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)

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)

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)

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)

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.

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)

. 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)

Two dichotomies are considered as the foundations of a scientific theory: the kind of infinity—either potential or actual-, and the kind of organization of the theory—axiomatic or problem-based. The original intuitionist program relied on the choices of potential infinity and the problem-based organization. I show that the logical theory of Kolmogorov’s 1932 paper relied on the same choices. A comparison of all other theories sharing the same foundational choices allows us to characterize their common theoretical development through a few logical (...) steps. The theory illustrated by Kolmogorov’s paper is then rationally re-constructed according to the steps of this kind of development. One obtains a new foundation of intuitionist logic, which is of a structural kind since it is based on and developed according to the structure of the above mentioned two fundamental choices. In addition, Kolmogorov’s illustration of his theory of intuitionist logic is an instance of rigorous reasoning of the intuitionist kind. (shrink)

All suggested notions of reduction of two scientific theories are critically reviewed and analyzed. In particular those applied to the case of the alleged reduction of Chemistry to Quantum mechanics are examined. Since it is recognized that the weakness of this field of research is the lack of a definition of a scientific theory, it is suggested that a scientific theory is characterized by two choices regarding two dichotomies, that is, the kind of mathematics and the kind of logic. According (...) to this view a reduction is only possible between two theories in which the same choices are shared. As a consequence, only one case of reduction in the history of physics is recognized: physical optics to electromagnetism, a case that is commonly accepted. The other cases of claimed reductions are recognized as impossible, owing to the different choices of the two theories at issue and hence the radical variations in meaning of their shared basic notions. In particular, the claimed reduction of Chemistry to Quantum mechanics is disproved in detail. (shrink)

Authoritative appraisals have qualified this book as an “axiomatic” theory. However, given that its essential content is no more than an analogy, its theoretical organization cannot be axiomatic. Indeed, in the first edition Dirac declares that he had avoided an axiomatic presentation. Moreover, I show that the text aims to solve a basic problem (How quantum mechanics is similar to classical mechanics?). A previous paper analyzed all past theories of physics, chemistry and mathematics, presented by the respective authors non-axiomatically. Four (...) characteristic features of a new model of organizing a theory were recognized. A careful examination of Dirac’s text shows that it actually applied this kind of organization of a theory, confirming formally what Kronz and Lupher suggested through intuitive categories (pragmatism and rigour), i.e. Dirac’s formulation of Quantum mechanics represents a distinct theoretical approach from von Neumann’s axiomatic approach. However, since the second edition Dirac has changed his approach: although relying again on analogy, his theory refers to the axiomatic method. Some considerations on the odd paths which led to the present formulation of QM are added. They suggest that a new foundation of this theory needs to be found. (shrink)

(1997). Information science as a paradigmatic instance of a problem‐based theory. World Futures: Vol. 49, The Quest for a Unified Theory of Information, pp. 251-273.

A re-visitation of Joule’s experiment motivates a critical analysis of thermodynamic notions: heat, total energy, first principle, organization of a scientific theory, its relationships with logic and mathematics. A rational re-construction of thermodynamics is suggested according to the model of a problem-based organization, that Sadi Carnot applied to his formulation. The new formulation accomplishes the long time theoretical process started by Joule’s experiment within physicists community's collective mind, i.e. the process of exiting out Baconian science for suggesting a first theory (...) out Newton’s paradigm, and eventually for introducing a pluralism of incompatible physical theories. (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)

As a basic work of a translation I suggest to be attentive to the doubly negated propositions because they do not belong to classical logic, rather to intuitionist logic. I offer several instances of these propositions and classify the typical ways of their occurrences in a text.

I prove that the three basic propositions of Vasiliev's paraconsistent logic have a semantic interpretation by means of the intuitionist logic. The interpèretation is confirmed by amens of the da Costa's model of Vasiliev's paraconsistent logic.