Topics in logical anti-exceptionalism and paraconsistent logics

Abstract

The rivalry between classical logic and its non-classical contenders occupies the centre stage in contemporary philosophical logic. The central issue is to know how to choose a logical system (or theory thereof) among the many available possibilities. A recent proposal, named logical anti-exceptionalism, claims that logical disputes may be settled through the employment of the same theory choice methods used in the hard sciences, i.e., by inference to the best explanation and the analysis of the theoretical virtues of each disputant theory. This philosophical thesis has been explored as a research agenda to investigate issues such as the revisability of logic, the a priori character of logical knowledge, the logical pluralism/monism debate, the methods for theory choice in logical theorizing, and other related questions. The present monograph is an investigation of foundational topics within logical antiexceptionalism and its relation to one specific class of non-classical logics, namely paraconsistent logics. For this, the thesis is composed of two parts. The first part explores foundational issues of the anti-exceptionalist debate by applying methods and conceptual tools from the philosophy of science. Topics such as theory-ladenness in logical theory choice, the underdetermined character of logical data, the adequate notion of data for paraconsistent logics, the role of theoretical virtues in logical disagreement, as well as the adequate notion of aprioricity for anti-exceptionalist purposes, are introduced and addressed. The second part of the thesis is devoted to technical aspects of paraconsistent logics. The main results are the introduction of a new family of nonmonotonic first-order paraconsistent logics capable of satisfying core metaproperties of nomonotonic logics. In addition, we introduce a novel proof of compactness for finitely-valued first-order logics endowed with a nondeterministic semantics.