Tag Info

I think one could argue that just as there are categorical versions of set theory, for example Lawvere's Elementary Theory of the Category of Sets, there are analogous categorical versions of ...

Many people find it natural to consider the set-theoretic analogue of mereology to be the inclusion relation $\subseteq$ rather than $\in$, since after all, $\subseteq$ is reflexive and transitive ...

Considering the nature of your question, you might be interested in the following paper by Geoffrey Hellman and Stewart Shapiro: "The Classical Continuum without Points", The Review of ...

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 $\...

If, for every atom $a$, $a \subseteq x$ implies $a \subseteq y$, then $x \subseteq y$. Assume $x \nsubseteq y$, then by Supplementation, there is a $z \subseteq x$ such that $\neg z \ O \ y$. By ...

The most sophisticated philosophical treatment of the relation between set theory and mereology is David Lewis' book Parts of Classes. For each non-empty set S, Lewis views the singleton set of each ...

Although Mereology cannot by itself manage to formalize most of ordinary mathematics, yet still it is not too far from it! An addition of a single primitive with rather trivial axioms about it can ...