The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g., that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up.

中文翻译：

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非凡的逻辑

这篇论文的目的是论证所有——或几乎all——逻辑规则有例外。特别是，有人认为这是我们应该从语义悖论中得出的一种道德。我们应该通过以某种方式修改逻辑来回应悖论的想法是熟悉的。但之前的提议主张用一些替代逻辑代替经典逻辑。也就是说，一些替代的规则系统，在这些系统中，这些规则毫无例外地被认为是理所当然的。目前的提议完全不同。据此，没有这样的替代逻辑。相反，古典逻辑保留了“一个真正的逻辑”的地位，但必须重新构想这种地位，以便与（几乎）所有允许例外的规则兼容。这似乎会对一系列广泛持有的关于逻辑的观点产生重大影响：例如，它是先验的，或者它是必要的。