Selected publications by Giuseppe Longo, after 1990
available as .dvi, .ps (some gzipped) or .pdf files by ftp and http

  1 -   Mathematical  Logic  and  Computer  Science.
  2 -   Cognition  and  Foundations  of  Mathematical  Knowledge.
  3 -   Theoretical  Biology.
  4 -   Interfaces  Computability,  Physics  and  Biology.
  5 -   Minima   Philosophica.
  6 -   Minima   Economica.
  7 -   1980's:   Some of the Good Old Papers that resist.

Two recent books:  
 Bailly F., Longo G., MATHEMATICS AND THE NATURAL SCIENCES. The Physical Singularity of Life, Imperial College Press, London, 2011 (introduction:  Main Page ).
 Longo G., Montévil M., PERSPECTIVES ON ORGANISMS: Biological Time, Symmetries and Singularities, Springer, 2014 (introduction:  Main Page ).
1 - Mathematical  Logic  and  Computer  Science   (selection after 1990; for about 70 more papers see ListPubJan2016.pdf)


Download in dvi gz or pdf format

Download in ps or ps gz format

Downloadable Book by individual chapters:
Andrea Asperti and Giuseppe Longo. Categories, Types and Structures. Category Theory for the working computer scientist. M.I.T. Press, 1991 (pp. 1 - 300)
(currently out of print and downloadable upon kind permission of the M.I.T. Press).


  Chapters:   Preface&Contents (and direct ftp addresses), Ch.1, Ch.2, Ch.3, Ch.4, Ch.5, Ch.6, Ch.7, Ch.8, Ch.9, Ch.10, Ch.11, Ch.12.

Giuseppe Longo and Eugenio Moggi . A Category-theoretic characterization of functional completeness. . Theoretical Computer Science, 70 (2), 1990, pp.193-211.

Luca Cardelli and Giuseppe Longo. A semantic basis for Quest. Journal of Functional Programming, 1 (4), pp. 417-458, October 1991.

Giuseppe Longo and Eugenio Moggi. Constructive natural deduction and its "omega-set" interpretation. Mathematical Structures in Computer Science, 1(2):215--253, 1991.


Kim Bruce, Roberto Di Cosmo, and Giuseppe Longo. Provable isomorphisms of types. Special issue: Mathematical Structures in Computer Science, 2(2):231--247, 1992. Longo's Invited Lecture, Proceedings of the Symposium on Symbolic Computation, E.T.H. Zuerich, March 1990.



Giuseppe Longo, Kathleen Milsted, and Sergei Soloviev. The Genericity Theorem and effective Parametricity in Polymorphic lambda-calculus. Theoretical Computer Science, 121:323--349, 1993. Invited paper, special issue of T.C.S. "A Collection of contributions in honour of Corrado Boehm" (Preliminary Version: IEEE Conference on Logic in Computer Science (LICS 93), pp. 1-6, Montreal, Jan. 1993).


Giuseppe Longo. Parametric and type-dependent polymorphism. Fundamenta Informaticae, 22(1-2):69--92, 1995. Invited paper, special issue on "Categorical Methods in Computer Science".


G. Castagna, G. Ghelli, and G. Longo. A calculus for overloaded functions with subtyping. Information and Computation, 117(1):115-135. Academic Press, 1995.


Giuseppe Longo, Kathleen Milsted, and Sergei Soloviev. A Logic of Subtyping. (Full paper; extended abstract in Logic in Computer Science (LICS), pages 292--300. IEEE, 1995. San Diego, June 1995.)


Gang Chen and Giuseppe Longo. Subtyping parametric and dependent types. Longo's Invited Lecture, School on Type Theory and Term Rewriting, September, 1996.


Giuseppe Longo, Kathleen Milsted, and Sergei Soloviev. Coherence and Transitivity of Subtyping as Entailment. Journal of Logic and Computation, vol. 10: 4, pp. 493--526, August 2000.



Giuseppe Longo. Prototype Proofs in Type Theory Mathematical Logic Quaterly, vol. 46, n. 3, 2000 (formely: Zeitscrift f. Math. Logik u. Grundlagen der Math.). 

Giuseppe Longo. Some Topologies for Computations. Invited Lecture, proceedings of Géométrie au XX siècle, 1930 - 2000 (2001), Hermann, Paris, 2004.



2 - Cognition  and  Foundations  of  Mathematical  Knowledge:
  (Directions for downloading, Mac and PC users: see end-note)

Giuseppe Longo. Logic as a Foundation and as a Tool in Computer Science (two papers):
1 - Reflections on formalism and reductionism in Logic and Computer Science. In European Conference of Mathematics 1992, pages 202 --  209. Panel on Foundations, Invited Lecture (A. Joseph et al., eds). Birkhauser, 1994.
2 - Some aspects of impredicativity: Weyl's philosophy of mathematics and today's Type Theory. In Logic Colloquium 87 (European Summer Meeting of the A.S.L.), pages 241--274. Invited Lecture (revised) (Ebbinghaus et al., eds). North-Holland, 1989.            (    (types-impred-weyl.pdf)

Giuseppe Longo. The difference between Clocks and Todays Computing Machines. Invited Lecture at ``Models of Cognition and Complexity Theory'', Roma, Novembre 1995. La Nuova Critica, 29 (1), 1997. Reprinted in Functional Models of Cognition, Kluwer, 1999.           ( )  (clocksVtodayM.pdf )

Giuseppe Longo.  The Lambda-Calculus: connections to higher type Recursion Theory, Proof-Theory, Category Theory. A short (advanced) course on lambda-calculus and its mathematics, Spring 1996. (These notes are based on an invited lecture delivered at the Conference, "Church's Thesis after 50 years" Zeiss (NL), June 1986 ("On Church's Formal Theory of Functions and Functionals", published in Annals Pure Appl. Logic, 40: 93-133, 1988).         (    (church-notes.pdf)   

Giuseppe Longo.  The Mathematical Continuum, from Intuition to Logic. In Naturalizing Phenomenology (section on Mathematics and Formal Methods). Invited Paper, (Petitot et al eds.) Stanford University Press, 1999.
  ( )   (the-continuum.pdf )

