The Deductibility of the Aristotelian Modal Syllogism E⼞I◇O-4 from the Perspective of Mathematical Structuralism

Volume 4, Issue 1, February 2024     |     PP. 23-33      |     PDF (229 K)    |     Pub. Date: April 18, 2024
DOI: 10.54647/philosophy720089    23 Downloads     2801 Views  

Author(s)

Feifei Yang, School of Philosophy, Anhui University, Hefei, China
Xiaojun Zhang, School of Philosophy, Anhui University, Hefei, China

Abstract
This paper firstly provides knowledge representations of Aristotelian modal syllogisms from the perspective of mathematical structuralism, and proves the validity of Aristotelian modal syllogism E⼞I◇O-4, and then by making full use of relevant definitions, facts, and some inference rules, formally derive other 30 valid modal syllogisms on the basis of one modal syllogism (i.e. E⼞I◇O-4) as a basic axiom. The reason why modal syllogisms are deducible is that the four Aristotelian quantifiers (i.e. all, no, some, and not all) can be mutually defined, and that so can the two modalities (i.e. ⼞ and ◇). Thus, one can establish a minimalist formal axiomatic system for modal syllogistic logic. This formal method is not only beneficial for the study of other types of syllogisms, but also for the development of a more intelligent inference engine for expert systems.

Keywords
Aristotelian modal syllogism; Aristotelian quantifier; symmetry; deducible relation

Cite this paper
Feifei Yang, Xiaojun Zhang, The Deductibility of the Aristotelian Modal Syllogism E⼞I◇O-4 from the Perspective of Mathematical Structuralism , SCIREA Journal of Philosophy. Volume 4, Issue 1, February 2024 | PP. 23-33. 10.54647/philosophy720089

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