Topology needs mereology needs topology and both need ontology.
”
We have again reached a general conclusion concerning the interplay of ontology, mereology, and
topology. And the conclusion is that each of these three dimensions must be carefully weighed. One
needs mereology because topology is mereologically unsophisticated. One needs topology because
mereology is topologically blind. And one must take ontology seriously because both topology and
mereology are incapable of making sense of important categorial distinctions.
”
Parts and Places – The Structures of Spatial Representation
By Roberto Casati and Achille C. Varzi
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SET THEORY AND MEREOLOGYAs a formal theory, mereology is simply an attempt to lay down the general principles underlying the relationships between
an individual and its constituent parts, just as set theory is an attempt to lay down the principles
underlying the relationships between a class and its constituent members. Unlike set theory, mereology
is not committed to the existence of abstract entities. The whole can be just as concrete as the parts. But
mereology carries no nominalistic commitment either. The parts can be just as abstract as the whole.
David Lewis’s Parts of Classes (1991), which effectively provides a mereological analysis of the set-
theoretic universe, is a good illustration of this “ontological innocence” of mereology.
an individual and its constituent parts, just as set theory is an attempt to lay down the principles
underlying the relationships between a class and its constituent members. Unlike set theory, mereology
is not committed to the existence of abstract entities. The whole can be just as concrete as the parts. But
mereology carries no nominalistic commitment either. The parts can be just as abstract as the whole.
David Lewis’s Parts of Classes (1991), which effectively provides a mereological analysis of the set-
theoretic universe, is a good illustration of this “ontological innocence” of mereology.
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“You are quickly moving up my list of smartest people I know.
You are actually dealing with stuff that excites me. Extending Ideas I didn’t have appropriate terms for in order to communicate.
“ thank you! I feel more like a librarian gaining surface knowledge in order to point smarter people than me where they need to go to further explore concepts in more depth than I could. But there’s a lot of territory to map this out 
===
“If topology and mereology need each other then ontology is needed to mediate between the two. Too bad ontology is fated to fail! For omniscience is need for ontology, and we are mighty far from omniscience…“
Yeah – I agree. A complete ontology that covers everything is likely impossible (or unlikely!) for little beings like us. Then again, no aliens are around to say we’re wrong 🙂 Still, I was fascinated by the Dewey Decimal system as a kid, and this idea that one could possibly categorize human knowledge properly fascinates me… or even that we try at all, really!
🙂 Still, I was fascinated by the Dewey Decimal system as a kid, and this idea that one could possibly categorize human knowledge properly fascinates me… or even that we try at all, really!=====