Giuseppe Longo.  De la Cognition à la Géométrie :
1 - Introduction: est-ce que les calamars font de la Géométrie? Compte rendu du livre "Les anatomies de la pensée'', par A. Prochiantz, Odile-Jacob, 1997. À paraître dans Les Archives de Philosophie.
2 - Géométrie, Mouvement, Espace: Cognition et Mathématiques . À partir du livre "Le sens du mouvement'', par A. Berthoz, Odile-Jacob, 1997. Intellectica, n.25, 1997.              (    (cogni-geometrie.pdf)

Giuseppe Longo.  Cerveau, nombres et bon-ordre, à partir du livre "La bosse des maths'', par S. Dehaene, Odile-Jacob, 1997.   Revue de l'Association Henri Poincare', n. 6, pp. 6-16, Juin, 1997.  (dehaene-franç  (dehaene-français.pdf)

Giuseppe Longo.  Principi di prova e principi di costruzione.  Riflettendo sul libro "Le ragioni della Logica" di C. Cellucci, Laterza, 1998.            (    (cellucci-rev.pdf)

Giuseppe Longo.  Mathematics and the Biological Phenomena.  Invited lecture, proceedings of the International Symposium on Foundations in Mathematics and Biology: Problems, Prospects, Interactions (Basti, ed.), Pontifical Lateran University, Vatican City, November, 1998.            (    (math-biophen.pdf)

Thomas Fruchart and Giuseppe Longo. Carnap's remarks on Impredicative Definitions and the Genericity Theorem. In Logic and Foundations of Mathematics (Cantini et al. eds). Kluwer Academic Publishers, 1999.            (carnapImpred.dvi)    (

Giuseppe Longo.  Mathematical Intelligence, Infinity and Machines: beyond the Goedelitis.  Invited paper, Journal of Consciousness Studies, special issue on Cognition, vol. 6, n. 11-12, 1999.         (    (incompl-inf.dvi.pdf)
A preliminary french version of this paper appeared as "L'intelligence mathématique, l'infini et les machines."   Article invitée, Revue de Synthèse, n. 1, Paris, 1999.        

Giuseppe Longo.  Mémoire et objectivité en mathématiques.  Conférence invitée, actes du Colloque Le réel en mathématiques (Cérisy, septembre 1999), Presses de la Rue d'Ulm (Cartier et Charaud eds.), 2003.            (    (memoire.pdf)

Giuseppe Longo.  Cercles vicieux, Mathématiques et formalisations logiques. Conférence Invitée, parue dans Mathématiques, Informatique et Sciences Humaines, n. 152, 2000.           (cercles-vicieux.pdf)             (

Giuseppe Longo.  Lo spazio, i fondamenti della Matematica e la resistibile ascesa della metafora: il cervello è un calcolatore digitale.   Lezione tenuta a Firenze, nell'ambito del ciclo "Sapere e Narrare: l'uomo e le macchine", Istituto di Studi Filosofici, Gabinetto Vissieux, Palazzo Strozzi, novembre 1999. Apparso in "L'uomo e le macchine", a cura di M. Bresciani Califano, Leo S. Olschki, Firenze, 2002.       (metafora-resist.pdf)       English: (Resistible-rise.pdf)

Giuseppe Longo.  The Constructed Objectivity of Mathematics and the Cognitive Subject.   In "Quantum Mechanics, Mathematics, Cognition and Action - Proposals in Epistemolgy." (M. Mugur-Schachter ed.), Kluwer, pp. 433-463, 2002.           (    (constr-obj.pdf)

Giuseppe Longo.  Proofs and Programs (Type Theory: an introduction, some reflections).  Synthese, vol. 134, nos. 1-2, pp. 85-117, Kluwer, Boston, 2003.           (    (proofs-progr.pdf)

Giuseppe Longo.  Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences. Invited lecture, First AMS/SMF meeting, Lyon, July, 2001   (space-time.pdf);     (version française reduite: Intellectica, 2003/1-2, n. 36-37,  (espace-temps.pdf))
Revised for the Handbook of the Mathematics of the Arts and Sciences, B. Sriraman (ed.), Springer, 2020   (SpaceTimeAMS-Rev.pdf).

Francis Bailly, Giuseppe Longo.  Space, time and cognition. From The Standpoint of Mathematics and Natural Science. Invited paper, Mind and Causality, (Peruzzi ed.), Benjamins, Amsterdam, pp. 149-199, 2004.      (   (space-cogni.pdf) ).
(Version française "Espace, temps et cognition. A partir des mathématiques et des sciences de la nature".  Revue de Synthèse, Presses de la rue d'Ulm, Paris, tome 124, 2003.      (   (espace-cogni.pdf) ).

Giuseppe Longo.  Geometry and Cognition From the foundations of mathematics to theories of knowledge and cognition. for the Springer volume Morphology, Neurogeometry, Semiotics: A Festschrift in honor of Jean Petitot's 80th birthday (Sarti ed.), 2023. English translation and a revision of the Introduction to the volume Géométrie et Cognition, G. Longo (éditeur), numéro spécial de la Revue de Synthèse, Editions de la rue d'Ulm, tome 124, 2004.           (GeoCo-Engl-forPetitot.pdf)   

  Giuseppe Longo. The Cognitive Foundations of Mathematics: human gestures in proofs, in Images and Reasoning, (M. Okada et al. eds.), Keio University Press, Tokio, pp. 105-134, 2005: incompl-images.pdf   (in italiano nel: volume edito da M. Cappuccio: la neurofenomenologia. esperienza, percezione, cognizione. Version préliminaire en français, étendue par un texte avec Francis Bailly, in Il pensiero filosofico di Giulio Preti, (Parrini, Scarantino eds.), Guerrini ed associati, Milano, 2004, pp. 305 - 340.    (incompl-incert.pdf))

Giuseppe Longo.  The reasonable effectiveness of Mathematics and its Cognitive roots.  In Geometries of Nature, Living Systems and Human Cognition   series in "New Interactions of Mathematics with Natural Sciences and Humaties" (L. Boi ed.), World Scientific, pp. 351 - 382, 2005.        (reason-effect.pdf)

Giuseppe Longo.  Laplace, Turing and the "imitation game" impossible geometry: randomness, determinism and programs in Turing's test. In Epstein, R., Roberts, G., & Beber, G.  (Eds.).  Parsing the Turing Test, pp. 377-413, Springer, 2008.      (turing-game.pdf)     (version préliminaire en français in Intellectica, n. 35, 2002/2, pp. 131-162:     (   (turing-jeu.pdf);   suivi d'une réponse aux commentaires publiés par la revue:  Continu vs. discret et régimes de causalité., pp. 199-216  (   (reponse-jeu.pdf)).

