Some Reflections on the Set-based and the Conditional-based Interpretations of Statements in Syllogistic Reasoning

TL;DR

This paper compares set-based and conditional-based interpretations of syllogistic statements, analyzing their implications for reasoning, especially regarding existential import, singular statements, and non-proportional quantifiers.

Contribution

It provides a detailed comparison of two main interpretations of syllogistic reasoning, highlighting their differences and implications for logical analysis.

Findings

Set-based interpretation emphasizes set relationships.

Conditional interpretation focuses on conditional propositions.

Differences impact reasoning about existential import and quantifiers.

Abstract

Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other one, the so-called conditional interpretation, assumes that quantified propositions talk about conditional propositions and how strong are the links between the antecedent and the consequent. Both interpretations are compared attending to three different questions (existential import, singular statements and non-proportional quantifiers) from the point of view of their impact on the further development of this type of reasoning.