It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance (...) with those of artistic beauty. For example, courses in art appreciation are fairly common; it is however unthinkable to find any mathematical beauty appreciation courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term beauty as it is currently used by mathematicians. (shrink)

Offers a glimpse into the world of science and technology between 1950 and 1990 as seen through the eyes of a mathematician, and debunks various myths of scientific philosophy. Portrays some of the great scientific personalities of the period, including Stanislav Ulam, who patented the hydrogen bomb, and Jack Schwartz, one of the founders of computer science. Also discusses phenomenology of mathematics, and philosophy and computer science. Includes book reviews. For students and academics. Annotation copyright by Book News, Inc., Portland, (...) OR. (shrink)

We shall argue that the attempt carried out by certain philosophers in this century to parrot the language, the method, and the results of mathematics has harmed philosophy. Such an attempt results from a misunderstanding of both mathematics and philosophy, and has harmed both subjects.

Husserl’s Third Logical Investigation, ostensibly dealing with the phenomenology of whole and parts, is actually meant to introduce the notion of Fundierung. This term is frequently used in the phenomenological literature, although little has been written about Fundierung itself since Husserl introduced it. Husserl himself, although he used it extensively, never again felt the need to reopen the discussion.

A plurality of axiomatic systems can be interpreted as referring to one and the same mathematical object. In this paper we examine the relationship between axiomatic systems and their models, the relationships among the various axiomatic systems that refer to the same model, and the role of an intelligent user of an axiomatic system. We ask whether these relationships and this role can themselves be formalized.

ARE MATHEMATICAL IDEAS INVENTED OR DISCOVERED? This question has been repeatedly posed by philosophers through the ages, and will probably be with us forever. We shall not be concerned with the answer. What matters is that by asking the question, we acknowledge the fact that mathematics has been leading a double life.

a Mathematicians, like Proust and everyone else, are at their best when writing about their first lovea (TM) a ] They are among the very best we have; and their best is very good indeed. a ] One approaches this book with high hopes. Happily, one is not disappointed. a ]In paperback it might well have become a best seller. a ]read it. From The Mathematical Intelligencer Mathematics is shaped by the consistent concerns and styles of powerful minds a three (...) of which are represented here. Kaca (TM)s work is marked by deep commitment and breadth of inquiry. Rota is the easiest of these authors to reada ]a delight: witty and urbane, with a clear and interesting agenda and an astonishing intellectual range. To read him is to be a part of a pleasant and rewarding conversation. Jacob T. Schwartz attacks problems ina ]computer science, mathematical economics, computer and instructional a ] No matter how slippery the problem, Schwartz manages to capture a substantial chunk of it in his mathematical net. a Mathematics Magazine This is a volume of essays and reviews that delightfully explore mathematics in all its moods a from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others. (shrink)

Cet article vise à montrer l’extrême proximité entre ces deux mathématiciens-philosophes que furent Gian-Carlo Rota et Gilles Châtelet disparus la même année. Au moins quatre points communs les relient : une philosophie romantique radicale ; une rigueur intellectuelle exemplaire ; une vision affine de la recherche mathématique ; une révolte intérieure exécrant tout sensus communis.This text shows the great proximity between two mathematicianphilosophers, Gilles Châtelet and Gian-Carlo Rota who both died in the same year (...) 1999. There are at least four common points amongst themselves: a radical romantic philosophy; an exemplary intellectual rigor; a great affinity in their vision of mathematical research; an inmost rebellion against all common sense. Quest’articolo tende a mostrare l’estrema prossimità tra due matematici-filosofi che furono Gian-Carlo Rota e Gilles Châtelet che ci hanno lasciato lo stesso anno. Ci sono almeno quattro punti comuni che le legano: una radicale filosofia romantica; un rigore intellettuale esemplare; una visione affine della ricerca matematica; una rivolta intima che esecra ogni senso comune.This article is in French. (shrink)

RésuméGian-Carlo Rota est l’un des rares grands mathématiciens de la deuxième moitié du XX e siècle dont l’intérêt pour la logique formelle soit aussi ouvertement déclaré et ne se soit jamais démenti, depuis sa formation d’étudiant à Princeton jusqu’à ses derniers écrits. Plus exceptionnel encore, il fait partie des rares lecteurs assidus de Husserl à s’être aperçu que la phé-noménologie poursuivait un projet de réforme de la logique formelle. L’article propose d’attester l’existence d’un tel projet chez Husserl ; (...) d’en examiner la réappropriation et les prolongements chez Rota.Gian-Carlo Rota is among the few great mathematicians of the second-half of the XXth century whose interest in formal logic is openly declared and has never flagged, since his training as a student in Princeton up to his last writings. Even more exceptional, he belongs to the rare diligent readers of Husserl, who noticed that phenomenology was pursuing a project of reform of formal logic. This paper propose to testify to the existence of such a project in Husserl; to examine how it is taken over and continued by Rota. Gian-Carlo Rota è uno dei pochi grandi matematici della seconda metà del ventesimo secolo, il cui interesse per la logica formale è, dalla sua formazione come studente a Princeton al suo ultimi scritti, apertamente dichiarato e mai negato. Cosa ancora più eccezionale, Rota è uno dei rari lettori assidui di Husserl ad aver percepito che la fenomenologia stava perseguendo un progetto di riforma della logica formale. L’articolo propone di attestare l’esistenza di un tale progetto in Husserl e di esaminare la sua riappropriazione e le sue estensioni proposte da Gian-Carlo Rota.This article is in French. (shrink)

Roshdi Rashed’s work illustrates perfectly what can be a conscious and cautious practice of reflection, with the purpose of setting history of science on renewed and deeper grounds.). This entails the methodical operations that he enumerates, such as enlargement towards undermined or ignored traditions, careful and reasoned decompartmentalization of disciplines, correlative changes of periodization. and appendices in The Notion of Western Science: “Science as a Western Phenomenon” and “Periodization in Classical Mathematics”.) Among mathematicians, Gian-Carlo RotaRota, Gian-Carlo (...) is certainly both exceptional and, for this reason, exemplary. By choosing this perspective as a tribute, I hope that Roshdi Rashed will consider my comments not too unworthy. For any philosopher of science not insensitive to history of science, and for any historian not completely allergic to philosophical reflection, studying Rota’s contribution in the fields of logic and phenomenology reveals itself instructive and fruitful. Contrary to dominant trends amongst his colleagues, in his own way, RotaRota, Gian-Carlo showed a strong and continuous interest in logic, history of science and philosophy. (shrink)

Volume XVIII Special Issue: Gian-Carlo Rota and The End of Objectivity, 2019 Aim and Scope: The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer. Contributors: Gabriele Baratelli, Stefania Centrone, Giovanna C. Cifoletti, Jean-Marie Coquard, Steven Crowell, Deborah De Rosa, Daniele De Santis, Nicolas de Warren, Agnese Di (...) Riccio, Aurélien Djian, Yuval Dolev, Mirja Hartimo, Burt C. Hopkins, Talia Leven, Ah Hyun Moon, Luis Niel, Fabrizio Palombi, Mario Ariel González Porta, Gian-Carlo Rota, Michael Roubach, Franco Trabattoni and Michele Vagnetti. Submissions: Manuscripts, prepared for blind review, should be submitted to the Editors electronically via e-mail attachments. (shrink)

