Intuitionism and logical revision
The topic of this thesis is logical revision: should we revise the canons of classical reasoning in favour of a weaker logic, such as intuitionistic logic? In the first part of the thesis, I consider two metaphysical arguments against the classical Law of Excluded Middle-arguments whose main premise is the metaphysical claim that truth is knowable. I argue that the first argument, the Basic Revisionary Argument, validates a parallel argument for a conclusion that is unwelcome to classicists and intuitionists alike: that the dual of the Law of Excluded Middle, the Law of Non-Contradiction, is either unknown, or both known and not known to be true. As for the second argument, the Paradox of Knowability, I offer new reasons for thinking that adopting intuitionistic logic does not go to the heart of the matter. In the second part of the thesis, I motivate an inferentialist framework for assessing competing logics-one on which the meaning of the logical vocabulary is determined by the rules for its correct use. I defend the inferentialist account of understanding from the contention that it is inadequate in principle, and I offer reasons for thinking that the inferentialist approach to logic can help model theorists
Murzi, Julien
Intuitionism and logical revision. The topic of this thesis is logical revision: should we revise the canons of classical reasoning in favour of a weaker logic, such as intuitionistic logic? In the first part of the thesis, I consider two metaphysical arguments against the classical Law of Excluded Middle-arguments whose main premise is the metaphysical claim that truth is knowable. I argue that the first argument, the Basic Revisionary Argument, validates a parallel argument for a conclusion that is unwelcome to classicists and intuitionists alike: that the dual of the Law of Excluded Middle, the Law of Non-Contradiction, is either unknown, or both known and not known to be true. As for the second argument, the Paradox of Knowability, I offer new reasons for thinking that adopting intuitionistic logic does not go to the heart of the matter. In the second part of the thesis, I motivate an inferentialist framework for assessing competing logics-one on which the meaning of the logical vocabulary is determined by the rules for its correct use. I defend the inferentialist account of understanding from the contention that it is inadequate in principle, and I offer reasons for thinking that the inferentialist approach to logic can help model theorists
logical revision topic logical revision revise canon classical reason favour logic logic first_part consider metaphysical argument classical law excluded middle whose main premise metaphysical claim truth argue first argument basic revisionary argument validate parallel argument_conclusion alike dual law excluded middle law non contradiction either unknown know know true second argument paradox offer_new reason_think adopt logic heart matter second_part motivate framework assess compete meaning logical vocabulary determine rule correct use defend account contention inadequate principle offer reason_think logic help model theorist