Why logical praxis? On the one hand, there’s practice; on the other, theory. Practice is about applying logic to different contexts, producing arguments, establishing beliefs or theories, communicating ideas, or engaging in dialectical enquiry. Theory is about establishing, understanding, and meeting logical standards for coherence.

In classical logic, the standards are consistency. Establishing these standards involves developing a theory of validity, using formal languages and models to understand truth preservation and contradiction avoidance, and choosing axioms and rules to create proofs that meet these standards. All that is theoretical. Practice, on the other hand, involves getting students to translate arguments into formal language, laying them out in a recognisable standard form, and testing them for validity. Practice also includes creating models for “real-world” concepts like arithmetic, knowledge, truth, or other ideas that allow for conceptual analysis and formalisation.

This traditional dichotomy between practice and theory is rather limited. There’s a much richer world out there fit for logical treatment, which is what "Logic in the Wild" explores, with the slogans of logic being the “guardian of coherence” and providing a “neutral space of dialectical enquiry.” With this broader framework, practice involves seeking coherence in arguments, beliefs, or theories and communicating constructively in a neutral space of enquiry. Theory, accordingly, becomes richer because coherence can be measured in various ways, with consistency being only one method suitable for mathematical contexts. For more fluid contexts, other standards are required—standards that are neither too strict to prevent progress nor too loose to allow incoherent thought.

It’s because both practice and theory become much richer in this approach that praxis becomes crucial. Praxis is the meeting point of practice and theory, the link between the two that allows for better theories that are fit for purpose and applications that are appropriately guarded.