Diagrams for Navya-Nyaya
Diagrams for Navya-Nyaya
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Navya-Nyaya 图表
DOI：
10.1007/s10781-020-09419-0
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发表时间：
2020
影响因子：
0.3
通讯作者：
Burton J
中科院分区：
文献类型：
--
作者：
Burton J
虽然许多作者在他们的Navya-Nyāya研究中广泛使用图表，但他们这样做是为了解释和说明概念，而不是为了用图表本身进行推理。图解推理的追随者通过指出图表和逻辑概念之间的关键结构对应关系来声称其潜力，可以说缺乏抽象表示，并使用诸如“良好匹配”和“象似性”等概念来描述这些关系。这种象似性的一个典型例子是使用欧拉图来描绘范畴三段论。由于印度逻辑中表达的意义在许多重要方面与西方传统逻辑不同，使用或改编后者发展的图表似乎排除了象似性。因此，以五经推理图式为中心的、反映Navya-Nyāya推理本质的图解的发展是有动机的。在本文中，我们扩展了Ganeri的方法，描绘了Vaie的本体与图形，包括语法旨在暴露的性质pentudāna。图给出了一个形式化的基础：即抽象语法，抽象定义的推理规则和图论语义。这些是第一个正式的逻辑图，旨在反映五言推理的性质。本文为进一步扩展形式主义以涵盖更多的Navya-Nyāya，并探索形式主义和Navya-Nyāya属性之间的对话奠定了基础。
Although a number of authors have used diagrams extensively in their studies of Navya-Nyāya, they have done so to explain and illustrate concepts, not with the goal of reasoning with the diagrams themselves. Adherents of diagrammatic reasoning have made claims for its potential by pointing to key structural correspondences between diagrams and logical concepts, arguably lacking in sentential representations, and describing these relations using concepts such as “well matchedness” and “iconicity”. A canonical example of this iconicity is the use of Euler diagrams to depict categorical syllogisms. Since the meaning of expressions in Indian logic differs in so many important ways from logic in the Western tradition, the use or adaptation of diagrams developed in the latter would seem to preclude iconicity. Thus, the development of diagrams which reflect the nature of inference in Navya-Nyāya, which centres on theanumānainference schema, is motivated. In this paper we extend Ganeri’s method of depicting the Vaiśeṣika ontology with graphs to include syntax intended to expose the nature ofanumāna. The diagrams are given a formal basis: i.e. abstract syntax, inference rules defined abstractly and a graph-theoretic semantics. These are the first formalised logical diagrams that aim to reflect the nature of theanumānainference. This paper lays the way for further work in extending the formalism to cover more of Navya-Nyāya, and in exploring a dialogue between properties of the formalism and of Navya-Nyāya.