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LOGICAL NIHILISM: COULD THERE BE NO LOGIC?*
Philosophical Issues Pub Date : 2018-09-25 , DOI: 10.1111/phis.12127
Gillian Russell 1
Affiliation  

Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all? Such a view might with justice be called logical nihilism and here I’ll assume a particular gloss on what that means: nihilism is the view that there are no laws of logic, so that all candidates—e.g. the law of excluded middle, modus ponens, disjunctive syllogism et. al.—fail. Nihilism might sound absurd, but the view has come up in recent discussions of logical pluralism. Some pluralists have claimed that different logics are correct for different kinds of case, e.g. classical logic for consistent cases and paraconsistent logics for dialethic ones. Monists have responded by appealing to a principle of generality for logic: a law of logic must hold for absolutely all cases, so that it is only those principles that feature in all of the pluralist’s systems that count as genuine laws of logic. The pluralist replies that the monist’s insistence on generality collapses monism into nihilism, because, they maintain, every logical law fails in some cases. 1(Cotnoir, forthcoming) distinguishes two kinds of logical nihilism, the first of which is the view that natural languages have no correct logic, and the second of which is that the consequence relation is empty. The view I have in mind here is the second. 2Monism has been the default view for many centuries, but it has recently been explicitly defended by Priest (2006). Pluralists include Carnap (1937), Varzi (2002), Beall and Restall (2006), Russell (2008) and Field (2009). There is not much recent mainstream literature on this kind of logical nihilism. Cotnoir (forthcoming) discusses a related view by the same name. Two close relatives of my version of nihilism are defended by Mortensen (1989), one based on the idea that nothing is necessary, the other on the idea that nothing is true in all mathematical models. Mortensen, on my reading, is a nihilist about logical truth, though I am unsure whether he would want to generalise this to logical consequence. Nihilism is also discussed in terms of models in Estrada-González (2015). 3Beall and Restall (2006); Priest (2006); Bueno and Shalkowski (2009); Russell (2013); Cotnoir (forthcoming) 4For example “The obvious reply to this argument is that it is only truth-preservation over all situations that is, strictly speaking, validity. One of the points about deductive logic is that it will work come what may: we do not have to worry about anything except the premises.” (Priest, 2006:202) 5“...we see no place to stop the process of generalisation and broadening of accounts of

中文翻译:

逻辑虚无主义:可能没有逻辑吗?*

逻辑一元论者和多元论者对正确的逻辑有多少存在分歧;一元论者说只有一个,多元论者说还有更多。难不成两者都错了,根本就没有逻辑?这种观点可能被称为逻辑虚无主义,在这里我将对其含义进行特殊的解释:虚无主义是这样一种观点,即不存在逻辑法则,因此所有候选者——例如排中律、modus ponens ,析取三段论等。al.——失败。虚无主义听起来可能很荒谬,但这种观点已经出现在最近关于逻辑多元主义的讨论中。一些多元论者声称不同的逻辑适用于不同的案例,例如经典逻辑适用于一致案例,超一致性逻辑适用于辩证案例。一元论者的回应是诉诸逻辑的一般性原则:逻辑定律必须绝对适用于所有情况,因此只有在所有多元主义系统中具有特征的那些原则才算作真正的逻辑定律。多元论者回答说,一元论者对一般性的坚持使一元论崩溃为虚无主义,因为他们坚持认为,在某些情况下,每条逻辑法则都失败了。1(Cotnoir,即将发表)区分了两种逻辑虚无主义,第一种是认为自然语言没有正确逻辑的观点,第二种是结果关系是空的。我在这里想到的观点是第二个。2 一元论已成为许多世纪以来的默认观点,但最近得到了 Priest (2006) 的明确辩护。多元主义者包括 Carnap (1937)、Varzi (2002)、Beall 和 Restall (2006)、Russell (2008) 和 Field (2009)。关于这种逻辑虚无主义,近期主流文献并不多。Cotnoir(即将出版)讨论了一个同名的相关观点。Mortensen (1989) 为我的虚无主义版本的两个近亲辩护,一个基于没有必要的想法,另一个基于在所有数学模型中都不是真的想法。在我的阅读中,莫腾森是逻辑真理的虚无主义者,尽管我不确定他是否想将其概括为逻辑结果。Estrada-González (2015) 的模型也讨论了虚无主义。3Beall 和 Restall (2006);牧师 (2006); 布埃诺和沙尔科夫斯基(2009 年);罗素(2013);Cotnoir(即将出版) 4例如“对这个论点的明显答复是,严格来说,只有在所有情况下都保持真实性才是有效的。关于演绎逻辑的要点之一是,无论发生什么,它都会起作用:除了前提之外,我们不必担心任何事情。” (Priest, 2006:202) 5“...我们认为没有任何地方可以阻止对
更新日期:2018-09-25
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