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Giuseppe Longo [45]G. Longo [11]Gianfranco Longo [4]Glanfranco Longo [1]
Giuseppe O. Longo [1]G. Abate Longo [1]Giulia Longo [1]Giuseppa Longo [1]

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Profile: Giuseppe Longo (École Normale Supérieure)
  1. Sul concetto teologico di tempo nella dimensione di mondo1.Gianfranco Longo - 2012 - Synesis 4 (1):24-37.
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  2.  32
    The Deluge of Spurious Correlations in Big Data.Cristian S. Calude & Giuseppe Longo - forthcoming - Foundations of Science:1-18.
    Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with (...)
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  3.  9
    The Web and its Sorceries.Giuseppe Longo - 2017 - AI and Society 32 (1):135-136.
  4.  5
    Epistemology of the Inert and Epistemology of the Living.Roberta Lanfredini & Giuseppe Longo - 2016 - Humana.Mente (31):37-55.
    The intellectual act of imposing borders to contain and delimit objects has been a constituent factor in physics since its origins, and is also fundamental for philosophical reflection. However, the characteristics of the conceptual universe thus constructed (tendency towards the ideal limit, invariance in variation, a conception of matter as residue, etc.) seem inadequate in biology. The essential characteristic of the living thing is, in fact, that of having a history: that is, of being the concrete trace of a memory. (...)
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  5.  7
    Set-Theoretical Models of Λ-Calculus: Theories, Expansions, Isomorphisms.Giuseppe Longo - 1983 - Annals of Pure and Applied Logic 24 (2):153-188.
  6. Mathematical Intuition and the Cognitive Roots of Mathematical Concepts.Giuseppe Longo & Arnaud Viarouge - 2010 - 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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  7.  16
    Lambda-Calculus Models and Extensionality.R. Hindley & G. Longo - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (19-21):289-310.
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  8.  33
    The Differential Method and the Causal Incompleteness of Programming Theory in Molecular Biology.Giuseppe Longo & Pierre-Emmanuel Tendero - 2007 - 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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  9.  8
    Lambda‐Calculus Models and Extensionality.R. Hindley & G. Longo - 1980 - Mathematical Logic Quarterly 26 (19‐21):289-310.
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  10.  24
    The Mathematics of Computing Between Logic and Physics.Giuseppe Longo & Thierry Paul - 2011 - In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific.
  11.  59
    Reflections on Concrete Incompleteness.G. Longo - 2011 - 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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  12. The Mathematical Continuum, From Intuition to Logic.Giuseppe Longo - 1999 - In Jean Petitot, Franscisco J. Varela, Barnard Pacoud & Jean-Michel Roy (eds.), Naturalizing Phenomenology. Stanford University Press.
     
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  13.  16
    On Church's Formal Theory of Functions and Functionals: The Λ-Calculus: Connections to Higher Type Recursion Theory, Proof Theory, Category Theory.Giuseppe Longo - 1988 - Annals of Pure and Applied Logic 40 (2):93-133.
  14.  11
    The Hereditary Partial Effective Functionals and Recursion Theory in Higher Types.G. Longo & E. Moggi - 1984 - 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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  15.  6
    Prototype Proofs in Type Theory.G. Longo - 2000 - Mathematical Logic Quarterly 46 (2):257-266.
    The proofs of universally quantified statements, in mathematics, are given as “schemata” or as “prototypes” which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of λ-calculus and act as “proof-schemata”, as for universally quantified types. We examine here the critical case of Impredicative Type Theory, i. e. Girard's (...)
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  16.  13
    What is Turing's Comparison Between Mechanism and Writing Worth?Jean Lassègue & Giuseppe Longo - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 450--461.
  17.  8
    Axiomatic Theory of Enumeration: A Note on the Axiom of Extensionality.P. L. Ferrari & G. Longo - 1978 - Studia Logica 37 (3):261-268.
  18.  30
    Proofs and Programs.Giuseppe Longo - 2003 - Synthese 134 (1-2):85 - 117.
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  19.  3
    From Fiat to Consumatum Est: The Eucharistic Being of Creation, Renovated Between Calvary and Resurrection of Jesus.Glanfranco Longo - 2013 - Synesis 5 (1):16-31.
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  20.  3
    The Present Inderteminable: Study of the Concepts of Nature and Perpetual in Creation.Gianfranco Longo - 2014 - Synesis 6 (1):26-109.
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  21.  9
    Information and the Mind-Body Problem.Giuseppe Longo - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 297--306.
  22.  9
    Dal fiat al consumatum est: L'eucaristico essere Della creazione, rinnovata tra calvario E resurrezione di gesù.Gianfranco Longo - 2013 - 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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  23. Review: C. P. J. Koymans, Models of the Lambda Calculus. [REVIEW]Giuseppe Longo - 1987 - Journal of Symbolic Logic 52 (1):284-285.
     
