I'm arguing that the fuzzy-ish definition that corresponds to our everyday experience/usage is better than the crisp one that doesn't.

Re IQ and "way of thinking", I'm arguing they both affect each other, but neither is entirely under conscious control, so it's a bit of a moot point.

Apropos the original point, under my usual circumstances (not malnourished, hanging out with smart people, reading and thinking about engaging, complex things that can be analyzed and have reasonable success measures, etc), my IQ is mostly not under my control. (Perhaps if I was more focused on measurements, nootropics, and getting enough sleep, I could increase my IQ a bit; but not very much, I think.) YMMV.