Part One of this paper is a case against classical mereology and for Heyting mereology. This case proceeds by first undermining the appeal of classical mereology and then showing how it fails to cohere with our intuitions about a measure of quantity. Part Two shows how Heyting mereology provides an account of sets and classes without resort to any nonmereological primitive.
"Nonclassical Mereology and Its Application to Sets." Notre Dame J. Formal Logic 43 (2) 79 - 94, 2002. https://doi.org/10.1305/ndjfl/1071509430