The Forms of Categorical Proposition

TL;DR

This paper provides an exhaustive analysis of categorical propositions, comparing Term Logic and First-Order Logic, and proposes methods to resolve the existential import problem through model- and language-adaptive strategies, emphasizing the need for automation.

Contribution

It introduces two novel strategies for solving the existential import problem and advocates for a logic-based approach, including the development of an automated Prolog-like system for analyzing logical relations.

Findings

Model-adaptive strategy validates the square of opposition by restricting models.

Language-adaptive strategy extends logical form to validate the square universally.

An automated Prolog-like system is proposed for analyzing relations between categorical propositions.

Abstract

An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown that the famous problem of existential import may be solved in two ways: with a model-adaptive strategy, in which the square of opposition is validated by restricting the models; with a language-adaptive strategy, in which the logical form of categorical propositions is extended in order to validate the square in every model. The latter strategy is advocated in the name of logic, which means truth in every model. Finally, the present paper needs some automatic process in order to determine the nature of logical relations between any pair of the available 256 categorical propositions. This requires the implementation of a programming machine in the style of Prolog.