[FOM] Mereological Logicism: A theory of atomic predicates and their extensions.
Zuhair Abdul Ghafoor Al-Johar
zaljohar at yahoo.com
Fri Mar 1 13:11:46 EST 2019
The linked article contains the program of Mereological Logicism.
Which provides a visualization into the nature of predicates and their
extensions, it develops a predicate hierarchy from very naive principles
about predication, on top of a rather trivial Mereological background
of Atomic Extensional Mereology. In short Mereological Logicism is
a first order theory with primitives of of "Part-hood", and "predication" binary
relations. It states that predicates are atoms if and only if they only predicate
atoms; also that for every formula in the pure predication language (i.e. doesn't
use part-hood) when closed on atoms, there exists a predicate that is definable
after that formula; and that two predicates are equal when they have the same
predication. The result is a hierarchy of atom predicates predicating atom
predicates, in which we can interpret all axioms of Ackermann's set theory minus
class comprehension axiom, which would interpret all axioms of Zermelo set
theory, and I'd think all of ZFC axioms as well. Stronger versions of Mereological
Logicism are obtained by adding the Unrestricted Composition Principle, to the
Mereological background language of this theory, resulting possibly in interpreting
full Ackermann's set theory.
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