Object, Structure, and Form

The main task of this paper is to develop the non-Platonist view of mathematics as a science of structures I have called, borrowing the label from Putnam, `realism with the human face'. According to this view, if by `object' we mean what exists independently of whether we are thinking about it or not, mathematics is a science of patterns (structures), where patterns are neither objects nor properties of objects, but aspects (or aspects of aspects, etc.) of concrete objects which dawn on us when we represent objects (or aspects of... within a given system (of representation). Mathematical patterns, therefore, are real, because they ultimately depend on concrete objects, but are neither objects nor properties of objects, because they are dependent, both metaphysically and epistemically, on systems of representation. Although the article has been written as a presentation of my view of mathematics, and of some of its advantages, the reader should keep in mind that this is essentially a `reply paper', as is shown by the fact that much of it is dedicated to the discussion of some issues which have become the focus of critical attention. Such issues are well expressed by the following questions: am I right in asserting that mathematical patterns are neither objects nor properties of objects? What is the difference, if any, between mathematical patterns and other mind-dependent entities such as the Cleveland Symphony Orchestra? Can mathematical patterns be always assimilated to relations? Can what I call `form of representation' be assimilated to structure? Can the standpoint I take on mathematics, which regards it as a science of patterns, be correctly described as Aristotelian

Mathematical Patterns and Cognitive Architectures

Mathematical patterns are an important subclass of the class of patterns. The main task of this paper is examining a particular proposal concerning the nature of mathematical patterns and some elements of the cognitive architecture an agent should have to recognize them

Creativity in Conceptual Spaces

The main aim of this paper is contributing to what in the last few years has been known as computational creativity. This will be done by showing the relevance of a particular mathematical representation of G"ardenfors's conceptual spaces to the problem of modelling a phenomenon which plays a central role in producing novel and fruitful representations of perceptual patterns: analogy

Book Review: Ferreiros,J. and Gray J. (eds.): 2006, The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press, Oxford.

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Bertrand Russell

Bertrand Russell has been one of the most influential philosophers of the 20th Century. The importance of his work can not be confined to a particular thematic area such as mathematical logic or philosophy of language. Extraordinary vital, extremely curious and with a very acute intellect, he has produced an immense body of work.Bertrand Russell è stato uno dei filosofi più influenti del '900. L'importanza del suo lavoro non può essere confinata ad un particolare ambito tematico quale la logica matematica o la filosofia del linguaggio. Dotato di una vitalità straordinaria, di una grande curiosità e di un intelletto acutissimo, la sua produzione scientifica è sterminata

The Matrix e il fumetto. Questioni filosofiche

Il presente articolo prende in esame il caso dell’interazione del fumetto Razzi Amari di S. Disegni e M. Caviglia con il notissimo film The Matrix di Larry e Andy Wachowski. Lo scopo principale della nostra indagine è mettere in evidenza e discutere l’influenza che i mezzi espressivi utilizzati nel fumetto e nel film esercitano sul modo in cui il lettore/spettatore medio si rapporta alle questioni filosofiche che emergono dalle vicende narrate. L’importanza del tema affrontato da questo articolo sta, tra le altre cose, nel rivelare che sia i film che i fumetti, oltre ad intrattenere piacevolmente lettori e spettatori appartenenti a classi sociali e generazioni diverse l’una dall’altra, possono influenzare le capacità critico/cognitive del lettore/spettatore medio, contribuendo così alla formazione di una consapevolezza di massa relativa a temi e problematiche anche molto specialistiche. In particolare, vedremo che: (1) nel film, a differenza del fumetto, l’impatto del dialogo viene rafforzato e amplificato dalla dimensione “teatrale” della rappresentazione tipica di questa forma di espressione artistica; e che (2) il contributo critico/cognitivo dato al lettore/spettatore medio dal fumetto e dal film passa, essenzialmente, attraverso la creazione e/o l’estensione dei cosiddetti «spazi di rappresentazione»

A Realist Philosophy of Mathematics

The realism/anti-realism debate is one of the traditional central themes in the philosophy of mathematics. The controversies about the existence of the irrational numbers, the complex numbers, the infinitesimals, etc. will be familiar to all who are acquainted with the history of mathematics. This book aims mainly at presenting and defending a non-Platonist form of mathematical structural realism which, in the respect of the history of mathematics, harmonizes with a plausible epistemology that naturally arises from it