Certainly it's possible, and in some ways it's actually being done. But recursive self-improvement isn't always a recipe for FOOMing; diminishing returns can lead to an asymptotic bound, Zeno-style, even if technical refinements remain theoretically possible. In particular, if there are diminishing returns which can't be overcome without radically changing the nature of the problem (for example, with the help of a brain-computer interface or a full-blown mind upload), then self-improvement of the human brain has to wait on those advances to make significant progress.
I'd argue that this is in fact the case. The human brain is a piece of special-purpose hardware that's already quite well optimized for its niche, albeit subject to any number of mind-killing barbarities of the ancestral environment which might not apply in the contemporary world (perennial famine being a cheap example). We're probably not at the peak of the fitness landscape for mammalian intelligence, but I'd be surprised if we weren't reasonably close to a local maximum; if that's true, we're likely to run into early limits to how much we can improve performance by tweaking parameters of a working brain. Generational improvements (genetic or environmental) probably have higher limits, but would take so long that even modest assumptions about the progress of AGI suggest it's the way to bet in the medium term.
Improving human thought is a slightly different topic, but it's pretty much synonymous with rationality as this site uses the term; its various subfields are also highly interdependent, so I don't think attempting to recursively improve any single one of them is going to fly. That said, I'm pretty sure there's a lot of potential latent in the prospect, but with the caveat that it's bounded above by human intelligence; a perfectly optimized rational thinker would probably look exceptionally smart to the likes of us, but even Socrates was proverbially mortal.
Interesting. In what sense are you using the word intelligence?
There's plenty of discussion about recursive self-improvement for AGIs, and self-improvement for ourselves, but I haven't come across (in memory) anything that specifically combines the two concepts. Arguably, increasing rationality skills would be recursive, but can anyone think of specific ways in which we can improve ourselves via iterative cycles? Is there a limit to how far we can currently improve our abilities by improving our abilities to improve our abilities? Or are these not the right questions; the concept a mere semantic illusion...
A place to start might be base-level anti-akrasia abilities. Are there physical steps we can do to force ourselves to self-improve when we otherwise lose the will or forget or move on to another interesting subject? Construct some sort of externally self-propelling regime that pulls us along a path to improvement? Could we "Incept" ourselves with the seed of a recursively self-improving paradigm?
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Forgive the overbearingly inquisitive tone. This is my first post after lurking a couple years, and I guess even in the discussion section I subconsciously avoid making any potentially low-status claims of my own!