of what threshold heritability coefficient?

This is what I meant about quantifying the probability estimate before clarifying the exact question. As I said originally, I'm skeptical of a strong heritability for rationality independent of IQ. I'm not sure what the correct statistical terminology is for talking about this kind of question. I think there is a low probability that a targeted genetic modification could increase rationality independent of IQ in a significant and measurable way. That belief doesn't map in a straightforward way onto a claim about the heritability of rationality. I'm expecting What Intelligence Tests Miss to help clarify my thinking about what kind of test could even be used to reliably separate a 'rationality' cognitive trait from IQ which would be a necessary precondition to measuring the heritability of rationality.

Given that memory, verbal intelligence, spatial reasoning and general intelligence all have values of H of around 0.4, it seems that P{H>0.3) ~ 70%

These all correlate significantly with IQ however I believe (correct me if you think I'm wrong on this). It's at least plausible that targeted genetic modifications could improve say spatial or verbal reasoning significantly more than IQ (perhaps by lowering scores in other areas) since there is some evidence of sex differences in these traits. Rationality seems more like a way of reasoning and a higher level trait than these 'specialized' forms of intelligence however.