Implicit and Explicit Stances in Logic
Johan van Benthem

Abstract:
We identify a pervasive contrast in logic between what we call implicit and explicit stances in design. Implicit systems change the meaning of logical constants and sometimes also the definition of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast in the traditional setting of intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, logics of games and other areas, to show the wide scope of these complementary styles of logical analysis and system design. Throughout we show how awareness of the implicit–explicit contrast leads to new logical questions, from straight- forward technical issues to when implicit and explicit systems can be translated into each other, raising new foundational issues about identity of logical systems. But we also show how a practical facility with these complementary working styles has philosophical consequences, as it throws doubt on strong philosophical claims made by just taking one stance and ignoring the alternative one. We will illustrate the latter benefit for the case of logical pluralism and hyper-intensional semantics. The definitive version of this paper has appeared in "The Journal of Philosophical Logic" on-line, autumn 2018.