Of course this degenerates into word-play quickly, but the problem itself isn't solved (or diminished) by word-play.
> It's not a high bar to achieve.
I'm not sure I agree. It's not trivial at all to produce a system that can support what you call logic and formal processes, both cognitively - you have to think it up in the first place and Turing and von Neumann and others were no slouches - and physically as the history of and continued development of computational circuitry shows. I think what you call rational or well-behaved systems are just mirages or shadows that pop into life once a specific pattern of fundamentally non-rational behaviours intersect just right.
I, of course, am unhindered by any actual knowledge or competency in this domain so I wouldn't read too much into what my unhinged subconscious is spewing forth.
Of course the foundations of logic are not logical themselves. Symbolic human thought grows from the natural capabilities of the brain, there are not universal axioms that can be extracted fully formed from the void. That's what rationalist philosophers for wrong (but then, they didn't have neuroscience and electric scanners).
> > It's not a high bar to achieve.
> I'm not sure I agree. It's not trivial at all to produce a system that can support what you call logic and formal processes
We're talking at different levels.
Building the concept of formal rational systems to order thoughts was a huge achievement of philosophers, first the Greeks and later XIX mathematicians like Bool and Russell and the computer builders.
But what I say that's easy is building a new specific system on top of those foundations. It may be as simple as writing a regular expression, which defines a full (if limited) formal grammar. I agree that their power to represent and order the patterns of thought you find in life is more limited than what engineers believe; but when you find a domain of science where it can be applied, it's a very powerful tool to explore consequences and avoid or fix biases and misconceptions.
There may be limits to rationality (both for being incomplete to describe the world and for generating results that can't be demonstrated within themselves), but being rational by itself is nothing more than the capability to apply formal logic, i.e the capability to generate a sequence of sentences derived from the previous steps and a limited number of rules of inference.