Non-Transitive Logics: A New Approach to Paradoxes

The Research Problem

paradox is a seemingly valid argument with seemingly true premises and seemingly false conclusion. Of course, not all these appearances can be true. Sometimes it is particularly difficult to reject the truth of the premises or the falsity of the conclusion, so that the only option left is revising the logic underlying the argument. This task can be carried out in different ways. In a first approach, we could reject some of the inferences present in the argument. This sort of strategy, however, comes usually with the unwanted loss of some concomitant inferences. 

Now arguments in general require a certain number of inferences in order to reach the conclusion from the premises. A second strategy consists, not in the rejection of some particular inference, but in the rejection of the way inferences are related in the argument (that is, in the rejection of some "metainference"). The present project aims to study the foundations, possibilities of formulation and application of a strategy of this second kind. According to this strategy, logical consequence might fail to be transitive.

Nested Applications




Pablo Cobreros, University of Navarra

Paul Egré, Institut Jean Nicod

Rosanna Keefe, University of Sheffield

Paloma Pérez-Ilzarbe, University of Navarra

David Ripley, University of Melbourne

Robert van Rooij, University of Amsterdam

Luca Tranchini, Tübingen university



  • 5-6 de mayo de 2017: Workshop on Logical Consequence.


  • 22-26 de agosto de 2016: Pablo Cobreros y José Martínez (22-26 de agosto 2016). Introducción a las Lógicas No-Clásicas. Curso de verano de las Universidades Navarras.

  • R. van Rooij (2016). `Comparing some Substructural Strategies Dealing with Vagueness', IPMU 2016, Eindhoven, The Netherlands.

    R. van Rooij (2016) `Analysing communicative diversity via the Stag Hunt',  ECAI 2016 International Workshop on Diversity-Aware Artificial Intelligence, The Hague, The Netherlands.

    R. van Rooij (2016),  `Stereotypes or Prototypes’, Conference on Cognitive Structures, Duesseldorf, Germany.

  • Mayo-Julio de 2016: David Ripley: Towards a naive type theory in:

    **History and Philosophy of Logic Session, ASL North American meeting 2016, University of Connecticut, May 2016
    ** Australasian Association for Logic 2016 meeting, July 2016

  • Junio de 2016: Pablo Cobreros: Identity and the sorites paradox. Fifth Italian Conference in Analytic Ontology, Padova.

  • 20 y 21 de mayo de 2016. Navarra Workshop on Logical Consequence

  • Febrero de 2016: David Ripley: Classical recapture via conflation in Logic and Metaphysics Workshop, CUNY Graduate Center.

  • 10 de febrero de 2016: Paloma Pérez-Ilzarbe. De primo ad ultimum. El encadenamiento de inferencias y la naturaleza del 'seguirse de'. Pamplona, Universidad de Navarra.


  • Agosto 2015: David Ripley: Axiomatisation without cut in SADAF, Buenos Aires, August 2015

  • 24, 25 y 26 de agosto de 2015: Curso Lógica y Fundamentos de la Matemática

  • Junio y Julio de 2015: 

David Ripley (2015) 'Transitivity' in:
** AAL 2015, University of Sydney, July 2015
** GroLog, University of Groningen, June 2015

  • Julio 2015: David Ripley: Vagueness, tolerance, and substructural logic in  AAP 2015, Macquarie University.

  • Junio 2015: David Ripley:  Uniqueness without reflexivity or transitivity in Non-classical Abstract Logics, Unilog 5.

  • 18 de marzo de 2015: 'The Sophisma Splendida: Transitivity of Consequence in Medieval Logic'. Lugar: Aula 30. Organiza: Proyecto Non-Transitive Logics. Contacto: Pablo Cobreros. 


  • 3 y 4 de noviembre de 2014, Mini-Course on Proof Theory by Luca Tranchini in the University of Navarra, Pamplona.

  • 201X (en evaluación) P. Cobreros, P Egré, D Ripley, R van Rooij, “Tolerance and degrees of truth”.

  • 201X (en evaluación) Paul Egré (con Emmanuel Chemla), “Suszko's Problem: Mixed Consequence and Compositionality”.

  • 201X (aceptado) P. Cobreros y L. Tranchini, “S’valuationism”, en S. Oms and E. Zardini eds. The Sorites Paradox, Cambridge University Press: Cambridge.

  • 201X (aceptado) Paul Egré (con Jérémy Zehr), “Are Gaps preferred to Gluts? A closer look at borderline contradictions”. En Elena Castroviejo, Galit Weidman Sassoon, y Louise McNally eds. The Semantics of Gradability, Vagueness, and Scale Structure - Experimental Perspectives. Language, Cognition, and Mind, Springer: Switzerland.

  • 201X (aceptado) Rosanna Keefe, “Prefaces, Sorites and Guides to Reasoning”, en L. Walters and J. Hawthorne eds. Conditionals, Probability, and Paradox: Themes from the Philosophy of Dorothy Edgington, Oxford University Press.

  • 201X (aceptado) Rosanna Keefe (con Jessica Leech), “Modal essentialism and logical pluralism”, en Ivette Fred and Jessica Leech eds. Being Necessary: Essays in Honour of Bob Hale, Oxford University Press.

  • 201X (aceptado) David Ripley, “On the 'transitivity' of consequence relations”. 

  • Journal of Logic and Computation, forthcoming.

  • 201X (aceptado) David Ripley, “Blurring: an approach to conflation”, Notre Dame Journal of Formal Logic.

  • 201X (aceptado) Luca Tranchini, “Natural deduction for bi-intuitionistic logic” en Journal of Applied Logic.