Giuseppe Longo. Mathematical Concepts and Physical Objects, in Rediscovering phenomenology, (L. Boi, P. Kerszberg, F. Patras eds.), Springer, 2007: ( conc-phys-obj.pdf).   (Capitolo tradotto dal francese da M. Castellana per il volume “Per una epistemologia dei contenuti” (Castellana ed.), Bari, 2007. (FondMatFys.pdf))

Francis Bailly, Giuseppe Longo.  Phenomenology of Incompleteness: from Formal Deductions to Mathematics and Physics. In Deduction, Computation, Experiment (Lupacchini ed.), Springer, 2008.       (incomplet-Bo.pdf)

Giuseppe Longo.  Theorems as Constructive Visions. Invited Lecture, Proceedings of ICMI 19 conference on Proof and Proving, Taipei, Taiwan, May 10 - 15, 2009, (Hanna, de Villiers eds.) Springer, 2010.       (proof-visions.pdf)

 Giuseppe Longo, Arnaud Viarouge.  Mathematical intuition and the cognitive roots of mathematical concepts. Invited paper, Topoi, Special issue on Mathematical knowledge: Intuition, visualization, and understanding (Horsten L., Starikova I., eds), Vol. 29, n. 1, pp. 15-27, 2010.       (TopoiIntuitCogni.pdf)

 Giuseppe Longo. Reflections on Concrete Incompleteness, in Philosophia Mathematica, 19(3): 255-280, 2011.       (Incompl-PhiloMath.pdf)
(revised version of On the proofs of some formally unprovable propositions and Prototype Proofs in Type Theory. Invited Lecture, Types for Proofs and Programs, Durham, (GB), Dec. 2000; LNCS, vol 2277 (Callaghan et al. eds), pp. 160 - 180, Springer, 2002)

 Giuseppe Longo. Synthetic Philosophy of Mathematics and Natural Sciences, Conceptual analyses from a Grothendieckian Perspective, Reflections on “Synthetic Philosophy of Contemporary Mathematics” by F. Zalamea, Urbanomic (UK) and Sequence Press (USA), 2012. Invited Paper, in Speculations: Journal of Speculative Realism, Published: 12/12/2015, followed by an answer by F. Zalamea.       (Review-Zalamea-Grothendieck.pdf)

 Arezoo Islami, Giuseppe Longo. Marriages of Mathematics and Physics: a challenge for Biology, Invited Paper, in The Necessary Western Conjunction to the Eastern Philosophy of Exploring the Nature of Mind and Life (K. Matsuno et al., eds), Special Issue of Progress in Biophysics and Molecular Biology, Vol 131, Pages 179­192, December 2017.      (DOI)      (SpaceTimeIslamiLongo.pdf)

 Giuseppe Longo. Le jeu difficile entre rigueur et sens. Dans La rigueur (T. Paul et al. eds.), Spartacus IDH, 2020 (jeu-rigueur-sens.pdf)     (English extended and revised version with E. Blanchard: From axiomatic systems to the Dogmatic gene and beyond. In Foundations of Mathematics and Theoretical Biology (E. Fimmel, A. Rodin, eds.), Special issue of Journal of Biosystems (axiomatic-gene))


3 - Theoretical  Biology:

Francis Bailly, Giuseppe Longo.  Objective and Epistemic Complexity in Biology.  Invited lecture, Proceedings of the International Conference on Theoretical Neurobiology, (N. D. Singh, ed.), National Brain Research Centre, New Delhi, INDIA , 2003, pp. 62 - 79.   (obj-epi-complex.pdf)

Giuseppe Longo, Pierre-E. Tendero.  The differential method and the causal incompleteness of Programming Theory in Molecular BiologyIn  Foundations of Science, n. 12, pp. 337-366, 2007   (DNA-incompl.pdf
(A version for Logicians and computer scientists: Dna_Differential_Methods_and_Bohm-out.pdfversion préliminaire et plus étendue dans   "Evolution des concepts fondateurs de la biologie du XXIe siècle", (Miquel ed.) DeBoeck, Paris, 2008   (alphaMdT-ADN.pdf);   una traduzione in italiano e' apparsa a cura di e per Naturalmente).

Francis Bailly, Giuseppe Longo.  Extended Critical Situations,  in J. of Biological Systems, Vol. 16, No. 2, pp. 309-336, June 2008.   (extend-criticJBS.html  or   extend-critic.pdf)    (A preliminary french version was a ``conférence invitée'' aux Actes du Colloque "Détermination et complexité", Cerisy, (P. Bourgine, ed.) La Découverte, Paris, 2008.   (situa-critiq.pdf) )

Francis Bailly, Giuseppe Longo.  Schèmes géométrique pour le temps biologique.  In "Sciences du vivant et phénoménologie de la vie" (P.A. Miquel, ed.), n. 14, Noesis-Vrin, automne 2008.   (geo-temps.pdf).   

Francis Bailly, Giuseppe Longo.  Biological Organization and Anti-Entropy.   In J. Biological Systems, Vol. 17, No. 1, pp. 63-96, 2009.   (anti-entropy.pdf)

Francis Bailly, Giuseppe Longo, Maël Montévil.    A 2-dimensional Geometry for Biological Time In Progress in Biophysics and Molecular Biology: vol. 106, n. 3, pp. 474 – 484, 2011.    (2-dimTime.pdf).   

Giuseppe Longo, Maël Montévil.    Protention and retention in biological systemsIn Theory in Biosciences: Vol. 130, Issue 2, pp. 107-117, 2011.    (proret.pdf).   

