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Profile: Giuseppe Longo (École Normale Supérieure)
  1. Giuseppe O. Longo (forthcoming). L'ambiguità tra scienza e filosofia. Nuova Civiltà Delle Macchine.
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  2. Gianfranco Longo (2014). L’indeterminabile presente. Studio Dei concetti di natura E di perpetuo nella creazione. Synesis 6 (1):26-109.
    È nel χρόνος, o epoche storiche, che il tempo si differenzia dalla contingenza che permette di individuare l’atto immediato e presente in una determinata circostanza, e d’altronde entrambi, cioè χρόνος e καιρός, sono descrivibili quali molteplici e plurali all’interno della possibilità eterna della tradizione e della trasformazione, nonché rinascita, di un concetto in semantiche sempre ulteriormente differenziabili. Il processo seguito per il raggiungimento e la specificazione del concetto tempo, quale caratterizzante il concetto stesso di universale, è stato quello dell’induzione, che (...)
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  3. Gianfranco Longo (2013). Dal fiat al consumatum est: L'eucaristico essere Della creazione, rinnovata tra calvario E resurrezione di gesù. Synesis 5 (1).
    Nella sofferenza del Calvario, Gesù dona di nuovo la Creazione di Dio Padre all’uomo proprio salvando quest’ultimo. La Resurrezione di Gesù è il sigillo definitivo che ricompone un vincolo di amore incrinato dal peccato originale permettendo al mondo e all’uomo la rinascita nella gioia di Cristo risorto.
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  4. Jean Lassègue & Giuseppe Longo (2012). What is Turing's Comparison Between Mechanism and Writing Worth? In S. Barry Cooper (ed.), How the World Computes. 450--461.
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  5. Gianfranco Longo (2012). Sul concetto teologico di tempo nella dimensione di mondo1. Synesis 4 (1).
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  6. G. Longo (2011). Reflections on Concrete Incompleteness. Philosophia Mathematica 19 (3):255-280.
    How do we prove true but unprovable propositions? Gödel produced a statement whose undecidability derives from its ad hoc construction. Concrete or mathematical incompleteness results are interesting unprovable statements of formal arithmetic. We point out where exactly the unprovability lies in the ordinary ‘mathematical’ proofs of two interesting formally unprovable propositions, the Kruskal-Friedman theorem on trees and Girard's normalization theorem in type theory. Their validity is based on robust cognitive performances, which ground mathematics in our relation to space and time, (...)
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  7. Giuseppe Longo (2011). Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time. [REVIEW] Foundations of Science 16 (4):331-333.
    This short note develops some ideas along the lines of the stimulating paper by Heylighen (Found Sci 15 4(3):345–356, 2010a ). It summarizes a theme in several writings with Francis Bailly, downloadable from this author’s web page. The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen’s paper. Heylighen adds a logical notion, consistency, in order to understand a possible origin of the selective process that may have originated this organization of natural (...)
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  8. Giuseppe Longo & Thierry Paul (2011). The Mathematics of Computing Between Logic and Physics. In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific.
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  9. Giuseppe Longo & Arnaud Viarouge (2010). Mathematical Intuition and the Cognitive Roots of Mathematical Concepts. Topoi 29 (1):15-27.
    The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational analysis (...)
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  10. Michel Bitbol, Carmelo Call, Massimiliano Cappuccio, Mauro Ceruti, Luisa Damiano, Giovanna Colombetti, Evan Thompson, Carlo Conni, Giuseppe Longo & Mauro Maldonato (2008). La neurofenomenologia esperienza, percezione, cognizione. Rivista di Estetica 48 (37):9-168.
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  11. Giuseppe Longo (2008). Fondamenti cognitivi Della matematica E analisi matematiche Del vivente. Rivista di Estetica 48 (37):113-124.
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  12. Giuseppe Longo (2007). Mathematical Concepts and Physical Objects. In Luciano Boi, Pierre Kerszberg & Frédéric Patras (eds.), Rediscovering Phenomenology: Phenomenological Essays on Mathematical Beings, Physical Reality, Perception and Consciousness (Phaenomenologica) (English and French Edition). Springer. 195-228.
     
