There are many values to studying the subject. I think the most important on are ethical reasons. But the common objections given include the "fact" that philosophy has not contributed to human knowledge and or human society's development. This is clearly wrong. Here's a list of all that philosophy has contributed in terms of knowledge both directly and indirectly (through methodology developed) and through social change.
Philosophy's contribution to our knowledge:
-Modern economics was first developed by the moral philosopher Adam Smith.
-Psychology, sociology political science all originated from the minds of philosophers.
-Modern work in logic was heavily influenced by philosophers. The truth table in logic e.g. was first seen in the work of a philosopher (1919 by Wittgenstein) which eventually lead to the electronic revolution of the 60s. The earliest development of modal logic is by Aristotle, C.I. Lewis, Ruth Marcus and Saul Kripke, all philosophers.
-Cybernetics, the science of regulatory systems was started by someone with a philosophy PhD (Norbert Weiner).
-Modern linguistics bases much of its work on formal semantics almost exclusively on the works of philosophers of language such as Frege, Russell, Kaplan, Montage, David Lewis and many others.
-The 2005 Nobel Prize for economics went to mathematician Robert Aumann who based his work on economic conventions on the work of David Lewis's notion of "common knowledge".
-The development of modern cognitive science, both its inception and developments within to this day to philosophers.http://en.wikipedia.org/wiki/List_of_cognitive_scientistsAnd much of decision theory have been developed by philosophers as well.ser.blogspot.com/2011/02/why-are-some-physicists-so-bad-at.html?commentPage=2
This is not mentioning all the knowledge developed in more traditionally understood philosophical areas.
To the shape of society and course of human history:
-Development of democratic theory
-Development of legal theory
-Various economic theories (capitalism, communism etc)
And so forth.
It's not only a myth that philosophy has not contributed to society, it seems to be one of those myths that's the opposite from the truth. Philosophy has had massive influence as my examples show.
