Title: Disagreeing and Agreeing in Logic

Abstract: The aim of the talk is to give an account of disagreement and agreement in
logic in terms of rules of acceptance, rejection, and suspension of
judgement. We thereby take acceptance, rejection, and suspension in logic to
be doxastic attitudes resulting from, respectively, assenting, dissenting,
or refraining from assenting and dissenting to arguments or propositions in
light of their logical validity/invalidity. We will characterize the notion
of disagreement between advocates of different logics as doxastic
noncotenability, and agreement in logic as a certain kind of doxastic
cotenability.
We will apply these notions of disagreement and agreement to
disagreements/agreements between advocates of three different logical
systems: classical logic, the paracomplete logic K3, and the paraconsistent
logic LP. In particular, we will discuss which doxastic attitudes those
logicians ought to have with regard to liar propositions.
In the last part of the talk, we will investigate in what sense a
disagreement in logic can be understood as a genuine form of disagreement.