We identify a pervasive contrast between implicit and explicit stances in logical analysis and system design. Implicit systems change received meanings of logical constants and sometimes also the notion of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast for intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. This gives a working understanding of the contrast, though we stop short of a formal definition, and acknowledge limitations and borderline cases. Throughout we show how awareness of the two stances suggests new logical systems and new issues about translations between implicit and explicit systems, linking up with foundational concerns 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 design stance and ignoring alternative ones. We will illustrate the latter benefit for the case of logical pluralism and hyper-intensional semantics.
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This paper is based on lectures at the Hans Kamp 70 conference in Stuttgart 2010, Advances in Modal Logic, Copenhagen 2012, the Heyting Conference, Amsterdam 2013, the FEW Workshop on Formal Epistemology, Seattle 2017, as well as seminar presentations in Amsterdam, Beijing, New York, and Stanford. I thank members of these audiences for their feedback, as well as the referees of this paper, and Wesley Holliday, Thomas Icard, Steve Kuhn and Sonja Smets.
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van Benthem, J. Implicit and Explicit Stances in Logic. J Philos Logic 48, 571–601 (2019). https://doi.org/10.1007/s10992-018-9485-y