With fluid concepts we are assuming analogy lies at the core of cognition. Analogy is what lets us handle abstract similarities. This is the isomorphisms I speak about with “smart” being related to what we have been exposed to previously. Gödel’s Incompleteness presents to us the inherent limitations of any formal axiomatic system, and it is via those limitations we find the capacity for massive creativity.

So the question becomes, is there a connection between the use of isomorphic relations used in cognition (related to fluid concepts) and the flexibility afforded cognition by way of incompleteness?

I would argue the flexibility afforded any computing machine by incompleteness is what makes things like analogy-forming possible. To find an analogy one must operate at a high level of abstraction while retaining the “essence” of the thing being observed. Only then can we bridge the seemingly disparate into some unified understanding of how 2 or more things relate. The key to operating at high levels of abstraction is to maneuver around low-level details to find the “essense” of the thing (one cannot generalize without first specializing…you have to go deep to know what can be generalized). Maneuvering around low-level details requires a great deal of representational capacity (this relates to universality); in other words, the machine must be able to “mold its clay” in many (many!) different ways if it is to find how one object relates to another.

Incompleteness is what arguably gives cognition the flexibility to mold its “clay” to find overlapping “shapes” between seemingly disparate concepts/ideas.

So I believe Hofstadter’s fluid concepts and Gödel’s Incompleteness are related, but such that fluid concepts depend on Incompleteness.