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The Making of Mathematics: An Interview with Carlo Cellucci
Get PDFCarlo Cellucci is professor emeritus of the Sapienza University of Rome, and has written books on logic, mathematics, and philosophy. In the following interview conducted via back-and-forth email correspondence, he discusses his 2022 book, The Making of Mathematics: Heuristic Philosophy of Mathematics [3], which presents a new paradigm for thinking about, doing, and teaching mathematics
Is Truth a Chimera?
No full textIn his book Perché ancora la filosofia Carlo Cellucci argues that truth does not play any role in (modern) science: truth is only a chimera that prevents us «from adequately understanding the character of knowledge» and therefore «must be disposed of». I summarize Cellucci’s evidence for his contention that truth is a chimera. I then raise four objections to Cellucci’s views on truth. My conclusion is that, Cellucci’s arguments notwithstanding, a notion of truth is necessary for the human activity of problem solving and therefore for an adequate understanding of the phenomenon of knowledge
What Mathematical Logic Says about the Foundations of Mathematics
No full textMy purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us to explain mathematical activity; the point is to discuss what and in which sense logic can "explain". For example, let's consider the basic concept of an axiomatic system: an axiomatic system can be very useful to organize, to present, and to clarify mathematical knowledge. And, more importantly, logic is a science with its own results: so, axiomatic systems are interesting also because we know several revealing theorems about them. Similarly, I will discuss other topics such as mathematical definitions, and some relationships between mathematical logic and computer science. I will also consider these subjects from an educational point of view: can logical concepts be useful in teaching and learning elementary mathematics
Modalità indiciate.
No full textSi presenta un nuovo linguaggio per la logica modale quantificata in cui gli operatori modali sono indiciati da termini: "è necessario per t1, ... , tn''. In questo linguaggio vengono definiti alcuni sistemi modali predicativi e si dimostra che sono completi rispetto alla semantica delle transizioni. Formule come la formula della Barcan o la formula di Ghilardi oppure la necessità dell'identià possono essere espresse in modo naturale e si dimostra che corrispondono a particolari proprietà della relazione di transizione
Strutture algebriche nella computazione quantistica
No full textShi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Abaronov quantum computational structure. Finally, we investigate the possibility of an algebraic abstraction from Hilbert-space structures, by proposing the notion of Toffoli-Hadamard algebra. From an intuitive point of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures
Introduction. From a heuristic point of view
No full textThe paper offers an outline of the heuristic point of view, in particular, the one put forward by Carlo Cellucci
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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