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The accident of logical constants
Thought: A Journal of Philosophy Pub Date : 2020-01-23 , DOI: 10.1002/tht3.440
Tristan Grøtvedt Haze 1
Affiliation  

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical.

中文翻译:

逻辑常量的意外

关于形式逻辑的性质和范围的工作过分关注逻辑词汇和逻辑外词汇之间的区别;哪种论证构成逻辑理论的面貌不仅取决于其逻辑术语的存量,还取决于其语法类别和构成方式的范围。此外,在某种意义上,逻辑术语是不必要的。Alexandra Zinke 最近指出命题逻辑可以在没有逻辑项的情况下完成。通过定义具有相同一阶逻辑的完整表达能力的无逻辑项的语言,我表明这更普遍地适用于逻辑。此外,在逻辑理论中,拥有不涉及逻辑术语的非平凡有效形式不仅仅是一种技术可能性。正如副词的情况所示,
更新日期:2020-01-23
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