Generalised Tarski’s Thesis Hits Substructure

  • Elia Zardini
Part of the Palgrave Innovations in Philosophy book series (PIIP)


At the core of JC Beall and Greg Restall’s brand of logical pluralism is Generalised Tarski’s Thesis, according to which an argument is valid iff, in every relevant case where every premise is true, so is the conclusion. I argue that the thesis implies that many philosophically interesting substructural logics are not legitimate relations of logical consequence. I then diagnose the clash as due to the fact that, in important ways, the thesis is not sensitive to intensional connections and to plurality in occurrences, values and models. Next, I extend the argument to the effect that the more general conception of logical consequence as guaranteed truth preservation clashes with substructurality. I conclude with a proposal as to how, for the substructural logics in question, we can still uphold a broadly semantic conception of logical consequence: given any such logic L, we can reinterpret truth-preservation conditionals with the notions of conjunction and implication available in L, and say that the fact that, in L, φ0, φ1, φ2 …, φi entail ψ is grounded in the fact that, in L, the conditional ‘If “φ0” is true and “φ1” is true and “φ2” is true … and “φi” is true, “ψ” is true’ is a logical truth. On this proposal, contrary to the contemporary Tarskian vulgate, it is logical consequence that is grounded in logical truth rather than vice versa.


Commutativity Contraction Generalised Tarski’s Thesis Logical consequence Logical pluralism Logical truth Monotonicity Reflexivity Substructural logics Transitivity Truth preservation 


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Elia Zardini
    • 1
    • 2
  1. 1.LanCog Research Group, Philosophy CentreUniversity of LisbonLisbonPortugal
  2. 2.International Laboratory for Logic, Linguistics and Formal Philosophy, School of PhilosophyNational Research University Higher School of EconomicsMoscowRussian Federation

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