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Giuseppe Longo [62]G. Longo [9]Gianfranco Longo [4]Giulia Longo [3]
Giuseppe O. Longo [2]Guiseppe Longo [1]Glanfranco Longo [1]Gianfresco Longo [1]

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Giuseppe Longo
École Normale Supérieure
  1. The Deluge of Spurious Correlations in Big Data.Cristian S. Calude & Giuseppe Longo - 2017 - Foundations of Science 22 (3):595-612.
    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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  2.  72
    No Entailing Laws, but Enablement in the Evolution of the Biosphere.G. Longo, M. Montévil & S. Kauffman - 2012 - In Genetic and Evolutionary Computation Conference. New York, NY, USA,: Acm. pp. 1379 -1392.
    Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...)
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  3. Marriages of Mathematics and Physics: A Challenge for Biology.Arezoo Islami & Giuseppe Longo - 2017 - Progress in Biophysics and Molecular Biology 131:179-192.
    The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...)
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  4.  13
    How Future Depends on Past and Rare Events in Systems of Life.Giuseppe Longo - 2018 - Foundations of Science 23 (3):443-474.
    The dependence on history of both present and future dynamics of life is a common intuition in biology and in humanities. Historicity will be understood in terms of changes of the space of possibilities as well as by the role of diversity in life’s structural stability and of rare events in history formation. We hint to a rigorous analysis of “path dependence” in terms of invariants and invariance preserving transformations, as it may be found also in physics, while departing from (...)
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  5. From Physics to Biology by Extending Criticality and Symmetry Breakings.Giuseppe Longo & Maël Montévil - 2011 - Progress in Biophysics and Molecular Biology 106:340 - 347.
    Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that (...)
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  6.  5
    Letter to Turing.Giuseppe Longo - 2019 - Theory, Culture and Society 36 (6):73-94.
    This personal, yet scientific, letter to Alan Turing, reflects on Turing's personality in order to better understand his scientific quest. It then focuses on the impact of his work today. By joining human attitude and particular scientific method, Turing is able to “immerse himself” into the phenomena on which he works. This peculiar blend justifies the epistolary style. Turing makes himself a “human computer”, he lives the dramatic quest for an undetectable imitation of a man, a woman, a machine. He (...)
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  7. The Inert Vs. The Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - An Overview.Giuseppe Longo & Maël Montévil - 2012 - Frontiers in Physiology 3:39.
    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...)
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  8. Protention and Retention in Biological Systems.Giuseppe Longo & Maël Montévil - 2011 - Theory in Biosciences 130:107-117.
    This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called “extended present” as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of (...)
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  9.  27
    Lambda-Calculus Models and Extensionality.R. Hindley & G. Longo - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (19-21):289-310.
  10.  16
    Set-Theoretical Models of Lambda-Calculus: Theories, Expansions, Isomorphisms.Giuseppe Longo - 1983 - Annals of Pure and Applied Logic 24 (2):153.
  11.  28
    Lambda‐Calculus Models and Extensionality.R. Hindley & G. Longo - 1980 - Mathematical Logic Quarterly 26 (19‐21):289-310.
  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.  89
    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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  14.  55
    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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  15. A 2-Dimensional Geometry for Biological Time.Francis Bailly, Giuseppe Longo & Maël Montévil - 2011 - Progress in Biophysics and Molecular Biology 106:474 - 484.
    This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (...)
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  16.  23
    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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  17.  1
    Scientific Thought and Absolutes: For an Image of the Sciences, Between Computing and Biology.David Gauthier & Giuseppe Longo - 2020 - Angelaki 25 (3):120-130.
    We propose a reflection on the construction of scientific knowledge and in so doing an image of this knowledge. This will allow us to develop a comparative analysis of some of the main principles underpinning the constitution of the different sciences. We will highlight the role of critical thought in science, or even “negative results,” which pose limits and hence open new trajectories. In particular, we will address a misleading point of view, based on some informal concepts taken from computer (...)
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  18. 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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  19.  26
    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.
  20.  25
    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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  21.  19
    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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  22.  2
    Models of the Lambda Calculus.Giuseppe Longo - 1987 - Journal of Symbolic Logic 52 (1):284-285.
