In recent years, there has been an increasing debate about some philosophical aspects of paraconsistent logics. The focus of this controversy has been on whether the notion of philosophical interpretation of a logic is separable or independent from the notion of application of a logic. The concept of application of a logic, or applied logic, comes from Priest (2005). Given a purely technical system, one can apply it to different domains, such as computer science, programming, formal linguistics, electric circuits, neural networks, control systems, reasoning, etc. On the other hand, Barrio (2018) and Barrio and Da R´e (2018) have argued that there is a third dimension of a logic that consists in its philosophical interpretation. This aspect is related to some intended meaning of the logical constants and the consequence relation of the pure system. In this sense, while Barrio and Da R´e have argued that, at least in some contexts, the concept of philosophical interpretation has an explanatory role, Arenhart (2022) has claimed that this concept can be reduced to the notion of application. In this article, we will show that the philosophical interpretation of a logic has a crucial role in the usual stances of logicians and philosophers, which can and must be distinguished from the application of the system. We will focus on paraconsistent logics as study cases for our points since the debate has developed almost entirely around these systems. However, most of our claims can be applied to any logical system. In fact, throughout the paper, we will also provide examples using non-paraconsistent logics.
Barrio et al. (Thu,) studied this question.