I teoremi di Gödel suscitano un interesse sempre crescente nella riflessione filosofica contemporanea. Rimane però in discussione fra gli studiosi come si sia arrivati alla loro scoperta e quale sia il loro significato per il dibattito sui fondamenti delle scienze. Nel volume si ripercorrono le vicende che portarono alla formulazione dei teoremi di incompletezza, a partire dall’incontro tra von Neumann e Gödel al Congresso di Königsberg nel 1930, e si indaga, riferendosi in particolare al lavoro di von Neumann, sull’impatto che (...) questi teoremi hanno avuto per il progetto hilbertiano di fondazione della matematica e delle scienze più in generale. Ne risulta un’immagine delle indagini di Hilbert meno rigida di quella finora corrente, in linea con le più recenti acquisizioni della storiografia, e soprattutto più rispettosa della stessa prassi assiomatica, che oscillava per Hilbert tra ambizioni fondazionaliste e istanze pragmatiche. È stato von Neumann a rendere esplicita, dopo la scoperta dei teoremi di Gödel, quella che si può definire come la “svolta pragmatica” nell’assiomatica. Il libro propone inoltre un chiarimento riguardo alla scoperta di von Neumann del secondo teorema di incompletezza. (shrink)

Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andréka-Németi group use several formal axiomatic theories together to re-capture, predict, recover or explain the phenomena of special relativity, general relativity (...) and classical kinematics. Their scientific methodology is close to Hilbert’s conceptions of how science should be done ideally. In this paper, we compare Formica’s reading of Hilbert’s axiomatic method to the method used by the Andréka-Németi group. (shrink)

In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. I (...) shall argue this point by examining four basic ideas embraced by von Neumann in his foundational considerations: a) the conservative attitude to assume in mathematics; b) the role that mathematics and the axiomatic approach have to play in all that is science; c) the notion of success as an alternative methodological criterion to follow in scientific research; d) the empirical and, at the same time, abstract nature of mathematical thought. Once these four basic ideas have been accepted, Hilbert’s spirit in von Neumann’s methodology of science will become clear. (shrink)

The paper deals with the controversial issue of realism in Wittgenstein’s Tractatus. Most of the problems are grounded in the logical-linguistic foundation of important ontological notions given within the text (such as object, state of affairs, fact, etc.). This has led some scholars to think that there is no conception of the world in the Tractatus that is independent of language and that in his work Wittgenstein is simply engaged in a logical investigation of what it is essential for any (...) language to represent reality. Therefore, no conclusions about a transcendent world can be drawn from it. Here we argue that it is true that the author of the Tractatus is engaged in a logical investigation, conducted a priori and internal to language, on the conditions that are (or have to be) satisfied by any significant language. However, what such an investigation reveals, given one of these languages, is the necessity to presuppose a world made in a certain way and transcendent to the language that pretends to describe it. Two issues are considered to clarify the sense of the realism of the Tractatus — that of the existence of simple objects, and that of the truth of propositions — and a new interpretative schema for the text is advanced. (shrink)

In "La science et l’hypothèse" Henri Poincaré scrive: «Compito dello scienziato è ordinare; si fa la scienza con i fatti, come si fa una casa con le pietre; ma un cumulo di fatti non è una scienza, proprio come un mucchio di pietre non è una casa» . Oltre a richiamare qualcosa che a molti potrebbe persino apparire ovvio – cioè che la scienza non possa in alcun modo ridursi ad un mero agglomerato di fatti che il ricercatore registra in (...) ambito osservativo, ma richieda piuttosto un attento processo di elaborazione razionale sia in fase preventiva rispetto al contesto dell’esperienza, sia in fase di valutazione dei dati sperimentali raccolti – questa affermazione ha il merito di ricordarci qualcosa che spesso viene passato sotto silenzio, vale a dire il fatto che durante il nostro tentativo di comprendere il mondo si dia alla conoscenza una materia, un complesso di "oggetti", tale da risultare determinante nella costruzione e nella formulazione delle nostre teorie. Se questo è vero, si può quindi parlare di una materia, e di una forma da essa distinta, della conoscenza scientifica, sebbene con alcune precisazioni. Nel contributo si preciserà questa distinzione facendo riferimento alle assiomatizzazioni di alcune discipline scientifiche condotte nella prima metà del secolo scorso. (shrink)

