Abstract
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.
Highlights
The history of logic has themes running from description of ontological structures in the world to elucidating patterns in inferential or communicative human activities
PAL update has a natural extension to dynamic-epistemic logics with much more drastic model changes modeling the dynamics of partly private information, and it is unclear if these richer transformations have any role in a dynamic semantics
Can we provide alternative explicit accounts leaving the notion of consequence standard, while adding vocabulary to bring out the origins of the new consequence notions? As in all our earlier illustrations, we need a semantic platform for doing so, and the choice for this will depend on the concrete motivation for the new consequence relation
Summary
The history of logic has themes running from description of ontological structures in the world to elucidating patterns in inferential or communicative human activities For both strands, the mathematical foundational era added a methodology of formal systems with semantic notions of truth and validity and matching proof calculi. There is another line, where we use new concepts to modify or enrich our understanding of what the old logical constants meant, or what the old notion of valid consequence was meant to do This leads to non-standard semantics, perhaps rethinking truth as ‘support’ or ‘forcing’, and to alternative logics whose laws differ from those of classical logic on the original vocabulary of connectives and quantifiers.
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