Giuseppe Longo, Maël Montévil.    From Physics to Biology by Extending Criticality and Symmetry Breakings Invited paper, special issue of Progress in Biophysics and Molecular Biology: 106(2):340 – 347, 2011    (symmExtCrit.pdf;  Reprinted in 2019: Acta europea Systemica

Giuseppe Longo, Maël Montévil.    Randomness Increases Order in Biological Evolution Invited paper, conference on ''Computations, Physics and Beyond'', Auckland, New Zealand, February 21-24, 2012; LNCS vol. 7318 (Dinneen et al. eds), pp. 289 - 308, Springer, 2012.    (anti-entrNZ.pdf).    (Also an invited lecture at the Conference in Honor of S.J. Gould, Venice (It.), May 10 - 12, 2012)

Giuseppe Longo, Maël Montévil.    The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - an overview Invited paper, special issue of Frontiers in Physiology, n. 3, 39, 2012.    (inertVSlife.pdf; inerteVSvivente.pdf).   

Giuseppe Longo, Maël Montévil, Stuart Kauffman.    No entailing laws, but enablement in the evolution of the biosphereInvited Paper, Genetic and Evolutionary Computation Conference, GECCO’12, July 7-11, 2012, Philadelphia (PA, USA); proceedings, ACM 2012.   (noentail.pdf).    Preliminary version:.   (      

Giuseppe Longo, Maël Montévil, Arnaud Pocheville.    From bottom-up approaches to levels of organization and extended critical transitions. Invited Paper, Frontiers in Physiology, 3: 232, July 2012.   (FromBottomLMP.pdf).

Giuseppe Longo, Paul-Antoine Miquel, Carlos Sonnenschein, Ana Soto.    Is Information a proper observable for biological organization? In Progress in Biophysics and Molecular Biology, Volume 109, Issue 3, pp. 108-114, August 2012.   (LMSSweb.pdf).

Marcello Buiatti, Giuseppe Longo.    Randomness and Multi-level Interactions in Biology Theory in Biosciences, vol. 132, n. 3:139-158, 2013.   (BuiattiLongo2.pdf)  (Traduction et réduction dans: B. Durrive, J. Henry (éds.) "Redéfinir l'individu à partir de sa trajectoire: Hasard, déterminismes et rencontres", Éditions Matériologiques, janvier 2015).

Giuseppe Longo, Maël Montévil.    Extended Criticality, Phase Spaces and Enablement in Biology. Invited Paper, Special Issue of Chaos, Solitons and Fractals, Volume 55, Pages 64–79, October 2013.   (ExtCritEnable.pdf).

Giuseppe Longo.   How Future Depends on Past Histories and Rare Events in Systems of Life,  Foundations of Science, (DOI), 23 (3):443-474, 2018     (biolog-observ-history-future.pdf)    (Révision en français dans La liberté de l’improbable (Berthoz, Ossola cur.), Collège de France, décembre 2016 : bio-evol-histoire-et-futur.pdf;     tradotto in italiano (bio-evol-histoire-et-futur.pdf) per Studi in memoria di Aldo Giorgio Gargani (Marinucci et al. cur.)).

Giuseppe Longo, Maël Montévil, Carlos Sonnenschein, Ana Soto.    In Search of Principles for a Theory of Organisms. In Journal of Biosciences, Springer, pp. 955–968, 40(5), December, 2015.   (LoMoSoSo-Search.pdf).

Giuseppe Longo, Maël Montévil.    From Logic to Biology via Physics: a survey. In Logical Methods in Computer Science, special issue in honor of P.-L. Curien, 2017, 13 (4), pp.1-15.   (LoMon-fromLogic-toBio.pdf).

Giuseppe Longo. Six co-authored papers:
     1 Table of Contents and Preface (TableContentsPreface+SixPapers2016.pdf)
     2 G. Longo & A.M. Soto, Why do we need theories? (01_theories.pdf)
     3 N. Perret & G. Longo, Reductionist perspectives and the notion of information (02_information.pdf)
     5 A.M. Soto, G. Longo, M. Montévil & C. Sonnenschein, The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms
     6 M. Mossio, M. Montévil & G. Longo, Theoretical principles for biology: Organization
     7 M. Montévil, M. Mossio, A. Pocheville & G. Longo, Theoretical principles for biology: Variation
     10 A.M. Soto, G. Longo, P.-A. Miquel, M. Montévil, M. Mossio, N. Perret , A. Pocheville & C. Sonnenschein, Toward a theory of organisms: Three founding principles in search of a useful integration.
     In   "From the century of the genome to the century of the organism: New theoretical approaches", a  Special issue of Progress in Biophysics and Molecular Biology, A.M. Soto, G. Longo, D. Noble (Editors), Vol. 122, Issue 1, Elsevier, 2016. (TableContentsPreface+SixPapers2016.pdf; introduzione in italiano: Dal-gene-all-organismoAltri-GL.pdf) 

Giuseppe Longo.    Information and Causality: Mathematical Reflections on Cancer Biology. In Organisms. Journal of Biological Sciences, vo. 2, n. 1, 2018.   (BiologicalConseq-ofCompute.pdf)

Giuseppe Longo, Matteo Mossio.    Geocentrism vs genocentrism: theories without metaphors, metaphors without theories. In Interdisciplinary Science Reviews, 45 (3), pp. 380-405, 2020.   (Metaphors-geo-genocentrism.pdf)

Giuseppe Longo.    Programming Evolution: a Crack in Science. A Review of the book by Jennifer A. Doudna and Samuel H. Sternberg "A Crack in Creation: Gene Editing and the Unthinkable Power to Control Evolution", in Organisms. Journal of Biological Sciences, Vol. 5, No. 1, 2021.   (LongoReview-DoudnaBook.pdf;     en français : Longo-compte-rendu-Doudna)

Marie Chollat-Namy, Giuseppe Longo.   Entropie, Neguentropie et Anti-entropie : le jeu des tensions pour penser le vivant. Invited paper in Entropies, ISTE OpenScience – Published by ISTE Ltd. London, UK, 2022.   (ChollatLongo-entropies.pdf).    

Caroline Petit, Giuseppe Longo.   THE PANDEMIC AND THE « TECHNO-FIX ».  Organisms. Journal of Biological Sciences, Vol. 5, No. 2 (2022).   (Petit-LongoPANDEMIC-TECHNO-FIX.pdf).    

