"If writing down your ideas always makes them more precise and more complete, then no one who hasn't written about a topic has fully formed ideas about it." Apparently, even writing it down didn't help the author with this flawed deduction.
How is it flawed logcally? Seems perfectly correct to me. Although I'd agree it's a bit over-literal. As if the emotional workings of the human mind can be precisely reasoned about (i.e. precisely enough to say "always"). Regardless, I've experienced this effect a lot when writing design docs. Iteration and objective criticism on a tangible thing (a doc) is an extremely effective way to see the problem from all sides…
But the quote above says "If..." and then makes a statement that isn't true and then having a conclusion based on that false premise. I can tell you it isn't true because I can recall countless times in the last few months alone where writing down my ideas has resulted in a muddier thought; lost ideas while writing them down; confusing me and missing some parts; it does not "always make them more precise and more complete". So the rest of the statement is just silly.
Sure, sometimes writing down ideas helps clear things up. Most times even. But always?! Definitely not.