This thesis investigates logico-philosophical aspects of using either a non-transitive or a non-reflexive logic to obtain a logic of truth in which truth is transparent. It enquires into and rejects the claim that restricting transitivity of entailment to accommodate transparent truth suffices to make the connective tonk acceptable by arguing that tonk as defined in a cut-free sequent calculus requires in addition that the logic is non-reflexive to be uniquely defined, and develops a semantics for tonk based on models with two valuations which delivers a non-transitive and non-reflexive logic. It develops a cut-free sequent calculus and two kinds of semantics for a non-reflexive logic of truth in which truth is transparent, one based on trivalent models and one based on models with two valuations. It shows how to define a non-transitive, a paraconsistent and a paracomplete logic of truth on the models with two valuations and develops a cut-free sequent calculus that captures all four logics. It investigates to which extent the non-reflexive and the non-transitive logic of truth can express their own meta-inferences, and shows among other things how one can employ the paraconsistent and the paracomplete logic to express the meta-inferences of the non-transitive and the non-reflexive logic respectively. Finally, it proves that the non-transitive logic of truth is omega-inconsistent and furthermore that transitivity is not required as assumption to establish that a logic in which truth satisfies the conditions of quantified standard deontic logic is omega-inconsistent.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:680981 |
| Date | January 2015 |
| Creators | Fjellstad, Andreas |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=228553 |
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