Giuseppe Longo.   Les nouveaux Organismes génétiquement modifiés (OGM) : pour un « principe de précaution scientifique ».  Philosophy World Democracy, 1 septembre, 2023.   (principe-de-precaution-scientifique).    English: (Precaution-sci-NGT-English).    Italiano: (Sci-precaution-principe-it.pdf).

Giuseppe Longo.   Emergence vs Novelty Production in Physics vs Biology.  Lecture presented at Open Historicity of Life. Theory, epistemology, practice, Paris, October, 2023 (to appear in the proceedings: Chollat, Montévil, Robert eds.):   (EmergeCompareBioNovelty.pdf)   (a few remarks on Large language Models in AI, extracted from the paper: LLM-Extract-AI.pdf).    


4 - Interfaces Computability, Physics and Biology:

Francis Bailly, Giuseppe Longo.  Randomness and Determination in the interplay between the Continuum and the Discrete. Special issue: Mathematical Structures in Computer Science 17(2), pp. 289-307, 2007  (DiscrContRand.pdf).

Francis Bailly, Giuseppe Longo.  Causes and Symmetries. The Continuum and the discrete in Mathematical Modelling.   in More Geometrico (Giorello et al. Eds.) Elsevier, 2008.  (cause-symMoreGeo.pdf) ( A preliminary french version was a conférence invitée, aux Actes du Colloque Logique et intéraction: pour une géométrie de la cognition (J. B. Joinet ed.), Presses Universitaires de la Sorbonne, 2008.      (   (cause-cont.pdf)).

Mathieu Hoyrup, Arda Kolcak, Giuseppe Longo.  Computability and the Morphological Complexity of some dynamics on Continuous Domains. Invited survey, Theoretical Computer Science, n. 398, pp. 170-182, 2008.   (CIM/comp-dynam.pdf)   

Giuseppe Longo.  From exact sciences to life phenomena: following Schrödinger and Turing on Programs, Life and Causality. Concluding lecture at "From Type Theory to Morphological Complexity: A Colloquium in Honor of Giuseppe Longo." In Information and Computation, special issue, n. 207, pp. 545-558, 2009.   (longoConf-english.pdf)  (Version française dans "Explication, modélisation et simulation en Biologie" (Barberousse et al. dir.), éd. Syllepse, Paris, 2008.)  

Giuseppe Longo.  Randomness and Determination, from Physics and Computing towards Biology. Invited Lecture at the 5th International Conference on: Current Trends in Theory and Practice of Computer Science, Spindleruv mlyn (Czech Republic), January 24-30, 2009. In Lecture Notes in Computer Science, LNCS 5404, 49-62, Springer, 2009. (random-determ.pdf

Matteo Mossio, Giuseppe Longo, John Stewart.  Computability of closure to efficient causation.   In, J. of Theoretical Biology, 257, 3, pp. 489-498, 2009.   (comp-closure.pdf).   

Giuseppe Longo, Thierry Paul.  The Mathematics of Computing between Logic and Physics.  Invited paper, "Computability in Context: Computation and Logic in the Real World", (Cooper, Sorbi eds), pp. 243 - 274, Imperial College Press, 2010.            (gius-thierCompWorld.pdf)

  Giuseppe Longo, Catuscia Palamidessi, Thierry Paul.  Some bridging results and challenges in classical, quantum and computational randomness.  In "Randomness through Computation", H. Zenil (ed), pp. 73–92, World Scientific, 2010.     (answersRandom.pdf)

Giuseppe Longo.  Incomputability in Physics and Biology.  Invited Lecture, Proceedings of Computability in Europe, Azores, Pt, June 30 - July 4, LNCS 6158, Springer, 2010.    (revised version in: Mathematical Structures in Computer Science, Vol. 22, n. 5, Special Issue, pp. 880 - 900, octobre 2012). (incomput-phys-bio.pdf

G. Longo, M. Montévil, A. Pocheville.    L’incompressible complexité du réel et la construction évolutive du simple. Article invité, actes du colloque : Complexité-Simplexité, (Berthoz, Petit, eds), Collège de France, 2014 (tous les articles).    (IncompressReel.pdf).

Giuseppe Longo, Maël Montévil.    Comparing Symmetries in Models and Simulations (former title: Models vs. Simulations: a comparison by their Theoretical Symmetries). Invited Paper, Springer Handbook of Model-Based Science (book website), 2017.   (LoMonModelsSym.pdf).

Cristian Calude, Giuseppe Longo.    Classical, Quantum and Biological Randomness as Relative Unpredictability. Invited Paper, special issue of Natural Computing, Volume 15, Issue 2, pp 263–278, Springer, March 2016.  (CaludeLongoRandom.pdf),    First online: 25/11/2015:   (CaludeLongoRandom).

Barbara Bravi, Giuseppe Longo.    The Unconventionality of Nature: Biology, from Noise to Functional Randomness. Invited Lecture, Unconventional Computation and Natural Computation Conference (UCNC)}, Auckland (NZ), 31/8 - 4/9/2015, proceedings in Springer LNCS 9252, Cristian S. Calude and Michael J. Dinneen (Eds.), pp 3-34, 2015.   (paper: Unconventional-NatureUCNC2015.pdf; video, second half: here).

Cristian Calude, Giuseppe Longo.    The Deluge of Spurious Correlations in Big Data.  Opening Lecture, Colloque Lois des dieux, des hommes et de la nature,     (BigData-Calude-Longo.pdf);    published in Foundations of Science, 1-18, March, 2016:   (BigData-Calude-Longo).  

