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)

Relational Bundles

RB+EOSR

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*

So... huh?

Interesting Items?

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)