OK, so I am having this massive love affair with structural realism, in particular the rather drastic form of it that claims that the fundamental ontological entities are relations, not individuals and that individuals may not even exist at all, or if they do, may not have any intrinsic properties. It makes a great sense to me, since, of course, mathematics is all about relations and structures rather than entities, and I am agreat fan of mathematics. Entities are defined in terms of their transformations and how they interact with other entities. (In fact I am becoming something like a mathematical platonist, admitting that pure mathematical structures may be quite real and fundamental entities in our reality).

A good way to look at the fundamental universe is graph theory. In graph theory all you have is nodes and edges. Nodes have no information attached to them, and edges are defined by some set of rules, governing possible paths from one node to another, and in particular, the minimal path one has to take to return to the node of origin. That set of rules may give rise to what we observe as elementary particles (whether quarks and gluons, preons or something even more basic is irrelevant here). Loop quantum gravity deals with very similar concepts.

Anyway, while thinking about it, I had what may be a totally pedestrian idea. Since a graph is a formal system, and determines how our Universe is, it would be subject to the Incompleteness theorem. So then, could the inherent Goedel undecidability of this formal set of rules that is the foundational ontological entity of our reality give rise on larger—quantum and above—scales to what we perceive as the uncertainty principle? After all, both Goedel's theorem and the UP describe the limits on the amount of information we can extract from a given system. Could there be some deeper connection between the two?