  Giuseppe Longo.  Interfaces of Incompleteness.  In Minati, G, Abram, M & Pessa, E (Eds.), Systemics of Incompleteness and Quasi-systems, Springer, New York, NY, 2018   (Incompleteness.pdf)   (Versione preliminare in italiano per "La Matematica", vol. 4, pp. 219 - 262, Einaudi, 2010:   Incompletezza.pdf;   traduite en français:   Incompletude.pdf)      

  Giuseppe Longo.  Information at the Threshold of Interpretation, Science as Human Construction of Sense.  In Bertolaso, M., Sterpetti, F. (Eds.) A Critical Reflection on Automated Science – Will Science Remain Human? pp. 67-100, Springer, Dordrecht, 2019   (Information-Interpretation.pdf)        

  Giuseppe Longo.  Naturalizing Physics. Or, embedding physics in the historicity and materiality of the living.   La Deleuziana – Online Journal of Philosophy – ISSN 2421-3098, N. 11, special issue on “Differential Heterogenesis: Deleuze, Mathematics And The Creation Of Forms”, April 2020   (NaturPhysics)        

  Giuseppe Longo.  Confusing biological twins and atomic clocks. Today’s ecological relevance of Bergson-Einstein debate on time.  In "Einstein vs Bergson. An enduring quarrel of time", A. Campo and S. Gozzano, eds, De Gruyter, 2021.   (TwinsVScloks.pdf)        

  Giuseppe Longo.  From Information to Physics to Biology.  Commentary to "The gene: An appraisal" by Keith Baverstock, PBMB, Volume 164, September 2021, pages 46-62, In Progress in Biophysics and Molecular Biology, Volume 177, January 2023, Pages 202-206.   (CommentaryBaverstock-paperPBMB.pdf)        

  Giuseppe Longo.  Preface to Angelo Marinucci, Theoretical Principles of Relational Biology. Space, Time, Organization, Springer, 2023,   (prefLongo-toMarinucciBook.pdf)        


5 - Minima philosophica:

  G. Longo.  Laplace (A note on incompleteness).  An item of J-Y. Girard's Logic Dictionnary , at the end of "Locus Solum", MSCS, vol.11, n.3, Cambridge Univ. Press, 2001.           (laplace.pdf)

  G. Longo.  Computer Modelling and Natural Phenomena.   Invited Lecture, Proceedings of the European Software Engineering Conference and ACM SIGSOFT Symposium, Helsinki, Finland, September 1-5, ACM Proceedings, New York, 2003. pp. 1 - 5.     (   (comp-model.pdf)

  G. Longo.  On the Relevance of Negative Results.   Conférence ''Négation, dualité, polarité”, Marseille, 2008 (proceedings in Influxus, [En ligne/Online Journal], 21 novembre 2012. URL : :  neg-resCE.pdf)    (A preliminary version in French of the first part appeared in Intellectica, vol. 40, n.1, 2005: neg-results.pdf;   tradotta in italiano, a cura di e per Naturalmente, anno 18, 3, 9/2005:  natural-neg-res.pdf)

  G. Longo.  Pensiero laico ed assoluti: i paradigmi della scienzaIn  Naturalmente, anno 19, 1, 10/2006.  (laico-assol.pdf)   (extensively revised, in English: Angelaki, Journal of the Theoretical Humanities, Volume 25, 2020 - Issue 3: special issue: ontogenesis beyond complexity. Issue editors: Cary Wolfe and Adam Nocek    (science-vs-absolutes.pdf))

  B. Saulnier, G. Longo.  Complexité et structures conceptuelles : les rapports inter-théoriques comme lieu de la signification et la question de l’expérience.  Conférence invitée aux Actes du Colloque "Intelligence de la complexité", Cérisy, Juin 2006, (Le Moigne, Morin, eds.), Editions de l’aube, Paris, 2007.     (complex-cerisy.pdf)

  G. Longo.  Discreto e continuo.  Introduzione (con R. Fabbrichesi) ed intervista al Convegno "Discreto e continuo", Gargnano, 5 - 7 ottobre, 2006 (apparso in Dedalus, n.2-3, 2007).            (discr-cont.pdf)

  G. Longo. "La singolarità fisica del vivente", Convegno, "I 90 anni di Pietro Omodeo", Pisa, feb. 2009: (trascrizione della presentazione orale: Omodeo)

  G. Longo.  Critique of Computational Reason in the Natural Sciences, In "Fundamental Concepts in Computer Science"   (E. Gelenbe and J.-P. Kahane, eds.), Imperial College Press, pp. 43-70, 2009   (CritiqCompReason-engl.pdf).      Versione preliminare in italiano:   Lezione Galileana, Pisa, Ottobre 2006; apparso in Pianeta Galileo (Peruzzi ed.), Firenze, 2007     (lez-galileana.pdf).

  G. Longo.  Prefazione.  A "Besinnung: scienza, complessità e fenomenologia", di Fausto Fraisopi, Aracne, Roma, 2009.       (prefaz-fraisopi.pdf)

  G. Longo.  Hommage à Francis Bailly, 5 février, 2009.       (HommageDecesBailly.pdf)

  G. Frezza, G. Longo.  "Variations on the theme of invariants: conceptual and mathematical dualities in physics vs biology,  in "Human Evolution", vol. 25, n. 3-4, pp. 167-172, 2010.     (variant-invariant.pdf)       (Versione preliminare in italiano in "Metafore del vivente", (a cura di) Gagliasso E. e Frezza G., FrancoAngeli, Milano 2010.    (Cross-over.pdf))

  G. Longo.  La rationalité mathématique et les formes de la connaissance : esquisse d’un projet entre mathématiques et cognition.  In "Geometria, intuizione, esperienza", Centro Enriques, Plus Edizioni, Livorno, 2010.            (EnriquesCogniMaths.pdf)

  G. Longo.  Symmetries and symmetry-breakings: the fabric of physical interactions and the flow of time.  A review article in "Foundations of Science", Vol. 16, Issue 4, pp. 331-333, 2011.            (Symmet-fabric-interact.pdf)

  G. Longo.  L’informatique aux interfaces des savoirs.  Aux actes du Colloque "Ouvrir la logique au monde. Philosophie et mathématique de l'interaction" (Joinet et al. eds), 2009, in Influxus, [En ligne/Online Jounal], le 30 août 2012. URL:            (informatique-savoirs.pdf). English version: (ComputerSci-InterfacesKnow.pdf)

 J. Lassègue, G. Longo.  What is Turing’s Comparison between Mechanism and Writing Worth?  Longo's invited lecture, Proceedings of "The Turing Centenary Conference (CiE 2012)", Isaac Newton Institute programme, Cambridge, June 18 - 23, 2012; in Computability in Europe, 2012, LNCS 7318 (S.B. Cooper, A. Dawar, and B. L¨owe, Eds.), pp. 451–462, Springer-Verlag Berlin Heidelberg, 2012.    (lass-longo.pdf)

