There was a time when ‘logic’ just meant classical logic. The climate is slowly changing, and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it is designed to study.

中文翻译：

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反对经典的次一致性元理论

曾几何时，“逻辑”仅指经典逻辑。气候正在缓慢变化，非经典逻辑不能立即被忽视。然而，用于研究非经典逻辑属性的元理论通常是经典的。在本文中，我们将论证这种依赖经典元理论的做法是有问题的。特别是，我们将证明这是一种糟糕的做法，因为用于研究非经典逻辑的元理论通常会排除它旨在研究的逻辑。