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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).

"cognitive skills" is not the only indispensable thing: knowledge, especially the knowledge about how to use your cognitive skills effectively is of paramount importance.

Thus I would not qualify such knowledge as ancillary: it is at least as much important as the raw cognitive skills.

there is still most certainly the need for clear logical thinking, reasoning, and communication.

It's unquestionable.

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.

You must do much more than keeping this in mind, for the ability to build models is one of the main skills of a scientist (at least in sciences like physics; pure mathematics is of course different).

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.

Granted.

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".)

No, it's most probably that the right mathematical language and/or concepts have not been invented yet.

I also would like to insist on the very important fact that even in hard sciences, using mathematics appropriately is often hard, because where the real art is is in devising the right model. As Einstein once said:
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

This is the problem I wanted to allude to, and I wanted to underline that any serious scientist must know these things.

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).

Actually, I have a fairly extended training (several years) in mathematics, although I decided not to become a professional mathematician.

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.

If you want to discuss the health of science in western countries (as I remember, the original question was around this), you need to understand how people use and/or understand science.

Thus it's pretty clear that there are lots of new innovative ways to use mathematics in many sciences, I don't want to deny that.

What I want to say is that lots of problems related to understanding of science by the public in the large stem from the fact that too often, extremists dominate the debate: on the one hand, in soft sciences, people sometimes use mathematics and logics as a quasi-mystical tool to enforce their (undeserved) authority. And on the other hand, other people (e.g. ID afficionados) are trying to dismiss rationality as a whole for the sole purpose of fullfilling their narrow political agenda.

All these people are enemies of science (and freedoms), and what we need is more people to transmit the basics of science to as large a public as possible, without turning it in what it is not (i.e.: not turning science to an authority which has answers for everything).

That's another thing I would like to say: the current problems about the health of science in the US and elsewhere are strongly related to the domination of extremists which monopolize the speech about science in the public debate.

And it is my feeling that if science as a whole, i.e. not only the "important cognitive skills", but also the context, i.e. how it works when you are practicing science, if these things were more widely known, then it would be much harder for the extremists to obtain the undeserved credence they seem to enjoy nowadays.

Henri