pivoxa15 said:
I am not a professional in education nor have I finished by undergrad degree so as Von Neumann puts it 'its better to be vaguely right than precisely wrong.'
If your premise is that a scientific education should be more highly valued than other forms of education, then this statement would be a direct contradiction of that premise. In science, it is better to be precisely wrong than vaguely right. Vagueness gets one nowhere; it cannot be tested. Something precisely wrong can be shown to be wrong, and leads to progress. Better to be clearly disproven in order to move forward than to have an entirely untestable claim because it is overly vague.
pivoxa15 said:
One of my main points is that students learn all subjects but come away with the impression that the sciences are more 'powerful' and appreciate it not just as a technical subject but also its influence on society and the history and philosophy of it.
When you say this is one of your main points, do you mean that is what you desire to happen, or something you have observed among your acquaintances, or are you asking if this is true on a broader scale?
Going back to the original post here, the two primary qualities of one's education are generally described as
breadth and
depth of knowledge. And there is a challenge in assessing this. I think each field has a pretty good handle on the criteria that need to be met to consider one's depth of knowledge in that field sufficient to call it an area of specialization, and the level to which one has specialized (undergraduate major, or Ph.D.), but breadth of knowledge is much harder to define. How much depth of knowledge do you need in fields outside your area of specialization in order to consider your breadth of knowledge adequate? The original question seems to be essentially asking this...how much education on science and math does a history major, for example, require in order to consider themselves to have an adequately broad education in subjects outside their field of history? One can turn around the question as well to be: "How much education on history or literature does a science or math major require to be considered to have a sufficiently broad education?"
I think the only way to even begin to answer that question is to look at how one will use their specialization, and how much impact the lack of breadth of knowledge would have on what they will do with their lives. For example, if a political science major is going to be influential in decisions that affect science policy, they better know enough about science to at least understand what the experts are telling them about the pros and cons of a particular policy, even if they are not able to study the field in depth.
Nobody can study all subjects in great depth. That's the assumption I'm going to start out with here. Which means the focus of an education, and one's knowledge base outside their own field cannot be to provide a sampling of every subject out there; there is simply not enough time to do that and still devote adequate time to your specialization. Rather, I argue that the focus of education is to learn how to learn independently, to know how to pick up a textbook, use the index, and know how to read for facts in a way that you acquire an accurate understanding of what you read without a teacher there to guide you. (I think many do not succeed in this area.) One should learn how to cross-check facts and references, how to use a library, to be aware that books can be wrong or quickly outdated, and to inquire into the most current information, or even how to locate experts to ask. Taking courses in a sampling of subjects outside of your field will allow you to see how to apply these skills in fields outside your own. If you can do that, and have a curiosity to continue learning throughout life, you will have succeeded in your education, and can always continue to acquire knowledge.