Krause, Décio
(2026)
Do we need to know what two is for defining `two'? Theory and metatheory: should they align?
[Preprint]
Abstract
In a recent debate after a PhD defence, we were involved in the discussion about what the mediaeval philosophers (after Buridan) called the \textit{logica utens}, the logic of common reason. The question was whether, in order to create a non-classical logical system or mathematical theory, we still use our standard logic in the metatheory, which, if pushed sufficiently, will approach \textit{classical logic}. All the contenders agreed that some further discussion was in order. In this note, I sketch my opinion with the intention of fostering discussion; the example of `defining two' serves as a background for the discussion.
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