Nonclassical logicians can apply classical metatheory while maintaining their principles, suggesting a new approach to logical validity.
Non-classical logicians may use a classical metatheory by admitting the permissibility of the classical inferences employed without admitting their logical validity. This way, non-classical logicians can use a classical metatheory without abandoning their non-classical principles. In the course of arguing for this claim, an analogy is drawn to the position most classical logicians are in with respect to classical metatheory requiring more mathematical inferences than most are willing to admit to be logically valid.
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Andrew Tedder (2025) studied this question.
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