Shortly after Kurt Gödel had announced an early version of the 1st incompleteness theorem, John von Neumann wrote a letter to inform him of a remarkable discovery, i.e. that the consistency of a formal system containing arithmetic is unprovable, now known as the 2nd incompleteness theorem. Although today von Neumann’s proof of the theorem is considered lost, recent literature has explored many of the issues surrounding his discovery. Yet, one question still awaits a satisfactory answer: how did von Neumann achieve (...) his result, knowing as little as he seemingly did about the 1st incompleteness theorem? In this article, I shall advance a conjectural argument to answer this question, after having rejected the argument widely shared in the literature and having analyzed the relevant documents surrounding his discovery. The argument I shall advance strictly links two of the three letters written by von Neumann to Gödel in the late 1930 and early 1931 (i.e. respectively that of November 20, 1930 and that of January 12, 1931) and finds the key for von Neumann’s discovery in his prompt understanding of the Gödel sentence A – as the documents refer to it – as expressing consistency for a formal system that contains arithmetic. (shrink)

Hilbert’s methodological reflection has certainly shaped a new image of the axiomatic method. However, the discussion on the procedural character of the method is still open, with commentators subs...

Giambattista Vico (1668-1744) was one of the most original and idiosyncratic philosophers before Kant and Hegel. Although Giorgio Vasari had already diagnosed a cycle of rise, blossoming and decline in the history of art, Vico was the first to base this on a philosophical system. Isolated in Naples from direct contact with the philosophical life of his times, he worked at his grand design of the cycles of rise, blossoming, decline and eternal return which he saw in all areas (...) of culture. His points of reference were ancient mythology and Greek and Roman history. To that extent, he is regarded today as the founder of the philosophy of history and the precursor of a tradition which extends to Hegel and Oswald Spengler's "Decline of the West". (shrink)

Bibliografia (p.[xvii]-xlvi) - Scritti autobiografici.- Dagli scritti filosofici anteriori alla "Scienza nuova."- Principj di scienza nuova.- Dagli scritti minori: filosofici e critici.- Dagli scritti minori: storici, biografici ed epigrafici.

The relatedness between a country or a firm and a product is a measure of the feasibility of that economic activity. As such, it is a driver for investments at a private and institutional level. Traditionally, relatedness is measured using networks derived by country-level co-occurrences of product pairs, that is counting how many countries export both. In this work, we compare networks and machine learning algorithms trained not only on country-level data, but also on firms, which is something not much (...) studied due to the low availability of firm-level data. We quantitatively compare the different measures of relatedness, by using them to forecast the exports at the country and firm level, assuming that more related products have a higher likelihood to be exported in the future. Our results show that relatedness is scale dependent: the best assessments are obtained by using machine learning on the same typology of data one wants to predict. Moreover, we found that while relatedness measures based on country data are not suitable for firms, firm-level data are very informative also for the development of countries. In this sense, models built on firm data provide a better assessment of relatedness. We also discuss the effect of using parameter optimization and community detection algorithms to identify clusters of related companies and products, finding that a partition into a higher number of blocks decreases the computational time while maintaining a prediction performance well above the network-based benchmarks. (shrink)

Sinopsi del diritto universale.--De universi iuris uno principio et fine uno.-- De constantia iurisprudentis.-- Notae in duos libros.--Dissertationes.

The Calabrian Mafia seems to be animated by a hunger for power with no precedent in other crime organizations, and an ability to hide its presence so much to make it an obvious and inevitable component of the decreed social system, deeply crept into the community cohabitation norms. In the study, we have aimed at investigating the Reggio Calabria flying squad policemen's representations and lived experiences. The qualitative analysis of the text, carried out through dedicated software, has pointed out two (...) super codes. In other words, “solitude” as lived experience is spatially contained in “aggression to connections” and “the absence of freedom” encloses the lived experience of constant and systematic danger. This means that the emotional elaboration on Mafia, carried out during the group process, has highlighted thinking categories connected to the coercion of relational space which articulate themselves along t.. (shrink)

Introduction et présentation de J.-B. Vico et de la Science nouvelle.--Philosophie.--Philologie et esthétique.--Philosophie de l'histoire.

v. 4. Reivindicaiones de Vico y otros escritos latinos -- v. 5. Escritos históricos : Gestas de Antonio Crafa y La conspiración partenopea (La conspiración de los príncipes napolitanos --.

The construction of body image consists of the ways in which the body is considered, perceived, and evaluated. The ideal body image has been changing considerably over the centuries; the discrepanc...

BIBLIOGRAPHICAL NOTE The standard edition of Vico's works is by Fausto Nicolini (8 vols. in 11; Ban, 1911-41). For a bibliography, see Benedetto Croce, ...