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Non-wellfounded Mereology

A.J. Cotnoir

Pages 383 - 387

Non-wellfounded Mereology 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 x1>x2>x3>... 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.

1Department of Philosophy, University of St Andrews

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