I know, I know... this is not a technical question. Nevertheless, I believe this is the right place to ask such question.

I am sure many of you read about philosophy, including philosophy of science, ethics and so on. If you read works from the ancient times, especially those written by non mathematicians, you may find mistakes simply because they used to think on the science the knew at the time. Actually, until a couple of hundred years ago, most natural philosophers (if not all of them) were scientists as well.

My question is:

Does the lack of knowledge about math or science in general, have an impact on a philosopher's ability to reason about the world and figure the right path to follow?

I know many philosophers or at least, people who have a degree in philosophy (either master or phd), and I find that they have no basic understanding of very simple facts, from physics all the way down to mathematics. For example, many of them would guess that, even in absence of friction, an object heavier than another would reach the ground faster. But, again this is only one of the many examples. I'm not even going to mention absence of both knowledge and intuition about markov-based processes, probability in general and so forth.

What is your opinion about this. Do you think philosophers should have a deeper basis in natural sciences in order to better understand the world and develop better ways of thinking?