A Pragmatic Defense of Logical Pluralism
Cian Guilfoyle Chartier
Summary:
In this thesis, logic is conceived as a formal presentation of a guide to undertaking a rational practice, a guide which is itself constituted by epistemic norms and their consequences. This pragmatic conception of logic is a basis for logical pluralism, the view that there is more than one good, right, or correct logic. After all there may be more than one good practice, and more than one way to conceive the practice. This conception of logical pluralism we refer to as thoroughgoing logical pluralism.
The first chapter of the thesis outlines what we mean by "formal" in "formal presentation", and what we mean by "epistemic norms". Furthermore, the first chapter shows how thoroughgoing logical pluralism holds up against the usual challenges to logical pluralism, namely that logical pluralism is self-defeating and that logical pluralism collapses into logical monism. Finally, some other approaches to logical pluralism are accounted for and contrasted with the present account, including those of J. C. Beall and Greg Restall, Nikolaj Pedersen and Michael P. Lynch, and Stewart Shapiro and Teresa Kouri Kissel.
The second chapter of the thesis defends the view that the goal of logical revision is merely reflective equilibrium with respect to the norms that constitute the practice that the logic is formalising, along with the norms of the formalisation itself. This stance is defended against some influential objections, and contrasted with a number of recent accounts under the umbrella of logical anti-exceptionalism (including Timothy Williamson's, Ole Thomassen Hjortland's, and Graham Priest's). The approach of logical anti-exceptionalism in general is shown to be incompatible with the pragmatic conception of logic outlined in the previous chapter.
The third chapter of the thesis outlines a family of solutions to the semantic paradoxes in line with the preceding account of logical revision: the practitioner identifies the norms that they wish to keep, and revise their practice or formalisation accordingly. The approach is sufficiently general that the third chapter is really more of a case study. In particular, in line with what Roy T. Cook has observed, revenge liar paradoxes can be reconceived as demonstrating that the concept of truth value is indefinitely extensible (in Michael Dummett's sense) when our truth-talk includes predicates (such as those for "true and false and 'true and false'") that allow us to formulate these paradoxes. Kripkean fixed point extensions are shown to exist for an ordinal-valued hierarchy of truth-and-paradoxicality predicates to support a formal articulation of the phenomenon of revenge liar paradoxes, insofar as we may wish to articulate that phenomenon.
The fourth chapter of the thesis shows an account of how practitioners of different logics may understand and learn from each-other's proofs, given that a formal translation of one logic inside another that is sufficiently informative to present this account is allowed within linguistic constraints. A notion of interpretation is defended based on a practice-oriented principle of charity: that we make the best sense of others when we suppose they are following epistemic norms with maximal epistemic utility with respect to our possible interpretations of what their instrumental (goal-directed) desires could be. This notion of interpretative charity is employed in a pragmatics of communication for practitioners of different logics. This pragmatics is managed with a variation of Craige Roberts' Questions Under Discussion framework, characterising the potential ability of the formal mathematician to make the relevant inferences. This framework is applied to a few examples of conversations between practitioners, such as between a hypothetical intuitionistic and classical mathematician.