 G. Longo.  Simmetrie e caso in Biologia. Riflettendo di democrazia e scienza.  Atti del convegno "In onore di Marcello Buiatti", Pisa, 2012; (E. Gagliasso ed.), Roma, 2013.    (atti-Buiatti.pdf)

 N. Pisanti, G. Longo.  A. M. Turing: dalla macchina a stati discreti alla genesi continua delle forme in biologia.  In "SAPERE", 28 - 31, agosto 2012.    (TuringPisantiLongo.pdf)

 G. Longo, N. Zakhama.  Le modèle comme regard organisateur du réel.  Exposé invité, Colloque "Naturaliser le modèle", Chambord, octobre, 2013. Version préliminaire du texte aux actes du colloque (Bayer, Migayrou, eds), FRAC-Centre, 2014 :    (LongoNaturModel.pdf)

 G. Longo.  Science, Problem Solving and Bibliometrics.  Invited Lecture, Academia Europaea Conference on "Bibliometrics: Use and Abuse in the Review of Research Performance", Stockholm, May 2013. Proceedings, Wim Blockmans et al. (eds), Portland Press, 2014.   (Bibliometrics9-13rev.pdf)

 G. Longo.  Le conseguenze della filosofia.  Conferenza invitata, convegno "A Plea for Balance in Philosophy", Firenze, aprile 2014. Atti a cura di R. Lanfredini, ETS, Pisa, 2015.   (Le-conseguenze-filosofia.pdf)
 (A reduced version has been translated for the first issue of Glass Bead, february 2016: English and Français;
 English audio recording, bottom of this page)

 G. Longo, E. Pagni.  Extended Criticality and Structural Stability: ''architectures'' of biological individuationIn Philinq, J. of Philosophy, III, pp. 1-30, 2015.  (Longo-Pagni_ExtCriticIndividuaMerleau.pdf)   

 G. Longo.  A review-essay on reductionism: some reasons for reading "Reductionism, Emergence and Levels of Reality. The Importance of Being Borderline", a book by S. Chibbaro, L. Rondoni, A. Vulpiani.  Urbanomic, London, May 8, 2016.    (Review-on-Reductionism)

 G. Longo, M. Montévil, A. Soto : deux synthèses des travaux récents, à l'occasion du colloque de Cerisy "Information et biologie", septembre 2016.  Du siècle du gène à celui de l’organisme : introduction à de nouvelles perspectives théoriques    (cerisy-theorie-organisme.pdf)    et    Big Data et connaissance biologique    (cerisy-bigdata.pdf; English revision, published in 2018: bigdata-knowledge.pdf),    in : Sciences de la vie, sciences de l’information. Sous la dir. de T. Gaudin, D. Lacroix, M.-C. Maurel et al. Paris : ISTE-Editions, 2017.

 G. Longo, N. Perret.  Rhythms, Retention and Protention: Philosophical Reflections on Geometrical Schemata for Biological TimeIn Building theories, Danks D., Ippoliti E. (Eds.), Springer-Verlag, Berlin, 2017  (RetenProten-preprint.pdf)    (Version préliminaire: Anticipation, protension et inertie biologique.  Article invité, Actes du colloque "Anticipation et Prédiction", Collège de France, 2013, (C. Debru, A. Berthoz eds), Odile Jacob, Paris, 2015.    (LoPerAnticipation.pdf))

 M. Bizzarri, AM. Soto, C. Sonnenschein and G. Longo.  Saving Science. And beyondIn Organisms. Journal of Biological Sciences, Vol. 1, 1, June, 2017:   (BizSoSoLoSavingSci.pdf)   

 G. Longo.  Letter to Alan Turing.  Invited, in Theory, Culture and Society, Posthumanities Special Issue, 2018:   (Letter-to-Turing.pdf)   (Version ''article'', en français, largement revue en collaboration avec Jean Lassègue pour Intellectica, 2020: Longo-Lassegue-Turing.pdf;   originale in italiano: Lettera-a-TuringIt.pdf;   con un'introduzione in inglese: Lettera-a-Turing.pdf;   auf Deutsch, "Inhalt" Internationales Jahrbuch für Medienphilosophie, De Gruyter, vol. 6, no. 1, 2020, pp. V-VIII: Brief-an-Alan-Turing.pdf)

 G. Longo.  Des hommes et des machines : comment reconnaitre une caricature ? aux Actes du Colloque "Le travail au XXIème siècle : Droit, techniques, écoumène", Collège de France, Paris, 26-27 février 2019:   (ReconnaitreCaricature.pdf)   

 G. Longo.  Corrélations artificielles vs intelligence des causesdans le Livre Blanc Tome 2 "Contribution des outils numériques à la transformation des organisations de santé", Commission des Affaires Sociales, Assemblée Nationale, Paris, 2019:   (CorrelCauses.pdf)   

 G. Longo, Sara Longo.  Among the trees: iterating geneses of forms, in art and in nature.  ISTE OpenScience, published by ISTE Ltd. London, UK, January 2020 (reprinted in ‘Mathematics in the Visual Arts’’ (R. Scheps and M.-C. Maurel ed.), ISTE-WILEY Ltd, London, 2020):   (iste_artsci20v4n2_1.pdf)   

 G. Longo, Sara Longo.  Infinity of God and Space of Men in Painting, Conditions of Possibility for the Scientific Revolution.  In ‘‘Mathematics in the Visual Arts’’ (R. Scheps and M.-C. Maurel ed.), ISTE-WILEY Ltd, London, 2020:   InfinitySpaceMenLoLo.   Version française: InfiniEspacePhenoMathsLongos.    (Vidéo de la présentation du livre de Sara Longo sur ces thèmes)

 G. Longo.  Information, science and democracy, for an ethics of scientific knowledge (a revised synthesis of the Interview: "Complexity, Information and Diversity, in Science and in Democracy"),  in "Trust", Studies in Applied Philosophy, Epistemology and Rational Ethics, 54, Springer 2020:   (Trust-InfoScientism-exInterv.pdf)   

 G. Longo.  Penser au-delà de l’ "épidémie d’épidémies", in "Penser l'épidémie Covid-19 autrement", Institut d'Etudes Avancées de Nantes, 2020:   (IEA-epidemie-Longo.pdf);   in English: (Epidemic-Engl.pdf);   in italiano: (Epidemic-Italiano.pdf)   

J. Lassègue, G. Longo.  Qu’est-ce qu’écrire une loi ? L’écriture informatique en science et en droit, dans S. Besson, S. Jubé (curat.) "Concerter les civilisations", Seuil, Paris, 2020:   (LassegueLongo-ecrire une loi.pdf).

