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
and proof-theorists alike justify their logical choices. I then scrutinize the
main meaning-theoretic principles on which the inferentialist approach to logic
rests: the requirements of harmony and separability. I show that these principles
are motivated by the assumption that inference rules are complete, and that the
kind of completeness that is necessary for imposing separability is strictly stronger
than the completeness needed for requiring harmony. This allows me to reconcile
the inferentialist assumption that inference rules are complete with the inherent
incompleteness of higher-order logics-an apparent tension that has sometimes
been thought to undermine the entire inferentialist project.
I finally turn to the question whether the inferentialist framework is inhospitable
in principle to classical logical principles. I compare three different regimentations
of classical logic: two old, the multiple-conclusions and the bilateralist
ones, and one new. Each of them satisfies the requirements of harmony and separability,
but each of them also invokes structural principles that are not accepted
by the intuitionist logician. I offer reasons for dismissing multiple-conclusions
and bilateralist formalizations of logic, and I argue that we can nevertheless be
in harmony with classical logic, if we are prepared to adopt classical rules for
disjunction, and if we are willing to treat absurdity as a logical punctuation sign.