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Results tagged with mereology
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user 95347
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
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Is this mereotopology theory consistent?
$ \newcommand{\Pt}{ \ \mathbb P \ }
\newcommand {\cz}{\ C_z \ }
\newcommand {\eps}{\ \varepsilon \ }$Logic: first order logic with equality
Extra-logical primitives:
"$\varepsilon$" standing for the …
- 11.3k
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182
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Can this Mereological system be synonymous with $\sf ZF(C)$?
\operatorname {atom} z: z \subseteq y \land z \subseteq C )$
This theory does not violate any of the tenets of Mereology, though it doesn't adopt the Unrestricted Composition principle. …
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Can this kind of Mereology be synonymous with Set Theory?
l: l=\{x\} \land \forall y: \{y\} \subseteq x \to \{\{y\}\} \subseteq x$
Choice: $\exists C \, \forall x \, \exists y : y=C(x) \land \exists \{y\} \subseteq x$
This theory does respect all tenets of Mereology … , the first four principles are the axioms of Atomic General Extensional Mereology "$\sf AGEM$". …
- 11.3k
-2
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2
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499
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Can Mereology be bi-interpretable with Set Theory, in absence of the bottom object?
This question is about synonymy between Set theory and Mereology.
David Lewis in Mathematics is Megethology tried to reduce Set Theory to Mereology augmented with a singleton function. … The following exposition is a formal capture of his Mereology. …
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Can this kind of formal Mereological based interpretation of Set Theory be significant in un...
So, in some sense this theory does reduce the standard Set Theory to this kind of Linked-Connective-Mereology + Size criterions. … In nutshell, that mathematics reduces to Set Theory which with the aid of some Mereology would be reducible to some size notions. …
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Can Set theory be interpreted in Relational Mereology?
I would say here that this theory itself can be captured in a mono-sorted way, especially in Mereology. … This is just a straightforward capture of relations in terms of Mereology, so the whole thought is about establishing a theory about relations. That's why I call it Relational Mereology. …
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Can we plausibly interpret the empty set in Mereology as a distant atom?
The other way to coin the empty set in Mereology is to actually consider it a non-labeling bottom atom. … The problem with rounding the mereological system to have a bottom object is that: first it violates a maxim of Extensional Mereology, that is Supplementation, so it is anomalous in Mereology, and the …
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2
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Can rules of set theory be founded by paralleling parts of atomic Mereology?
I observed that all rules of $\text{ZF}$ can be derived from the following Mereology-Set translation rule:
If $\phi$ is a formula in the pure language of mereology (only uses $P$ and $=$ as predicates … paralleling or rather mimicking the atomic part-hood relation of Mereology. …
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Which of the known alternative set theories is near in structure to this theory with a unive...
The idea is to work in Atomic General Extensional Mereology "AGEM", one can think of it easily as a theory about collections of atoms, where atoms are indivisible objects, i.e. objects that do not have …
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