended. Probably this manuscript is one of the last missing (...) papers of the “Senatore folder”, given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. (shrink)

We give an accurate historical and scientific account of a practically unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in English translation. It is likely related to an invited talk for a conference at Leningrad in 1933 which, however, Majorana never attended. Probably this manuscript is one of the last missing papers of the “Senatore (...) folder,” given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. (shrink)

After a quick historical account of the introduction of the group-theoretical description of quantum mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved by him in frontier research topics as well as in physics teaching point out that the Italian physicist can be well considered as a follower of Weyl in his reformulation of quantum mechanics.

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical (...) nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed. (shrink)

The two-electron atom is the simplest nontrivial quantum system not amenable to exact solutions. Today, its relevance in the development of quantum mechanics and its pedagogical value within the realm of atomic physics are widely recognized. In this work, an historical review of the known different methods and results devised to study such a problem is presented, with an emphasis to the calculations of the ground state energy of helium. Then we discuss several, related, unpublished results obtained around the same (...) years by Ettore Majorana, which remained unknown till recent times. Among them a general variant of the variational method appears to be particularly interesting, even for current research in atomic and nuclear physics: it takes directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Further relevant contributions, specialized to the two-electron problem, include the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results) and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable. Finally a survey of results, relevant mainly for pedagogical reasons, is given; in particular we focus on simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as on a simple alternative to Hylleraas’ method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas. (shrink)

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear (...) process, which is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics. (shrink)

Il s’agit d’affronter la « figure » d’Ettore Majorana et d’en proposer un premier « profil philosophique ». La question des « fictions » apparaît alors centrale chez Majorana. On établit ensuite la dimension surrationaliste et européenne de ses affinités électives avec Giovanni Gentile Junior. Les deux oeuvres sont restituées dans le cadre d’un mathématisme constructif et inductif (Gaston Bachelard, puis Robert Blanché) qui s’oppose au géométrisme classique (Emile Meyerson) et au pythagorisme spiritualiste (Arthur Eddington).

Logic was understood by the Stoics in a broad sense, as the doctrine that included analysis of the forms of argumentation, rhetoric, theory of concepts and propositions, epistemology, and philosophy of language. The distinguishing characteristic of Stoic logic is the fact that it is fundamentally a logic of propositions, unlike the logic of terms belonging to the Aristotelian tradition. This study offers a new treatment of Stoic logic, in which the various topics are retraced and critically assessed.

Since the first decade of the 14th Century, Thomas Aquinas’s disciples have struggled to explain and defend his doctrine of analogy. Analogy after Aquinas: Logical Problems, Thomistic Answers relates a history of prominent Medieval and Renaissance Thomists’ efforts to solve three distinct but interrelated problems arising from their reading both of Aquinas’s own texts on analogy, and from John Duns Scotus’s arguments against analogy and in favor of univocity in Metaphysics and Natural Theology. The first of these three problems concerns (...) Aquinas’s at least apparently disparate statements on whether a name is said by analogy through a single concept or through diverse concepts. The second problem concerns the model of analogy suited for predicating names analogously across the categories of being or about God and creatures. Is “being” said analogously about God and creatures, or substance and accidents, on the model of how “healthy” is said of medicine and an animal, or on the model of how “principle” is said of a point and a line? The third problem comes from outside challenges to Aquinas’s thought, in particular Scotus’ claims that univocal names alone can mediate valid demonstrations, and any demonstration that failed to use its mediating terms univocally would fail by the fallacy of equivocation. Analogy after Aquinas makes a unique contribution to the study of philosophical theology in the tradition of Thomas Aquinas by showing the historical and philosophical connection between these three problems, as well as the variety of solutions proposed by leading representatives of this tradition. Thomists considered in the book include: Hervaeus Natalis (1250-1323), Thomas Sutton (1250-1315), John Capreolus (1380-1444), Dominic of Flanders (1425-1479), Paul Soncinas (d. 1494), Thomas dio vio Cajetan (1469-1534), Francis Silvestri of Ferrara (1474-1528), and Chrysostom Javelli (1470-1538). (shrink)

This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

The strongly innovative theory of whole-parts relations outlined by Husserl in his Third logical Investigation—to which he attributed a basic value for his entire phenomenology—has recently attracted a renewed interest. Although many important issues have been clarified (especially by Kit Fine) the subject seems still worth being revisited. To this aim Husserlian universes are introduced. These are lower bounded distributive lattices endowed with a unary operation of defect and a binary relation of isogeneity. Husserl's contents are identified with nonzero elements (...) of a Husserlian universe and the dependence relations among contents are defined and studied starting from the idea that the defect of xis what x needs in order to ‘exist’ i.e., in order to be ‘closed’ with respect to the closure operation defined as the sup of x and its defect. It turns out that there are (at least) eight dependence relations which are worth to be considered. Many other questions concerning the world of contents (among them the proofs of the famous Husserl's Sätze) may now be discussed and clarified. Then the theory of species and genera is developed. Ultimate species (for short: species) are identified with equivalence classes of contents modulo isogeneity, and species in general (for short: genera) are identified with arbitrary unions of species. On the basis of the relation obtaining among two contents when they are isogeneous to two contents the first of which is a part of the second it becomes possible to develop a rather satisfying interpretation of Husserl's theory of the dependencies among species and genera and of the material a priori laws. By strengthening the notion of Husserlian universe into the notion of rigid Husserlian universe, the theory of species and genera obtains a stronger version. Three models of the theory are exhibited. The first one, suggested by combinatorial-topological considerations, identifies contents with finite non-empty sets of natural numbers; the second one identifies contents with non-empty sets of formulas of a formal language; the third one (not totally ‘rigid’) identifies contents with positive integers. (shrink)

Per uscire dalle aporie delle proprie conseguenze, la scienza deve vedere riconosciuto l'atto come uno dei propri principi fondamentali (accanto all'ente e alla parola). Scienza è, infatti, mettere in relazione le cose (la "natura") con delle leggi matematiche (vale a dire con dei simboli e dei concetti). Ma mettere in relazione è un atto. Sicché, la scienza si fonda su tre principi (ente, parola, atto) e sui corrispettivi campi filosofici (ontologia, logica, etica). Tenere conto di quest'ambito triadico serve a mostrare (...) che l'epistemologia non è un sapere neutro e descrittivo, ma è un prendere partito: al tempo stesso dal punto di vista etico, politico, morale e giuridico. (shrink)

The mental representation of one’s own body does not necessarily correspond to the physical body. For instance, a dissociation between perceived and actual reach-ability has been shown, that is, individuals perceive that they can reach objects that are out of grasp. We presented participants with 3D pictures of objects located at four different distances, namely near-reaching space, actual-reaching space, perceived-reaching space and non-reaching space. Immediately after they were presented with function, manipulation, observation or pointing verbs and were required to judge (...) if the verb was compatible with the object.Participants were faster with function and manipulation verbs than with observation and pointing verbs. Strikingly, with both function and manipulation verbs participants were faster when objects were presented in actual than the perceived reaching space. These findings suggest that our knowledge of the world is implicitly built online through behaviour, and is not necessarily reflected in explicit estimates or conscious representations. (shrink)

This book is focused on the first three parts of Bolzano's Theory of Science and introduces a more systematic reconsideration of Bolzano's logical thought. In undertaking this task, the book is intended as an exploration, not so much of the more specifically discursive aspects of Bolzano's logical thought - already amply studied - as much as on identifying the singularly coherent and systematic nature of the logic presented in Bolzano's work.