The following is Hofstadter-Gödel reasoning with my own speculative layer on top. (I don't care if I'm correct, but I do want to understand.)
tldr: Logic itself cannot be fully defined, but it can define itself perfectly well, and can be used to create definitions for logical destinations we hadn't thought of before. There's a logical asymptote in every system.
Longer version:
Arranging formal components of logic (according to their own rules) always leads to valid logical statements. (Source: Principia Mathematica, via Hofstadter.)
There are valid logical statements that cannot be proven by the components of logic at hand. (Source: Gödel's incompleteness theorems, via Hofstadter.)
Arrangements of formal components of logic can themselves be validly arranged. let's call this these "hyper-logic components". we can get just as much logical flexibility from these as from the original, more-fundamental pieces. including, inevitably, the ability to construct a valid but unprovable hyper-logical statement. (This is my interpretation of Hofstadter.)
Components of hyper logic can be recombined to form hyper-hyper-logic components, which afford more valid-but-unprovable arrangements. (This is my own speculative theory here.) In this fashion, we can look back to our original components of logic, and then our components of hyper-logic, then our new level of hyper-hyper-logic, and we can anticipate infinitely increasing levels beyond that. at every level, there's always an open door of unprovability. It's a logical asymptote, though. We can keep going on forever, and we'll always get closer (i.e. more logically precise), but we'll never reach the limit.
Pretty sure this leads to recursively open doors, btw.
I'd like to say "assume nothing about each other", but to speak any language at all requires some assumption. (Even if it's the assumption that the other person can hear.) We have to make some assumptions about what we're up for, but always leave a door open for someone to say "hey, I want something else".
When making a product, ensure that it is at its core infinitely reconfigurable, infinitely flexible, in such a way that a configuration of the product can work around limitations in the product itself.
are great for this. (Locksmith has locks, keys, and key conditions; Mechanic has events, tasks, and actions.)