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Erik Stei, Non-Normative Logical Pluralism and the Revenge of the Normativity Objection, The Philosophical Quarterly, Volume 70, Issue 278, January 2020, Pages 162–177, https://doi.org/10.1093/pq/pqz040
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Abstract
Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that |$\mathcal {L}_{1}$| and |$\mathcal {L}_{2}$| are correct logics that coincide except for the argument from Γ to ϕ, which is valid in |$\mathcal {L}_{1}$| but invalid in |$\mathcal {L}_{2}$|. If you accept all sentences in Γ, then, by normativity, you make a mistake if you reject ϕ. In order to avoid mistakes, you should accept ϕ or suspend judgment about ϕ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative.