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Results tagged with mereology
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user 1946
Atomic Mereology, Gunk Mereology, Mereology with Bottom, General Extensional Mereology, Mereology and Set Theory, Mereotopology, Boundaries, Grounding point free Geometry, Lewis's Mereology, philosophy of Mereology
6
votes
Can Mereology be bi-interpretable with Set Theory, in absence of the bottom object?
In a set-theoretic context, my view is that the most compelling concept of mereology is simply the $\subseteq$ relation, and so my conception of set-theoretic mereology is simply the theory of the $\subseteq … Namely, we study the relation $\subseteq$ in a model of set theory, and we regard this theory as "set-theoretic mereology." …
- 236k
10
votes
Accepted
Can rules of set theory be founded by paralleling parts of atomic Mereology?
If one does proceed with $\subseteq$ as the basis of set-theoretic mereology, then there is a bit of literature. … Various posts in the mereology tag on my blog, which includes the articles above as well as various other expository posts I've made and the mereology talks I've given. …
- 236k
43
votes
Accepted
Why hasn't mereology succeeded as an alternative to set theory?
Joel David Hamkins and Makoto Kikuchi, Set-theoretic mereology, Logic and Logical Philosophy, special issue “Mereology and beyond, part II”, vol. 25, iss. 3, pp. 285-308, 2016. arxiv.org/abs/1601.06593 … Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. …
- 236k