How Classical, Paracomplete and Paraconsistent Logicians (Dis-)Agree

Abstract

This paper develops an account of disagreement and agreement in logic in terms of rules of acceptance, rejection, and suspension of judgement. Acceptance, rejection, and suspension in logic are thereby taken 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. Disagreement between advocates of different logics is characterized as a form of doxastic noncotenability. A full account of agreement in logic does not only require doxastic cotenability between two logicians. It is also necessary that they share the reasons that ground their respective doxastic attitudes. These notions of disagreement and agreement will be applied to disagreements/agreements between advocates of three different logical systems: classical logic, the paracomplete logic K₃, and the paraconsistent logic LP. In particular, it will be discussed which doxastic attitudes those logicians ought to have with regard to a proposition expressed by the Liar sentence. In the last part of the paper, it will be examined in what sense a disagreement in logic can be understood as a genuine disagreement, even if no single neutral intertheoretic concept of validity is available that is shared by all logicians.