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  13. Giuseppe Longo & Pierre-Emmanuel Tendero (2007). The Differential Method and the Causal Incompleteness of Programming Theory in Molecular Biology. Foundations of Science 12 (4):337-366.
    The “DNA is a program” metaphor is still widely used in Molecular Biology and its popularization. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our arguments (...)
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  14. Giuseppe Longo (2006). Between Scylla and Charybdis. Metascience 15 (3):617-621.
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  15. G. Longo & P. Scott (2003). New Programs and Open Problems in the Foundation of Mathematics. Bulletin of Symbolic Logic 9 (2):129-130.
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  16. Giuseppe Longo (2003). Proofs and Programs. Synthese 134 (1-2):85 - 117.
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  17. G. Longo (2000). Prototype Proofs in Type Theory. Mathematical Logic Quarterly 46 (2):257-266.
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  18. Giuseppe Longo (2000). Mathematics and the Biological Phenomena. Aquinas 43 (2):331-354.
    The first part of this paper highlights some key aspects of the differences in the use of mathematical tools in physics and in biology. Scientific knowledge is viewed as a network of interactions, some than as a hierarchically organized structure where mathematics would display the essence of phenomena. The concept of "unity" in the biological phenomenon is then discussed. In the second part, a foundational issue in mathematics is revisited, following recent perspective in the physiology of action. The relevance of (...)
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  19. Giuseppe O. Longo (2000). Intelligenza della mente intelligenza del corpo. Studium 96 (3/4):509-531.
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  20. Giuseppe Longo (1999). Mathematical Intelligence, Infinity and Machines: Beyond Godelitis. Journal of Consciousness Studies 6 (11-12):11-12.
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  21. Giuseppe Longo (1999). The Mathematical Continuum, From Intuition to Logic. In Jean Petitot, Franscisco J. Varela, Barnard Pacoud & Jean-Michel Roy (eds.), Naturalizing Phenomenology. Stanford University Press.
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  22. Gianfresco Longo (1996). Il concetto di mutamento costituzionale in Hans Kelsen e Carl Schmitt. Rivista Internazionale di Filosofia Del Diritto 73:256-262.
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  23. Giuseppe Longo (1994). Review: Boris Trakhtenbrot, Comparing the Church and Turing Approaches: Two Prophetical Messages. [REVIEW] Journal of Symbolic Logic 59 (4):1434-1436.
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  24. G. Longo (1993). Review of Feferman's Paper\ Weyl Vindicated, Das Continuum 70 Years Later. [REVIEW] Journal of Symbolic Logic 58 (3).
     
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  25. Giuseppe Longo (1993). Feferman Solomon. Weyl vindicated:“Das Kontinuum” 70 years later. Atti del congresso, Temi e prospettive della logica e della filosofia della scienza contemporanee, Organizzato dalla Società Italiana di Logica e Filosofia delle Scienze (SILFS), Cesena, 7–10 gennaio 1987, Volume I, Logica, edited by Cellucci Carlo and Sambin Giovanni, CLUEB, Bologna 1988, pp. 59–93. [REVIEW] Journal of Symbolic Logic 58 (3):1085-1086.
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  26. Giuseppe Longo (1993). Review: Solomon Feferman, Atti del Congresso, Temi e Prospettive della Logica e della Filosofia della Scienza Contemporanee, Organizzato dall Societa Italiana di Logica e Filosofia delle Scienze (SILFS), Cesena, 7-10 gennaio 1987. [REVIEW] Journal of Symbolic Logic 58 (3):1085-1086.
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  27. Giuseppe Longo (1991). Information and the Mind-Body Problem. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. 297--306.
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  28. Giuseppe Longo & Andrea Sgarro (1991). A Pragmatic Way Out of the Maze of Uncertainty Measures. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. 370--376.
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  29. Giuseppe Longo (1988). On Church's Formal Theory of Functions and Functionals. Annals of Pure and Applied Logic 40 (2):93-133.
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  30. Giuseppe Longo (1988). On Church's Formal Theory of Functions and Functionals: The Λ-Calculus: Connections to Higher Type Recursion Theory, Proof Theory, Category Theory. Annals of Pure and Applied Logic 40 (2):93-133.
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  31. Giuseppe Longo (1987). Review: C. P. J. Koymans, Models of the Lambda Calculus. [REVIEW] Journal of Symbolic Logic 52 (1):284-285.
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  32. M. Hyland Gurevich, G. Kreisel, G. Longo, D. S. Scott & D. van Dalen (1986). The Philosophy Department of the Rijksuniversiteit Utrecht Organizes the Conference “Church's Theses After Fifty Years”. Among the Invited Speakers Are E. Borger, RO Gandy, J.-Y. Girard, Y. [REVIEW] Annals of Pure and Applied Logic 30:330.
     
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  33. E. Casari, E. J. Fenstad, G. Lolli, G. Longo, A. Marcja & D. Van Dalen (1984). Meeting of the Association for Symbolic Logic: Florence, Italy 1982. Journal of Symbolic Logic 49 (2):683 - 710.
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  34. E. Casari, E. J. Fenstad, G. Lolli, G. Longo, A. Marcja & D. van Dalen (1984). Meeting of the Association for Symbolic Logic: Florence, Italy 1982. Journal of Symbolic Logic 49 (2):683-710.
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  35. G. Longo & E. Moggi (1984). The Hereditary Partial Effective Functionals and Recursion Theory in Higher Types. Journal of Symbolic Logic 49 (4):1319-1332.
    A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals, defined by a direct elementary technique, turn out to be the computable elements of the hereditary continuous partial objects; moreover, there is a commutative system of enumerations of any given type by any type below (relative numberings). By this and by results in [1] and [2], the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) (...)
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  36. Giuseppe Longo (1983). Set-Theoretical Models of Λ-Calculus: Theories, Expansions, Isomorphisms. Annals of Pure and Applied Logic 24 (2):153-188.
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  37. R. Hindley & G. Longo (1980). Lambda‐Calculus Models and Extensionality. Mathematical Logic Quarterly 26 (19‐21):289-310.
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  38. P. L. Ferrari & G. Longo (1978). Axiomatic Theory of Enumeration: A Note on the Axiom of Extensionality. Studia Logica 37 (3):261-268.
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  39. Giuseppa Longo (1976). On the Problem of Deciding Equality in Partial Combinatory Algebras and in a Formal System. Studia Logica 35 (4):363 - 375.