Inquisitive Semantics and the Paradoxes of Material Implication
Pawel Lojko

Abstract:
The Paradoxes of Material Implication concern entailments which are
valid according to Classical Propositional Logic but which contradict
universal linguistic intuitions. These contradictions constitute one
of the best-known objections to the classical truth-functional account
of indicative conditionals.
  In this thesis we give an Inquisitive Semantic account of the
Paradoxes of Material Implication. We focus on the sixteen paradoxical
inferences that can be found in the literature. We formalize, motivate
and discuss two inquisitive systems: Basic Inquisitive Semantics and
Radical Inquisitive Semantics. Further, we compare the Basic
Inquisitive Semantic and the Radical Inquisitive Semantic account of
the Paradoxes of Material Implication with the accounts given by
Lewis' Strict Conditional Logic S2, Stalnaker's Conditional Logic C2,
Update Semantics and Relevance Logic B. We also discuss the extent to
which the inquisitive account of implication reflects the
philosophical underpinnings of different non-classical accounts.
  We demonstrate that Radical Inquisitive Semantics is the only system
that allows us to account for all of the Paradoxes of Material
Implication.  We conclude that the account given by Inquisitive
Semantics is better than the classical account and has certain
advantages over other systems. Finally, we also suggest and discuss
several possibilities for further research.