Denial and Disagreement
Denial and Disagreement
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否认和分歧
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Massimiliano Carrara
中科院分区：
文献类型：
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作者：
Julien Murzi;Massimiliano Carrara
我们对Graham Priest最近提出的建议表示怀疑，即过剩理论家可以通过否认$$A$$ A来表达对$$A$$ A断言的异议。我们表明，如果否认是表达异议的一种手段，那么它必须是排他性的，也就是说，只有当被否认的东西是错误的时候，它才是正确的。因此，它不能用过剩理论家的语言表达，本质上和布尔否定不能用这种语言表达的原因是一样的。然后，我们转向另一种建议，Beall最近为其辩护(在分析73(3):438-445,2013；Rev Symb Log, 2014)，只表达真理和谬误，因此不同意。根据这一点，$$A$$ A的排他性语义状态，即$$A$$ A要么是真要么是假，可以通过在一个人的理论中添加一个形式为$$A wedge lnot A vdash ot $$ A∧A∈⊥的尖叫规则来表达，其中$$ot $$⊥包含琐碎性。然而，我们认为这个提议也行不通。结果是，供过于求的理论家面临两难境地：他们要么表示否认，要么表示反对，但不能两者兼而有之。在此过程中，我们为过剩理论家提供了一个排他性否认的双边逻辑——通常称为$$mathsf {LP}$$ LP的逻辑的扩展。
We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of $$A$$A by denying$$A$$A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of $$A$$A, that $$A$$A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form $$A wedge lnot A vdash ot $$A∧¬A⊢⊥, where $$ot $$⊥ entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called $$mathsf {LP}$$LP.