The calculus of names -- The legacy of Jan {\L}ukasiewicz

TL;DR

This paper explores Jan {2}ukasiewicz's foundational work on the calculus of names, highlighting its historical development, extensions, and its significance in modern logic and syllogistic studies.

Contribution

It presents the origins of the calculus of names, extends Lukasiewicz's initial system, and discusses alternative modern approaches, emphasizing Lukasiewicz's lasting legacy.

Findings

Lukasiewicz's calculus of names initiated the study of logical systems involving names and functors.

Extended systems build upon Lukasiewicz's original framework, broadening its scope.

Modern logic offers alternative approaches to Lukasiewicz's syllogistic analysis.

Abstract

With his research on Aristotle's syllogistic, Jan {\L}ukasiewicz (1934, 1939, 1957, 1963) initiates the branch of logic known as the calculus of names. This field deals with axiomatic systems that analyse various fragments of the logic of names, i.e., that branch of logic that studies various forms of names and functors acting on them, as well as logical relationships between sentences in which these names and functors occur. In this work, we want not only to present the genesis of the calculus of names and its first system created by {\L}ukasiewicz. We also want to deliver systems that extend the first. In this work, we will also show that, from the point of view of modern logic, {\L}ukasiewicz's approach to syllogistic is not the only possible one. However, this does not diminish {\L}ukasiewicz's role in the study of syllogism. We believe that the calculus of names is undoubtedly the legacy of {\L}ukasiewicz.