Variations on intra-theoretical logical pluralism: internal versus external consequence

  • Bogdan DicherEmail author


Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland (Australas J Philos 91(2):355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form of intra-theoretical logical pluralism.


Logical pluralism Intra-theoretical pluralism Logical consequence Internal consequence External consequence 



I am grateful to the audiences at the ALOPHIS Research Seminar (University of Cagliari), The Institute for Research in the Humanities (University of Bucharest), Triennial Conference of the Italian Society for Logic and Philosophy of Science (University of Bologna), ENFA 7: Encontro Nacional de Filosofia Analitica, 7th edition (University of Lisbon) where I have presented previous versions of this paper. I owe special thanks to Francesco Paoli for many helpful discussions on the issues broached here as well as for encouraging me to actually write this paper. At different stages, this work was supported by Regione Autonoma Sardegna within the Project CRP-78705 (L.R. 7/2007) “Metaphor and argumentation” and by the FCT – Fundação para a Ciência e a Tecnologia, Portugal, through the grant SFRH/BPD/116125/2016.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Centre for PhilosophyUniversity of LisbonLisbonPortugal

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