Gideon Noß
University of Bonn
“Semantic paradoxes like Curry’s paradox arise in every language with sufficient expressive power to be able to express self-referential sentences and contain a naive truth predicate. They question our beliefs about rationality and valid reasoning, as they seem to lead from acceptable premises to unacceptable conclusions with otherwise acceptable reasoning.
Recently, a class of logics which challenge the validity of central structural rules of classical logic has been developed and applied to truth theoretic considerations in order to solve the problem of arising semantic paradox.
As such structural rules like transitivity, monotonicity, or contraction are deemed by many to be necessary properties of logical consequence, critics question the logicality of the emerging systems. Further, there is no consensus as to which of the structural rules might be the key component of paradoxicality, while abandoning each of them leads to wide ranging changes on the consequence relation. Critics, then, argue that abandoning one or more structural rules is an ad hoc theory choice which is not to be preferred over existing approaches like Dialetheism which seem to maintain at least all structural rules of the classical logical consequence relation. Proponents of the new approaches reply that going substructural allows to formulate solutions to all semantic paradoxes with a unity that the existing approaches can not reach.
Relying on a pluralistic notion of logical consequence and questioning the necessity of the substructural properties for the consequence relation, I will consider several desiderata for theories of truth as well as traditional criteria for theory choice and compare how well a non-transitive, a non-contractive, and a dialetheistic logic measure among these. Taking Curry’s paradox as an example phenomena to be explained by a proper theory of truth, I aim to show that from these competitors, the substructural approaches satisfy more of the relevant criteria, hence abductively justifying the conclusion that we have solid ground to consider substructural approaches as good explanations for what goes wrong with paradoxical reasoning.”
Chair: Ante Debeljuh
Time: 03 September, 15:20 – 15:50
Location: SR 1.007
SOPhiA 2026 