M. Montévil,  B. Stiegler,  G. Longo,  A. Soto,  C. Sonnenschein,  ANTHROPOCÈNE, EXOSOMATISATION ET NÉGUENTROPIE, dans B. Stiegler (curat.) "BIFURQUER, Eléments de réponses à Antonio Guterres et Greta Thunberg", PARIS, 2020:   (AnthropoceneNeguEntrop.pdf).

 G. Longo. Sara Longo.  Réinventer le corps et l’espace, in "In difesa dell’umano" (a cura di Boi, Curi, Maffei, Miraglia), 2021:   (Longos-ReinventerCorps-espaces.pdf);   in italiano: (Longos-ReinventareCorpo-spazio.pdf)       (Vidéo de la présentation du livre de Sara Longo sur ces thèmes)

 G. Longo.  Science in the storm, in "Agnotology, Artificial Intelligence, and Democracy." Philosophy World Democracy Journal. Special issue: " The dusk of theoretical controversies in current sciences.", 2021:   (V. Chaix, G. Longo and M. Montévil. Introduction);   (G. Longo. Section 4)   

 A. Angelini, G. Longo.  Comparing Artificial, Animal and Scientific Intelligence: A Dialogue with Giuseppe Longo, in Theory, Culture & Society, special section edited by R. Bishop, Volume 39 Issue 7-8, December 2022.   (ComparingIntelligence;  preliminary draft: AngeliniLongo-Internation-AI-BigData-Stiegler.pdf )   

 G. Longo.  Ces molécules et ces intelligences qui ne meurent pas : comment sortir de ces langages sans sens ni vie, in "Plus d’une discipline : actualité de La vie la mort" (De Michele et al. Cur.), Hermann, 2023.   (La-vie-la-mort-pourDerrida_Longo.pdf)   

 G. Longo.  Le nez de Pangloss : Ex-aptation et overloading, entre biologie et organologie, in "Bernard Stiegler. Panser les savoirs dans le milieu numérique" (Alombert, Krzykawski et Maronneau, Cur.), Revue Le Portique, 2024.   (Pangloss-exaptation.pdf)    (traduzione e riduzione di E. Toffoletto: Il tempo del vivente. Riflessioni epistemologiche tra fisica, economia e biologia, in "Equilibri Magazine", 18 dicembre 2023.   (Il tempo del vivente))


6 - Minima œconomica:

 G. Longo.  La dette publique et le système fiscal italien.  In "Alternatives Economiques", n. 115, pp. 14 - 18, Mars 1994.

 T. Felin, S. Kauffman, R. Koppl, G. Longo.  Economic Opportunity and Evolution: Beyond Bounded Rationality and Phase Space.  In "Strategic Entrepreneurship Journal", vol. 8, issue 4: 269–282 (2014), (preliminary version: FelinKauffmanKopplLongoSEJ2014.pdf;    journal web site, 21 May 2014: DOI: 10.1002/sej.1184)

 R. Koppl, S. Kauffman, T. Felin. G. Longo, Economy for a Creative World.  Preliminary version of this target article in "Journal of Institutional Economics", Vol. 11, Issue 01, pp 1 - 31, March 2015.   (In September 2016, in Boston, this paper was awarded the prize for best paper appearing in JOIE in the previous calendar year - this prize is entitled to Elinor Ostrom, 2009 Nobel Award winner in Economy)   (EconoCreative-jan2014web.pdf);   answers to comments:    (Koppl-al-Longo-answers.pdf)


7 - 1980's: Some of the Good Old Papers that resist:

 G. Longo.  Set-Theoretical Models of lambda-calculus: Theories, Expansions, Isomorphisms.  "Annals of Pure and Applied Logic", Vol. 24, 153 - 188, 1983.   (Set-TheorModelsLamdaCalcul.pdf)
              (for recent references, see:
              D. Pattinson, ‎L. Schröder eds, Proceedings of the 11th International conference on Coalgebraic Methods in Computer Science, LNCS 7399, Springer, 2012;      A. Kurz, D. Petrisan, P. Severi, F-J. De Vries, Nominal Coalgebraic Data Types with Applications to Lambda-Calculus, Logical Methods in Computer Science, Vol. 9(4:20), pp. 1–51, 2013;      E. Prebet, Typed Behavioural Equivalences in the Pi-Calculus, PhD Thesis, Ens de Lyon & Università di Bologna, defended September 27, 2022)

 G. Longo, E. Moggi.  The Hereditary Partial Effective Functionals and Recursion Theory in Higher Types.  "The Journal of Symbolic Logic", Vol. 49, No. 4 , pp. 1319-1332, Dec., 1984.   (HPEF-recur-higher-types.pdf)

 G. Longo, E. Moggi.  Cartesian closed categories of enumerations and effective type structures.  in: Khan, MacQueen, Plotkin (Eds.), Symposium on "Semantics of Data Types", LNCS, vol. 173, Springer Verlag, 1984.   (CCcateg-for-types.pdf)
              For the exchange that motivated these two papers: Four Letters by Georg Kreisel
              (for a recent reference to these two papers, see a very interesting one:
              J.R. Cockett, P.J. Hofstra, Introduction to Turing categories, Annals of Pure and Applied Logic 12; 156(2-3):183-209, 2008.)

(This section 7 is dedicated to the Journals' Impact Factor that is based on the citations in the two years following publication and to the referee of one of the papers in Biology above who wrote: ``the authors should not quote papers that are more than two or three years old'' ... see Bibliometrics9-13rev.pdf for more.)

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