Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-12T22:29:25.704Z Has data issue: false hasContentIssue false
  • English
  • Français

Consistency of lesniewski's mereology

Published online by Cambridge University Press:  12 March 2014

Czesław Lejewski
Czesław Lejewski*
Affiliation:
University of Manchester, England
Get access Rights & Permissions [Opens in a new window]

Extract

According to Sobociński's recollection, the consistency of Mereology was proved by Leśniewski by means of an appropriate interpretation within the framework of the theory of real numbers. His proof was never published, but in a recent paper R. E. Clay has succeeded in reconstructing a version of it.1 Clay's result amounts to showing that if Lesniewski's Ontology expanded by the addition of the axioms for the real numbers is consistent then Mereology is consistent. Without casting any doubts on the validity of the proof one can hardly fail to note that here we have a case where the consistency of a conceptually simple theory is made to depend on the consistency of a theory which from the point of view of intuition is far from being obvious.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 321 - 328
Copyright
Copyright © Association for Symbolic Logic 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Clay, R. E., Consistency of Leśniewski's mereology relative to real number system, this Journal, vol. 33 (1968), pp. 251–257.Google Scholar
[2]Lejewski, C., A note on a problem concerning axiomatic foundations of mereology, Notre Dame journal of formal logic, vol. 4 (1963), pp. 135–139.CrossRefGoogle Scholar
[3]Leśniewski, S., O podstawach matematyki (On the foundations of mathematics), Przegląd filozoficzny (Philosophical review), vol. 30 (1927), pp. 164–206; vol. 31 (1928), pp. 261-291; vol. 32 (1929), pp. 60-101; vol. 33 (1930), pp. 75-105; vol. 34 (1931), pp. 142-170.Google Scholar
[4]Słupecki, J., S. Leśniewski's calculus of names, Studia logica, vol. 3 (1955), pp. 7–76.CrossRefGoogle Scholar
[5]Sobociński, B., L'analyse de l'antinomie russellienne par Leśniewski, Methodes, vol. 1 (1949), pp. 94–107, 220-228, 308-316; vol. 2 (1950), pp. 237-257.Google Scholar
[6]Sobociński, B., Studies in Leíniewski's mereology, Year book for 1954–55 of Polish Society of Arts and Sciences Abroad, vol. 5 (1955), pp. 34–48.Google Scholar