  • 201X (aceptado) Luca Tranchini, “Proof-theoretic harmony: Towards an intensional account”, Synthese. DOI: 10.1007/s11229-016-1200-3

  • 201X (aceptado) Luca Tranchini Pablo Cobreros, “Proof analysis of global consequence”, Logique et Analyse, Special Issue: How to say 'yes' or 'no': Logical approaches to modes of assertion and denial.

  • 201X (aceptado) P. Cobreros, P Egré, D Ripley, R van Rooij, “Tolerant Reasoning: Nontransitive or Nonmonotonic?” Synthese

  • 2017. Pablo Cobreros, Lógica matemática. Diccionario Interdisciplinar Austral, Claudia E. Vanney, Ignacio Silva and Juan F. Franck eds. =ógica_matemática

  • 2017. Paul Egré (con E. Chemla y B. Spector). Characterizing logical consequence in many-valued logics, Journal of Logic and Computation.


  • 2017. Robert van Rooij, “As knowable as possible”, en C. Baskent, L. Moss y R. Ramanjum eds. Rohit Parikh on Logic, Language and Society, Springer: 53-65.

  • 2017. David Ripley,  “Bilateralism, coherence, warrant”, en Friederike Moltmann Mark Textor eds. Act-Based Conceptions of Propositional Content, Oxford University Press.

  • 2017. David Ripley, Vagueness is a kind of conflation, Logic and Logical Philosophy, 26(1):115-135.

  • 2017. Luca Tranchini, Peter Schroeder-Heister, Ekman's paradox, Notre Dame Journal of Formal Logic. DOI: 10.1215/00294527-2017-0017

  • 2016. P. Cobreros, P Egré, D Ripley, R van Rooij, Comparing some Substructural Strategies Dealing with Vagueness, J.P. Carvalho,M-J.Lesot, U. Kaymak, S. Vieira, B. Bouchon-Meunier, R. Yager (eds.),in Information Processing and Management of Uncertainty in Knowledge Based Systems, IPMU, Springer: 161-172.

  • 2016. Pablo Cobreros, Filosofía de las matemáticas. Diccionario Interdisciplinar Austral, Claudia E. Vanney, Ignacio Silva and Juan F. Franck eds.ía_de_las_matemáticas

  • 2016. Paloma Pérez-Ilzarbe, Jerónimo Pardo on the formality of the expository syllogism, en Formal Approaches and Natural Language in Medieval Logic (L. Cesalli et al, eds.), Barcelona-Roma: 325-340.

  • 2016. Luca Tranchini, Proof-theoretic semantics, paradoxes and the distinction between sense and denotation, Journal of Logic and Computation 26(2), pp. 495-512. DOI:10.1093/logcom/exu028

  • 2015. P. Cobreros, P Egré, D Ripley, R van Rooij, “Pragmatic interpretations of vague expressions: strongest meaning and nonmonotonic consequence”, Journal of Philosophical Logic 44: 375–393

  • 2015. P Cobreros, P Egré, D Ripley, R van Rooij, “Vagueness, Truth and Permissive Consequence”, en Acourioti, T et al. (eds) Unifying the Philosophy of Truth, Springer.

  • 2015. Rosanna Keefe, Modelling Higher-Order Vagueness: Columns, Borderlines and Boundaries, Proceedings of the Aristotelian Society, Supplementary Volume 89: 89-108.

  • 2015. Paloma Pérez-Ilzarbe, reseña de Friend, M., Pluralism in mathematics: a new position in philosophy of mathematics (2014). En Mathematical Reviews.

  • 2015. David Ripley, Naive set theory and nontransitive logic, Review of Symbolic Logic, 8(3):553-571.

  • 2015. David Ripley, Contraction and closure, Thought, 4(2):131-138.

  • 2015. David Ripley, Comparing substructural theories of truth, Ergo, 2(13):299-328.

  • 2015. David Ripley, 'Transitivity' of consequence relations, en Logic, Rationality, and Interaction: Proceedings of LORI V, Wiebe van der Hoek, Wesley Holliday y Wen-Fang Wang eds: 328-340.

  • 2015. David Ripley (con Rohan French), Contractions of noncontractive consequence relations, Review of Symbolic Logic, 8(3):506-528.

  • 2015. Luca Tranchini, Harmonising harmony, The Review of Symbolic Logic 8(3): 411-423. DOI: 10.1017/S1755020315000179

  • 2014. P. Cobreros, P Egré, D Ripley, R van Rooij, Priest's motorbike and tolerant identity. En Roberto Ciuni, Heinrich Wansing, Caroline Wilkommen, Recent Trends in Philosophical Logic: 75-85.

  • 2014. Rosanna Keefe, What Logical Pluralism Cannot Be, Synthese 191: 1375-1390.

  • 2014. Paloma Pérez-Ilzarbe, María Cerezo, Truth and Bivalence in Aristotle: An Investigation into the Structure of Saying, en N. Öffenberger, A. Vigo, eds.: Logik, Naturphilosophie, Dialektik. Neue internationale Beiträge zur modernen Deutung der Aristotelischen Logik Olms, Hildesheim/Zürich/New York: 75-103.

  • 2014. Paloma Pérez-Ilzarbe, reseña de Oliver, A. y Smiley, T., Plural logic (2013). En Mathematical Reviews.

  • 2014. Robert van Rooij, Tolerant identity, en D. Gutzmann, J. Köpping, and C. Meier eds. Approaches to Meaning: Composition, Values, and Interpretation, Brill, Leiden:187-202.