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However, the ability to use logical reasoning, clear logical communication, critical thinking, and problem solving (have I missed any important cognitive skills?)

Logical/mathematical abilities are not at all the only important abilities in science.

Abilities which are more often found in art/literature based curriculums are in fact required, especially:

1) Critical thinking. Without which it is difficult to be creative, because without the ability to criticize, you are not free, you accept dogmas. Accepting dogmas is of course the opposite of a genuine scientific attitude, which should not fear challenging authority when appropriate. A well-known example in recent history is e.g. the criticism Feynman made of NASA's engineering of the space shuttle.

2) Knowing that there is something called a "culture" in science too, which is the set of all the works in the history of science. This is especially important, because great discoveries often stem from cross-fertilizing from one scientific domain to another. Another reason why it is important is that although works of the past become outdated (this stems from the very nature of science), the spirit in which even outdated works were carried out can learn a lot to the apprentice scientist. Some attitudes/heuristics are more fertile than others. Example: "One must build a model of reality to study a problem [in physics], and to be useful, such a model should be sufficiently simple, but not too much" (Einstein).

3) Knowing the limits of logic/mathematical reasoning. Outside of "hard sciences" like physics or chemistry (e.g., in social sciences, economy, etc.), the very use of mathematics is debatable. Although logic and mathematics are of course very useful, their exclusive use should absolutely not be dogmatically accepted in such domains, for in fact, the difficulties of using logic for reasoning about the real world are well-known (at least since Aristotle). These difficulties raise problems which are not really solved today, thus it should be understood that the kind of modelling one can do in social sciences is always much less faithful than the kind of quasi-perfect models one can achieve in physics. In social sciences, lots of things depend on human factors, thus on the context, and also on the culture of the people involved in the phenomenons under study (although it doesn't means that everything would be equivalent to anything and/or "relative" somehow). As Antoine de St-Exupery (which was also a fertile inventor) used to put it: "Pure logic is the ruin of the spirit".

4) Knowing that there is something called a "community", and that science as a whole (as well as our modern "open societies") is built on the principle of sharing ideas. Especially, in science, when some people are more equal that others, it is not okay, it should always ring the alarm bell (although in practice, human nature being what it is, such tendencies are always more or less latent. Hintikka once explained why it is so in a brilliant essay, as far as I can remember). Another important thing to know is that ideas in science are always built by means of a kind of logic: the consequence of this is that two persons can find the same idea independently (compare this to litterature or music: in such domains, it is impossible that two different persons author exactly the same poem or the same song). As a consequence of this, work in science is much more incremental and collective than it is in arts. As the cathedral builders of the middle ages used to state it: "We are like dwarfs sitting on the shoulders of giants. We see more, and things that are more distant, than they did, not because our sight is superior or because we are taller than they, but because they raise us up, and by their great stature add to ours" (Bernard of Chartres, circa 1130).

I read again what I just wrote, and I cannot prevent me from thinking that (at least in western democracies) it's clear that science is deeply involved with the surrounding culture.

This is why the kind of spirit which pervaded over the last few years, which exploits and raises fear and sheeplike attitudes in the collective psyche, seems extremely injurious and toxic, because in such trends, the very roots of the scientific spirit in our societies are quite directly put under attack.

This is not a matter of which party do you belong to: the point is that science is one of the roots of freedom in an open society like ours. In this respect, the kind of principled contempt for science we see these days should be considered as the symptom of a deeper problem: a lack of willingness and/or ability to consider reality honestly.

This is why it's difficult to be 100% optimistic about the health of science in the US, as well as elsewhere in the western world, because it seems that science, along with the kind of human attitudes it praises, tends to be considered as politically incorrect, these days.

But I'm afraid that in the long run, it's not possible to get the science without the accompanying style, without the necessary freedoms, and without the essential understanding of such style and freedoms being widely supported and respected in our society and/or our culture.

Thus sooner or later, there will be a choice, along with a hard work to repair the damage.

Henri