Cet article vise à montrer l’extrême proximité entre ces deux mathématiciens-philosophes que furent Gian-Carlo Rota et Gilles Châtelet disparus la même année. Au moins quatre points communs les relient : une philosophie romantique radicale ; une rigueur intellectuelle exemplaire ; une vision affine de la recherche mathématique ; une révolte intérieure exécrant tout sensus communis.This text shows the great proximity between two mathematicianphilosophers, Gilles Châtelet and Gian-Carlo Rota who both died in the same year (...) 1999. There are at least four common points amongst themselves: a radical romantic philosophy; an exemplary intellectual rigor; a great affinity in their vision of mathematical research; an inmost rebellion against all common sense. Quest’articolo tende a mostrare l’estrema prossimità tra due matematici-filosofi che furono Gian-Carlo Rota e Gilles Châtelet che ci hanno lasciato lo stesso anno. Ci sono almeno quattro punti comuni che le legano: una radicale filosofia romantica; un rigore intellettuale esemplare; una visione affine della ricerca matematica; una rivolta intima che esecra ogni senso comune.This article is in French. (shrink)

Shaftesbury señala la belleza de la teoría matemática y le asigna relevancia en el despliegue y en la estructura misma del pensamiento. Esta nota considera a la vez dicha reflexión y los asertos del matemático Gian-Carlo Rota acerca de tópicos análogos e intenta dilucidar, dentro de lo posible, ambas intuiciones.

Mathematical Essays in Honor of Gian-Carlo Rota, Boston, Basel, Berlin, ... Crapo, H. (1993), On the Anick-Rota Representation of the Bracket Ring of the ...

In this paper, following an elementary line of thought which somewhat differs from the usual one, we prove once more that any deterministic theory predictively equivalent to quantum mechanics unavoidably exhibits a contextual character. The purpose of adopting this perspective is that of paving the way for a critical analysis of the use of counterfactual arguments when dealing with nonlocal physical processes.

Tomo I. Religione ed eterodossia, Normatiavità e non conformismo: Dallo gnosticismo al Romanticismo nelle prime tre edizioni -- Tomo II. Appendice alla IV edizione -- Appendice alla V edizone -- Dopo e a lato, Rassegna bibliografica ragionata sulle origini dell'Islam e la loro importanza nel determinarne i succesivi sviluppi -- Marginalia.

Describing and defining what 'Japan style' is, this book explores specific achievements in Japanese art and architecture, offering an analysis of the Japanese culture, its vision of the world and of humankind.

Dopo un esame del contesto politico nel quale si colloca l'opera di Pietro, cioè le vicende che seguirono al conflitto tra Bonifacio VIII e Filippo il Bello, l'A. esamina il trattato De potestate papae valutando i temi principali che vi sono affrontati: i beni della Chiesa, il potere papale, il rapporto fra potere spirituale e temporale ed il rapporto del papato con il regno di Francia e l'Impero. Le fonti che maggiormente orientano il trattato sono le Bolle di Bonifacio VIII (...) Unam Sanctam e Ausculta, fili e il De ecclesiastica potestate di Egidio Romano. La posizione di Pietro non è completamente conforme all'ideale teocratico: essa si avvicina piuttosto, sottolinea l'A., al pensiero di Giovanni da Parigi nel tentativo di mitigare le istanze teocratiche e riconoscere una certa autonomia al potere temporale. (shrink)

Recently a quite stimulating paper (Heaney et al. arXiv:0911.0770v2 [quant-ph], 2010) dealing with the possibility of exploiting the nonlocal aspects of a superposition of states of a single photon appeared. We regard as greatly relevant the results which have been obtained. However we think that the presentation of the matter and the way to derive the conclusion are not fully satisfactory and do not put the necessary emphasis on some subtle basic aspects like locality and realism. In view of its (...) interest we consider it useful to reconsider the line of reasoning of Heaney et al. (in arXiv:0911.0770v2 [quant-ph], 2010) and to derive once more its results by following a procedure which seems to us more lucid and which makes fully clear the role of the various conceptual aspects of the treatment. We hope that our analysis will contribute to clarify and to deepen the interesting results of Heaney et al. (in arXiv:0911.0770v2 [quant-ph], 2010). (shrink)