•  45
    ‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a val…Read more
  •  11
    Ways of Abstraction
    Culture and Dialogue 4 (1): 83-112. 2016.
    The invention of “artificial perspective” revealed the ideal character of Euclidean geometry already in the Renaissance Europe of the fifteenth century. To the extent to which it made painting a “science” relying on mathematical rules, it made mathematics an “art” independent of the “geometry of nature.” It was the artistic vision emerging from perspective drawing that paved the way for scientific abstraction. However, it was only in the nineteenth century that the discovery of non-Euclidean geo…Read more
  •  20
    Any thorough discussion of computing machines requires the examination of rigorous concepts of computation and is facilitated by the distinction between mathematical, symbolic and physical computations. The delicate connection between the three kinds of computations and the underlying questions, "What are machines?" and "When are they computing?", motivate an extensive theoretical and historical discussion. The relevant outcome of this..
  •  80
    Machines, Logic and Quantum Physics (review)
    with David Deutsch and Artur Ekert
    Bulletin of Symbolic Logic 6 (3): 265-283. 2000.
    §1. Mathematics and the physical world. Genuine scientific knowledge cannot be certain, nor can it be justified a priori. Instead, it must be conjectured, and then tested by experiment, and this requires it to be expressed in a language appropriate for making precise, empirically testable predictions. That language is mathematics.This in turn constitutes a statement about what the physical world must be like if science, thus conceived, is to be possible. As Galileo put it, “the universe is writt…Read more
  • L’inimitabile Intelligenza Del Vuoto
    Discipline Filosofiche 21 (1). 2011.
  •  118
    Machines, logic and quantum physics
    with David Deutsch and Artur Ekert
    Bulletin of Symbolic Logic 6 (3): 265-283. 2000.
    §1. Mathematics and the physical world. Genuine scientific knowledge cannot be certain, nor can it be justified a priori. Instead, it must be conjectured, and then tested by experiment, and this requires it to be expressed in a language appropriate for making precise, empirically testable predictions. That language is mathematics.This in turn constitutes a statement about what the physical world must be like if science, thus conceived, is to be possible. As Galileo put it, “the universe is writt…Read more
  •  33
    Hilbert's Axiomatics as ‘Symbolic Form’?
    Perspectives on Science 22 (1): 1-34. 2014.
    Both Hilbert's axiomatics and Cassirer's philosophy of symbolic forms have their roots in Leibniz's idea of a 'universal characteristic,' and grow on Hertz's 'principles of mechanics,' and Dedekind's 'foundations of arithmetic'. As Cassirer recalls in the introduction to his Philosophy of Symbolic Forms, it was the discovery of the analysis of infinity that led Leibniz to focus on "the universal problem inherent in the function of symbolism, and to raise his 'universal characteristic' to a truly…Read more
  •  15
    The essays collected in this volume address such questions from different points of view and will interest students and scholars in several branches of scientific knowledge.
  • Gli strumenti nella storia e nella filosofia della scienza
    Rivista di Filosofia 78 (2): 317. 1987.