Previously, I discussed a paper of mine that I think has some interesting implications (no pun)
This is semi-permanently hosted here and here (though you may need to be logged in to see the attached documents)
This is an incomplete work - a fact that isn't helped by the outstanding MS Paint skills
So What Is It?
From my LinkedIn: "This paper delivers a decisive defense for Eliminative Ontic Structural Realism demonstrating the logical and semantic coherence of the concept - it's not "everything's connected" it's "there are only connections not things", addressing the problem of an infinite ontology, and most importantly delivering a noun-less proto-language (the second to my knowledge and the first explicit attempt) in which Arithematic, the Ordinals, and Category Theory can be constructed. Really, there's two pieces in here - a philosophical defense of a purely relational ontology (it needn't be understand as metaphysics but as ontological engineering say for a computer science domain) which has closer analogies to functional programming rather than so-called "Relational Logic". The second is a new way of building ontologies and thinking mathematically. The work is semi-complete."
Nounless? Well, there are no objects - normally we parse a natural language sentence as predicate-object which gives rise to simple and corresponding Grammar Trees and Predicate Logic expressions - here we don't have any such objects - that's part of the difficulty since all natural languages include some kind of nounlike and hence, object-like entities built in ... yes, even this one
Foundations of Math?
A criterion of evaluation: if a legitimate theory of mathematics (e.g. ZF/C Set Theory, Category Theory, etc.) A can be reconstructed or built out of another non-identical (trivial or otherwise) theory B, then B is both legitimate and more fundamental
Categories can be constructed in relational bundle theory
Ordinals can be constructed in relational bundle theory
Pardon the chicken scratch:
More like functional programming rather than so-called "Relational Logic"
Inner identity: a relational bundle is defined by the relations that compose it
Outer identity: a relational bundle is defined by the relations within which it stands
What are the funky functions? No corresponding relation type in known math? Legitimate?
Does thinking of things in object-based terms constrain our mathematical thinking?
There are certain properties of definition and composition present here that aren't present with objects (like sets) such that a definition could contain itself (in set theory you can't construct a set that contains itself as an element - that's a kind of class - the broader family of entities that got Cantor into trouble)