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  23.  41
    Proofs and Programs.Giuseppe Longo - 2003 - Synthese 134 (1-2):85 - 117.
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  24.  10
    Espace, temps et cognition.Francis Bailly & Giuseppe Longo - 2003 - Revue de Synthèse 124 (1):61-118.
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  25.  27
    Prototype Proofs in Type Theory.Giuseppe 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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  26.  11
    L’intelligence mathématique, l’infini et les machines.Giuseppe Longo - 1999 - Revue de Synthèse 120 (1):111-138.
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  27.  11
    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.  13
    On the Problem of Deciding Equality in Partial Combinatory Algebras and in a Formal System.Giuseppa Longo - 1976 - Studia Logica 35 (4):363 - 375.
  29.  9
    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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  30.  7
    Meeting of the Association for Symbolic Logic Florence, Italy 1982. E. Casari, E. J. Fenstad, G. Lolli, G. Longo, A. Marcja & D. van Dalen - 1984 - Journal of Symbolic Logic 49 (2):683 - 710.
  31. 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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  32.  23
    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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  33. 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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  34. Antinomie e polarità, determinazione e aleatorietà nel processo vivente della materia.Giuseppe Longo - 2009 - Discipline Filosofiche 19 (1).
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  35. Andata e ritorno dalla finanza alle matematiche passando per la biologia.Giuseppe Longo - 2011 - Nuova Civiltà Delle Macchine 29 (4).
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  36.  6
    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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  37.  2
    Brief an Alan Turing.Giuseppe Longo - 2020 - Internationales Jahrbuch Für Medienphilosophie 6 (1):15-44.
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  38.  38
    Big Data E Intelligenza Artificiale: Che Futuro Ci Aspetta?Giuseppe Longo - 2018 - Scienza E Filosofia 20.
    BIG DATA AND ARTIFICIAL INTELLIGENCE: A LOOK INTO THE FUTURE To say or write something innovative on the ongoing revolution in the fields of Big Data and Artificial Intelligence is very difficult. The advent of these two new technologies is in fact among the most relevant events in human history since in a little more than a decade it will likely lead to the creation of the First Artificial Intelligence of the Fourth level: i.e capable to think and create autonomously. (...)
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  39.  11
    Between Scylla and Charybdis.Giuseppe Longo - 2006 - Metascience 15 (3):617-621.
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  40.  15
    Boris Trakhtenbrot. Comparing the Church and Turing Approaches: Two Prophetical Messages. The Universal Turing Machine, A Half-Century Survey, Edited by Rolf Herken, Kammerer & Unversagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988, Pp. 603–630. [REVIEW]Giuseppe Longo - 1994 - Journal of Symbolic Logic 59 (4):1434-1436.
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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.  10
    C. P. J. Koymans. Models of the Lambda Calculus. CWI Tract No. 9. Centrum Voor Wiskunde En Informatica, Amsterdam1984, Iii + 181 Pp. [REVIEW]Giuseppe Longo - 1987 - Journal of Symbolic Logic 52 (1):284-285.
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  43.  39
    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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  44. Di fronte alla tecnologia.Giuseppe Longo - 2000 - Nuova Civiltà Delle Macchine 18 (4):90-101.
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  45. Dal Golem a Godel e ritorno.Giuseppe Longo - 1994 - Nuova Civiltà Delle Macchine 12 (4):28-38.
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  46.  25
    “Everything Has Its Time.” Kierkegaard’s Reading of Ecclesiastes.Giulia Longo - 2017 - Kierkegaard Studies Yearbook 2017 (1):211-244.
    Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 2017 Heft: 1 Seiten: 211-244.
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  47.  12
    Fondamenti cognitivi Della matematica E analisi matematiche Del vivente.Giuseppe Longo - 2008 - Rivista di Estetica 37:113-124.
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  48.  9
    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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  49. Francesco Lerda e l'intelligenza artificiale.Giuseppe Longo - 1994 - Nuova Civiltà Delle Macchine 12 (4):13-16.
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  50.  8
    Géométrie et cognition.Giuseppe Longo - 2003 - Revue de Synthèse 124 (1):1-10.
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