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)

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.

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)

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)

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, ...

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)

Malebranche and the Search after Lost Identity. Legacy and Uncertainty of His Philosophy between the Eighteenth and Twentieth Centuries. Starting from the Œuvres complètes edited by Robinet, the article summarizes the vicissitudes through which the French historical scholarship with its leading figure Victor Cousin have restored the imagine and the correspondence of Malebranche, beginning with the dissemination of the original documents, conserved throughout the eighteenth century by P. Lelong, P. André, and finally P. Adry. In spite of his great historical (...) contribution, the French scholarship generally stressed an inadequate assessment of this philosophy, sharply suspected of spinozism, a judgment inherited by the handbooks of the history of philosophy edited between the XIX and the XX Century, as proved by the case of Grundriss der Geschichte der Philosophie by Überweg. The article concludes with three minimalist but creative readings of Malebranche by Proust, Heisenberg, Dalì. (shrink)

In the same year that, just a few days before his death, Locke was penning instructions to for the publication of some of his unprinted works, in particular of the Paraphrases on the Epistles of Saint Paul, a book entitled The Two Covenants of God with Mankind was published in London. The author, Thomas Taylor, had been for some time a staunch supporter of the thought and work of Malebranche, to whom the subtitle made explicit reference. It was during his (...) studies at Oxford that Taylor had begun to approach Malebranche’s thought, very probably through John Norris his chief English mentor. Indeed, Taylor referred to Norris in the notice To the Reader in his work, both explicitly as—“one who best understands [Malebranche]”—and by reutilising the encomiastic optical and astronomical metaphors with which Norris introduced the French philosopher at the beginning of The Theory of the Ideal or Intelligible World. Also traceable to the authority of Norris was Taylor’s eulogy of the Recherche de la vérité—“a Book that is alone a Library”—that he had translated 10 years earlier, which, along with the almost contemporary translation by Richard Sault, rendered Malebranche’s most influential work accessible to English readers. Taylor’s translation can be set within the context of Locke’s earliest stances regarding the theory of ideas of Malebranche and Norris, the principal documentation of which was to be found in Of Seeing all Things in God, another of the unpublished works mentioned by Locke in the letter to Peter King. King did indeed publish it in the Posthumous Works, albeit without the polemical initial paragraphs directed against Norris, whereas the editorial history of the Paraphrases was to be different. (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...

In his small but priceless treatise entitled De dignitate et de augmentis scientiarum,1 Francis Bacon undertakes to point i (Of the Dignity and Advancement ...

The Autobiography of Giambattista Vico is significant both as a source of insight into the influences on the eighteenth-century philosopher's intellectual development and as one of the earliest and most sophisticated examples of philosophical autobiography. Referring to himself in the third person, Vico records the course of his life and the influence that various thinkers had on the development of concepts central to his mature work. Beyond its relevance to the development of the New Science, the Autobiography is also (...) of interest for the light it sheds on Italian culture in the seventeenth and eighteenth centuries.Still regarded by many as the best English-language translation of this classic work, the Cornell edition was widely lauded when first published in 1944. Wrote the Saturday Review of Literature: "Here was something new in the art of self-revelation. Vico wrote of his childhood, the psychological influences to which he was subjected, the social conditions under which he grew up and received an education and evolved his own way of thinking. It was so outstanding a piece of work that it was held up as a model, which it still is.". (shrink)

_A fresh translation of _The New Science_, with detailed footnotes that will help both the scholar and the new reader navigate Vico’s masterpiece_ _The New Science_ is the major work of Italian philosopher Giambattista Vico. First published in 1725 and revised in 1730 and 1744, it calls for a reinterpretation of human civilization by tracing the stages of historical development shared by all societies. Almost unknown during his lifetime, the work had a profound influence on later thinkers, from Montesquieu (...) and Marx to Joyce and Gadamer. This edition offers a fresh translation and detailed annotations which enable the reader to track Vico’s multiple allusions to other texts. The introduction situates the work firmly within a contemporary context and newly establishes Vico as a thinker of modernity. (shrink)

Vico's earliest extant scholarly works, the six first statement of ideas that Vico would continue to refine throughout his life. Delivered between 1699 and 1707 to usher in the new academic year at the University of Naples, the orations are brought together here for the first time in English in an authoritative translation based on Gian Galeazzo Visconti's 1982 Latin/Italian edition. In the lectures,Vico draws liberally on the classical philosophical and legal traditions as he explores the relationship between the Greek (...) dictum "Know thyself' and liberal education. As he sets forth the values and goals of a humanist curriculum, Vico reveals the beginnings of the anti-Cartesian position he will pursue in On the Study Methods of Our Time. Also found in the orations are glimpses ofVico's later views on the theory of interpretation and on the nature of language, imagination, and human creativity, along with many themes that were to be fully developed in his magnum opus, The New Science. On Humanistic Education will be welcomed by Vichians and their students, intellectual historians, and others in the fields of philosophy, literary theory, history and methods of education, classics, and rhetoric. (shrink)

Electronic text edition of Giambattista Vico, De nostri temporis studiorum ratione, in Latin. It includes the page numbers of the original edition of 1709, available among the online resources of the ISPF web portal www.giambattistavico.it.