论文标题
古代量词逻辑
Ancient Quantifier Logic
论文作者
论文摘要
在本文中，我们认为并提供了证据，证明了在古代哲学中使用自然扣除规则。更具体地说，我们提供了对此类规则的使用和理解的证据，用于多次量化，而不是非必要的单质谓词和嵌套的量词，而不是不必要的修正谓词 - 所有这些都符合具有处理多种一般性的机制。这项工作旨在补充Bobzien和Shogry \ Cite {Mult}的论文，该论文认为Stoic逻辑学家已经拥有处理多种一般性所需的所有要素。虽然我们还从Sextus Empiricus（Stoic Logic的常见来源）中提取了一些证据，但我们的重点不是Stoics，而是在亚里士多德，Euclid，Galen和Proclus的逻辑方面。 Bobzien和Shogry主张Stoic逻辑通过制度和通用 - 通用量化表达多重普遍性的能力是由TIS + Ekeinos在有条件下的构造表达的 - 但对推论规则的说法相对较少。我们的重点是量化器规则本身，特别是从自然推论的角度，有些入侵依赖性型理论。本文与Bobzien和Shogry分享了主张从亚里士多德到弗雷格的多元普遍性的逻辑的“更逐步发展”的总体目的。
In this paper we argue and present evidence for the use of the natural deduction rules for universal and existential quantifiers in ancient philosophy. More specifically, we present evidence for the use and understanding of such rules for multiple quantification over non-necessarily monadic predicates and nested quantifiers over non-necessarily monadic predicates - all which amounts to the possession of mechanisms for dealing with multiple generality. This work aims to complement the paper by Bobzien and Shogry\cite{mult} which argues that Stoic logicians had already all the elements necessary to deal with multiple generality. While we also draw some evidence from Sextus Empiricus (a common source for Stoic logic) our focus is not on the Stoics but on logical aspects of Aristotle, Euclid, Galen and Proclus. Bobzien and Shogry argued for the ability of Stoic logic to express multiple generality through regimentation and anaphora - universal quantification is expressed by the tis + ekeinos construction on conditionals - but say relatively little about deduction rules. Our focus is on the quantifier rules themselves, specifically from the point of view of natural deduction with some incursions into dependent-type theory. This paper shares with Bobzien and Shogry the general aim of arguing for a 'somehwhat more gradual development' of the the logic of multiple generality from Aristotle to Frege.
