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Home arrow Philosophia Contributions to Philosophy arrow Non-wellfounded Mereology _From Handbook of Mereology
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A. J. Cotnoir

Non-wellfounded Mereology _From Handbook of Mereology


ISBN: 978-3-88405-638-7

Price: €14.80 (including 19 % tax)


A binary relation R is said to be wellfounded on a domain if and only if every non- empty subset of that domain has an R-minimal element; equivalently, iff every descending R chain is finite. A proper parthood relation can be non-wellfounded in various ways; here are three: (i) gunk: for all x there is a y such that y is a proper part of x; (ii) bounded infinite descent: there is an infinite chain of distinct proper parts 1>2>3>… which (after infinitely many steps) terminates in a smallest element y; (iii) loops: there are x and y such that x is a proper part of y and y is a proper part of x. Classical extensional mereology (CEM) is compatible with (i) and (ii), and hence models of CEM are not always wellfounded. A non-wellfounded model in sense (ii) is the set of non-empty subsets of the real interval from 0 to 1 with parthood interpreted as the subset relation. A non-wellfounded model in sense (i), due to Tarski 1956, is the set of nonempty regular open sets of the same real interval with the standard topology. However, there are no type (iii) models of CEM, since proper parthood in CEM is irreflexive and asymmetric. …




 





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