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Henri:

You expounded upon the Critical Thinking skill I listed nicely. And while I don't disagree that there is a "community" and "culture" (actually, "cultures", plural) in science, I'm not so sure I would consider them "important cognitive skills". (Though they are important ancillary information for all to keep in mind, whether scientist or simply citizen).

As to the "limits of logic/mathematical reasoning." I would raise a red flag of warning here! First, again this is not an "important cognitive skill", even if it is something to keep in mind. Second, while, unfortunately, "mathematics" may be of more limited applicability in the "soft sciences" (e.g. social sciences, economics, psychology, etc.), there is still most certainly the need for clear logical thinking, reasoning, and communication.

If logical reasoning cannot be applied to such "soft sciences" then, perhaps, they have usurped the designation "science", and don't deserve such. (See Feynman's many criticisms of such so called "sciences".)

On the other hand, logic and mathematics is certainly not the all-and-be-all of science. I most certainly agree that science is a creative endeavor, especially in the creation of scientific theories. (One need only look into the history of science and the evolution of individual theories through the creators' earlier works: The formative works.) The creation of anything new most certainly requires creativity. (This sounds like a tautology to me.) Simply following logical reasoning, in the formative stages, at least, will almost certainly never get you there. :-)

Actually, if you believe that mathematics and creativity are at odds then I suggest you have little true understanding of the nature of mathematics (vs. arithmetic). :-) Arithmetic is certainly highly related to pure logic (this is why computers do so well at both). Mathematics, on the other hand, requires a great deal of the creative/intuitive right hemisphere of our brains (while still using the logical left hemisphere). In fact, I would suggest that mathematics requires approximately equal portions of both (more of one or the other at different times, of course).

As for the applicability, or not, of logic and/or mathematics to fields such as sociology, economics, and psychology, have you noticed the advancements made via the use of differential equations within economics, or the suggestions made by many in sociology and/or psychology that their disciplines should be reworked upon the basis of quantum mechanics rather than the present foundation of Newtonian mechanics? Perhaps the problem has more to do will a lack of vision toward the use of new forms of mathematics, than to any inapplicability per se.

Just a few thoughts on "important cognitive skills". Yes, perhaps I should have added creative thinking and/or other forms of creativity to my list of "important cognitive skills". :-)

David