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In a BBC radio programme Popper acknowledged his debt to Einstein saying that Einstein’s influence on his thinking was immense and that he mainly made explicit certain points that were implicit in the work of Einstein. In fact, in... more
In a BBC radio programme Popper acknowledged  his debt to Einstein saying that  Einstein’s influence on his thinking was immense and that  he mainly  made explicit certain points that were implicit in the work of Einstein. In fact, in various writings Einstein presents his critical attitude toward any scientific theory:  of particular interest is Einstein’s article «Induktion und Deduktion in der Physik» (1919)  that can be  considered  a concentrate of Popper’s views of science.  In the second part of the paper are presented the views of Popper on quantum mechanics and his defense of objectivity and realism. Popper opposes the idea, which he associates with the Copenhagen interpretation, that the theories describing quantum phenomena are about the subjective states of the human observers. Following the lead of Einstein, Popper emphasizes that scientific theories should be interpreted as attempts to describe a mind-independent  reality.
A scientific theory must be falsifiable, and scientific knowledge is always tentative, or conjectural. These are the main ideas of Popper’s Logic of Scientific Discovery. Since 1960 his writings contain some essential developments of... more
A scientific theory must be falsifiable, and scientific knowledge is always tentative, or conjectural. These are the main ideas of Popper’s Logic of Scientific Discovery. Since 1960 his writings contain some essential developments of these views and make some steps towards epistemological optimism. Although we cannot justify any claim that a scientific theory is true, the aim of science is the search of truth and we have no reason to be sceptical about the notion of getting nearer to the truth. Our knowledge can grow, and science can progress. Nevertheless, Popper’s theory of approximation to the truth is problematic and is still the subject of studies and discussions.
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Leon Battista Alberti ha lasciato la sua impronta quasi in ogni campo del sapere; fu architetto e teorico delle arti, latinista e filosofo, cultore di musica e di matematica. Ma si deve ricordare anche il suo fondamentale contributo in... more
Leon Battista Alberti ha lasciato la sua impronta quasi in ogni campo del sapere; fu architetto e teorico delle arti, latinista e filosofo, cultore di musica e di matematica. Ma si deve ricordare anche il suo fondamentale contributo in un campo meno noto, quello della crittografia, cioè dell'arte di nascondere i messaggi. L'Alberti inventò un metodo per generare messaggi criptati, con l'aiuto di un disco cifrante, che ha segnato una svolta rispetto ai metodi di cifratura in uso ai suoi tempi e che è stato un punto di riferimento per la crittografia dei secoli a venire, fino quasi ai nostri giorni.
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La filosofia della scienza è una disciplina di confine fra materie scientifiche e materie umanistiche. Vogliamo presentarla ai lettori de La Reggia facendo riferimento all'opera di uno studioso mantovano, il professor Vittorio Somenzi,... more
La filosofia della scienza è una disciplina di confine fra materie scientifiche e materie umanistiche. Vogliamo presentarla ai lettori de La Reggia facendo riferimento all'opera di uno studioso mantovano, il professor Vittorio Somenzi, che fu titolare della prima cattedra universitaria di filosofia della scienza all'Università di Roma
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Lettera matematica Pristem,  2004
According to Popper, mathematical objets are human creations: once created, they have properties which we have great difficulty in discovering and which are possessed indipendently of our knowledge of them. In this way, Popper overcomes... more
According to Popper, mathematical objets are human creations: once created, they have properties which we have great difficulty in discovering and which are possessed indipendently of our knowledge of them. In this way, Popper overcomes the traditional dichotomy betweeen discovery and creation in mathematical experience. Mereover, Popper answers another question: how mathematics, which is our creation, so often turns out to be  useful in describing aspects of the physical world.
In this paper we analyse the philosophy of mathematics developed by Imre Lakatos. In his view mathematics is fallible and its products, including concepts and proofs, can never be considered final or perfect, but may require adjustments... more
In this paper we analyse the philosophy of mathematics developed by Imre Lakatos. In his view mathematics is fallible and its products, including concepts and proofs, can never be considered final or perfect, but may require adjustments when standards of rigour change, or new meanings emerge. The logic of mathematical discovery involves the method of conjectures, proofs and refutations. Moreover, final attempts of refutations may be  starting points of mathematical research programmes.  At the end of the paper we present Lakatos' view that the most interesting analysis of Greek geometry were pre-Euclidean and their role was to generate Euclid's axiomatic system.
In this paper the author describes Enriques' ideas on the concept of space and on the relations between geometry and physics. Enriques criticized the views of Kant and Poincaré, considered geometry as an empirical science and anticipated... more
In this paper the author describes Enriques' ideas on the concept of space and on the relations between geometry and physics. Enriques criticized the views of Kant and Poincaré, considered geometry as an empirical science and anticipated some aspects of recent epistemology
An interesting article by Gila Hanna summarizes the recent debate on the value of proof. The author of this paper remarks that an analogous discussion arose in Italy after the pubblication of Morris Kline's work: "Mathematics. The Loss... more
An interesting article by Gila Hanna summarizes the recent debate on the value of proof. The author of this paper remarks that an analogous discussion arose in Italy after the pubblication of Morris Kline's work: "Mathematics. The Loss of Certianty". In the second part of the paper are considered the views of Popper and Lakatos on the explanatory power of mathematical proofs and are presented some reflections about the teaching in the classroom.
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