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  24.  12
    Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time. [REVIEW]Giuseppe Longo - 2011 - 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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  25.  3
    Meeting of the Association for Symbolic Logic: Florence, Italy 1982.E. Casari, E. J. Fenstad, G. Lolli, G. Longo, A. Marcja & Dalen D. Van - 1984 - Journal of Symbolic Logic 49 (2):683 - 710.
  26.  3
    L’indeterminabile presente. Studio Dei concetti di natura E di perpetuo nella creazione.Gianfranco Longo - 2014 - 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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  27.  5
    On Church's Formal Theory of Functions and Functionals.Giuseppe Longo - 1988 - Annals of Pure and Applied Logic 40 (2):93-133.
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  28.  5
    Mathematical Intelligence, Infinity and Machines: Beyond Godelitis.Giuseppe Longo - 1999 - Journal of Consciousness Studies 6 (11-12):11-12.
    We informally discuss some recent results on the incompleteness of formal systems. These theorems, which are of great importance to contemporary mathematical epistemology, are proved using a variety of conceptual tools provably stronger than those of finitary axiomatisations. Those tools require no mathematical ontology, but rather constitute particularly concrete human constructions and acts of comprehending infinity and space rooted in different forms of knowledge. We shall also discuss, albeit very briefly, the mathematical intelligence both of God and of computers. We (...)
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  29.  4
    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]Giuseppe Longo - 1993 - Journal of Symbolic Logic 58 (3):1085-1086.
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  30.  3
    Between Scylla and Charybdis.Giuseppe Longo - 2006 - Metascience 15 (3):617-621.
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  31.  10
    New Programs and Open Problems in the Foundation of Mathematics.G. Longo & P. Scott - 2003 - Bulletin of Symbolic Logic 9 (2):129-130.
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  32.  2
    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]Giuseppe Longo - 1993 - Journal of Symbolic Logic 58 (3):1085-1086.
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  33.  6
    On the Problem of Deciding Equality in Partial Combinatory Algebras and in a Formal System.Giuseppa Longo - 1976 - Studia Logica 35 (4):363 - 375.
  34.  1
    Mathematics and the Biological Phenomena.Giuseppe Longo - 2000 - 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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  35. La neurofenomenologia esperienza, percezione, cognizione.Michel Bitbol, Carmelo Call, Massimiliano Cappuccio, Mauro Ceruti, Luisa Damiano, Giovanna Colombetti, Evan Thompson, Carlo Conni, Giuseppe Longo & Mauro Maldonato - 2008 - Rivista di Estetica 48 (37):9-168.
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  36. 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]M. Hyland Gurevich, G. Kreisel, G. Longo, D. S. Scott & D. van Dalen - 1986 - Annals of Pure and Applied Logic 30:330.
     
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  37. Logic Colloquium '82 Proceedings of the Colloquium Held in Florence, 23-28 August, 1982.G. Lolli, Giuseppe Longo & A. Marcja - 1984
     
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  38. Antinomie e polarità, determinazione e aleatorietà nel processo vivente della materia.Giuseppe Longo - 2009 - Discipline Filosofiche 19 (1).
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  39. Andata e ritorno dalla finanza alle matematiche passando per la biologia.Giuseppe Longo - 2011 - Nuova Civiltà Delle Macchine 29 (4).
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  40. A Pragmatic Way Out of the Maze of Uncertainty Measures.Giuseppe Longo & Andrea Sgarro - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 370--376.
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  41. Che cosa narrano le scienze?Giuseppe Longo - 2000 - Nuova Civiltà Delle Macchine 18 (1):67-76.
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  42. Di fronte alla tecnologia.Giuseppe Longo - 2000 - Nuova Civiltà Delle Macchine 18 (4):90-101.
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  43. Dal Golem a Godel e ritorno.Giuseppe Longo - 1994 - Nuova Civiltà Delle Macchine 12 (4):28-38.
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  44. Fondamenti cognitivi Della matematica E analisi matematiche Del vivente.Giuseppe Longo - 2008 - Rivista di Estetica 48 (37):113-124.
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  45. Francesco Lerda e l'intelligenza artificiale.Giuseppe Longo - 1994 - Nuova Civiltà Delle Macchine 12 (4):13-16.
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  46. Giuseppe O. Longo.Giuseppe Longo - 2001 - Nuova Civiltà Delle Macchine 19 (2):71-81.
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  47. Homo technologicus: tecnologia ed evoluzione.Giuseppe Longo - 1996 - Nuova Civiltà Delle Macchine 14 (1/2):145-155.
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  48. Il concetto di mutamento costituzionale in Hans Kelsen e Carl Schmitt.Gianfresco Longo - 1996 - Rivista Internazionale di Filosofia Del Diritto 73:256-262.
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  49. Intelligenza della mente intelligenza del corpo.Giuseppe O. Longo - 2000 - Studium 96 (3/4):509-531.
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  50. Koymans C. P. J.. Models of the Lambda Calculus. CWI Tract No. 9. Centrum Voor Wiskunde En Informatica, Amsterdam 1984, Iii + 181 Pp. [REVIEW]Giuseppe Longo - 1987 - Journal of Symbolic Logic 52 (1):284-285.
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