Philosophy of non-classical logics: Towards problems of paraconsistency & paracompleteness

June 26-27, 2015

Workshop organized by

Marcos Silva
(Federal University of Ceara, Brazil)


Ingolf Max
(University of Leipzig, Germany)

You can download here the poster

There is an ongoing philosophical and logical debate about motivations in accepting or rejecting the principle (law) of (non-)contradiction and the principle (law) of excluded middle. A logic rejecting the principle of non-contradiction is called paraconsistent and a logic rejecting the principle of excluded middle is called paracomplete. If both principles are duals of each other we have some reason to reject both principles and get paranormal systems. But what does it really mean to reject a classical principle (law)? And what are the philosophical consequences for this refusal? In which sense would it still be possible to defend nowadays that there is just one true logic, if we have such a great diversity of logics?

Among the famous logical systems which are paraconsistent but not paracomplete are, for instance, the da Costa systems. Intuitionist logics are paracomplete but not paraconsistent. And a lot of systems of relevant logic are paraconsistent as well as paracomplete. To evaluate these systemsí philosophical relevance, we have to inter alia examine the logical form of their atomic formulas, the logical behavior of their negation, conjunction and disjunction as well as the properties of logical consequence relations. From a philosophical point of view it is very important to understand which elements are responsible for such deviations from classical logic. E.g., do we have only local reasons? In the case of Jaskowski's version of paraconsistent logic we have to change the conjunction. In the da Costa systems mainly negation is under attack. Or do we have global reasons like in systems of first degree entailments? (Belnap, Dunn, Priest). What is the position of paracomplete, intuitionist approaches (Brouwer, Heyting and their followers)?

This workshop shall represent a privileged platform to evaluate proposals for a more integrated and general approach to philosophical motivations and consequences in the emergence of non-classical logics.

Call for papers

Topics may include:

  • logical monism & logical pluralism
  • philosophical motivations for creating non-classical logics (dialethism, anti-realism, relevantism etc.)
  • local vs. global and formal vs. application-oriented reasons for paraconsistency and/or paracompleteness
  • non-explosiveness of logical consequence
  • trivialization strategies and classical logic
  • philosophy of contradiction and inconsistency (Hegel, Wittgenstein, Meinong, Heraclites, Indian Philosophy etc.)
  • philosophy of constructivism (Poincaré, Brouwer, Heyting, Kolmogorov, Wittgenstein, Lorenzen, Dummett, Prawitz etc.)
  • philosophical relations between paraconsistency and paracompleteness

Abstracts (500 words maximum) should be sent via e-mail before November 15th 2014 to:  

Notification of acceptance: December 1st 2014.








Keynote Speaker

Graham Priest
City University of New York, USA

Contributing Speakers

Patrick Allo, Centre for Logic and Philosophy of Science, Free University of Brussels, VUB, Belgium, Hard and soft logical information

Diderik Batens, Ghent University, Belgium, A piece of logical handicraft illustrating a philosophical position

Ross Brady , Dpt of Philosophy, La Trobe University, Australia, The use of definitions and their logical representation in paradox derivation

Walter Carnielli and Abilio Rodrigues, State University of Campinas and Federal University of Minas Gerais, Brazil, An epistemic approach to paraconsistency: dealing with evidence and truth

Massimiliano Carrara, University of Padua, Padova, Italy, On the exclusivity of logical negation

Cian Chartier ILLC, University of Amsterdam, The Netherlands, Indefinite extensibility from revision sequences

Diogo Henrique Bispo Dias Dpt of Philosophy, USP, Brazil, A paraconsistent defense of logical pluralism and relativism

Matthias Jenny, Dpt of Philosophy, Massachussets Institute of technology, Cambridge, USA, Denial won't get you anywhere

Ingolf Max, University of Leipzig, Germany, The explication of paraconsistency, dialetheism and paracompleteness in classical logic syntactically extended by functorial variables

David Miller, University of Warwick, UK, The non-classical side of classical logic

Itala M. Loffredo D'Ottaviano and Evandro Gomes State University of Campinas and State University of Maringa, Brazil Vasiliev's ideas for non-Aristotelian logics: insight towards paraconsistency

Pawel Pawlowski and Rafal Urbaniak Ghent University, Belgium, Gdansk University, Poland, First steps towards non-classical logic of informal provability

Abilio Rodrigues and Walter Carnielli, Federal University of Minas Gerais and State University of Campinas, Brazil, What would be a falsitymaker for the principle of non-contradiction

Fabien Schang, National Research University Higher School of Economics, Moscow, Russia, Catuskoti: Paracomplete, Paraconsistent, Both, or None?

Koji Tanaka, Australian National University, Canberra, Australia, Paraconsistency and external justification

James Trafford University for the Creative Arts, Epsom, United Kingdom, Abstract duality and co-constructive logic

Alper Turken, Bogazici University, Istanbul, Turkey Hegel and the idea of negative self-relatedness

Elia Zanardi, University of Lisbon, Portugal, Against the world