Leśniewski's systems of logic and foundations of mathematics
type: Item
instance of: scholarly article
title: Leśniewski's systems of logic and foundations of mathematics
zbMATH Open document ID: 1280.03004
DOI: 10.1007/978-3-319-00482-2
author: Rafal Urbaniak
published in: Trends in Logic -- Studia Logica Library
publication date: 2013-06-18T00:00:00Z
review text: From the author's introduction: ``[M]y intention is to provide a survey that covers many aspects of what Leśniewski published, make a clear distinction between what views can be assigned to him based on textual evidence and what he is reported or believed to have claimed, and, when his philosophical views are discussed, assesses them critically.'' ``[T]he intended audience of this book includes philosophy majors, graduate students and professional philosophers interested in logic, mathematics and their philosophy and history.'' Also very short comments on other surveys of Leśniewski's work, a brief biography, and a survey of primary sources are given in the introduction. Chapter 2 is a discussion of Leśniewski's early philosophical views. Chapter 3 concerns Protothetic. The author describes here the historical context of the development of Protothetic, explains the notorious notation used by Leśniewski and his motivations for Protothetic. Also, all the gradually developed systems of Protothetic are described, and examples of proofs are given. In Chapter 4, devoted to Ontology, the differences of Ontology from classical logic are pointed out, and the language and the original axiomatization of the former are described. Also, some philosophical moments and relations between Ontology and Russell's theory of descriptions are discussed here. The subject of Chapter 5 is Mereology. First, Leśniewski's motivation -- a nominalistically acceptable alternative to the Cantorian set theory as a foundational system -- is analyzed in detail. Then the author compares four successive axiomatizations of Mereology (given by Leśniewski himself) and analyzes the potential role of Mereology in the foundations of mathematics; his assessment is rather negative. The goal of Chapter 6 is to trace the origin and development of a popular misunderstanding that the consistency and conservativeness requirements on definition go back to Leśniewski's work. It is explained why Leśniewski's definitio…
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A70
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B15
Mathematics Subject Classification ID: 03E99
zbMATH DE Number: 6176496
zbMATH Keywords: higher-order quantification
zbMATH Keywords: Leśniewski
zbMATH Keywords: Mereology
zbMATH Keywords: Ontology
zbMATH Keywords: paradoxes
zbMATH Keywords: Protothetic
zbMATH Keywords: set theory
zbMATH Keywords: theory of definitions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-00482-2
OpenAlex ID: W615916062
Wikidata QID: Q114964646
description: scientific article; zbMATH DE number 6176496