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The consistency of Leśniewski's mereology relative to the real number system1

Published online by Cambridge University Press:  12 March 2014

Robert E. Clay
Robert E. Clay*
Affiliation:
University of Notre Dame
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Extract

It is known that Leśniewski constructed an interpretation of mereology in the real number system using binary expansions.2 Unfortunately, this construction is no longer extant. The following paper, except for a slight variation, is an attempt to reconstruct this interpretation.

Leśniewski probably considered sequences of 0's and I's (except for the sequence of all 0's) and defined a first sequence as an element of the second if every place in which the first has a I, so also does the second.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 251 - 257
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

This paper is part of a thesis written under the direction of Professor Boleslaw Sobociński and submitted to the graduate school of the University of Notre Dame in partial fulfillment of the requirements for the degree of Doctor of Philosophy with Mathematics as major subject in August, 1961.

References

[1]Clay, R. E., The relation of weakly discrete to set and equinumerosity in mereology, Notre Dame Journal of formal logic, vol. VI (1965), pp. 325–340.Google Scholar
[2]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
[3]Sobociński, B., Studies in Lešniewsk's mereology.Yearbook for 1954–55 of Polish Society of Arts and Sciences Abroad, vol. V. London, 1955, pp. 34–48.Google Scholar