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SOME REMARKS ON SUPPLEMENTATION PRINCIPLES IN THE ABSENCE OF ANTISYMMETRY

Published online by Cambridge University Press:  20 December 2012

LIDIA OBOJSKA
LIDIA OBOJSKA*
Affiliation:
Department of Mathematics and Physics, University of Natural Sciences and Humanities
*
*DEPARTMENT OF MATHEMATICS AND PHYSICS UNIVERSITY OF NATURAL SCIENCES AND HUMANITIES UL. 3 MAJA 54, 08-110 SIEDLCE, POLAND E-mail: lidiaobojska@gmail.com
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Abstract

In response to the paper by Cotnoir and Bacon published in RSL 2/2012, we would like to add some remarks regarding supplementation principles. It is known that in a classical mereology, the Strong Supplementation Principle (SSP) together with antisymmetry enforces the Weak Supplementation Principle (WSP). Instead, in the nonwellfounded mereology, the failure of extensionality causes the failure of antisymmetry (Cotnoir, 2010), hence the investigated model is also nonantisymmetric. Cotnoir supposes that the failure of antisymmetry implies the failure of (WSP) when (PP1) is applied, however gives no explicit argument, which we would like to supply in this paper. Additionally, when (PP2) is applied, (SSP) implies (WSP), hence the failure of antisymmetry does not necessarily imply the failure of (WSP).

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 343 - 347
Copyright
Copyright © Association for Symbolic Logic 2012 

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References

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