I do not think your argument fair. In fact I find it disappointing. Some things lend themselves to collecting numbers and figures and measurements, and other things quite simply do not. Philosophy, history, literature, and human languages are what first come to my mind as important fields of study that have significant impact on our outlook on the universe, but we can't scientifically measure them. Indeed it is philosophical thought and ideas that underpin our modernity. Moreover, much of our collective advancement is in significant peril because 'the arts' have been devalued so much. (Although William H. Miller just donated a significant sum to the John Hopkins philosophy department since he felt his degree in philosophy made him so successful.)

What you go on to speak of in your second paragraph is the art of rhetoric, and ironically you have unwittingly engaged in the very sort of ad hominem attack which you are complaining that you think that liberal arts scholars would use to defend their position.

An ad hominem attack is a classic logical fallacy and that is something that I suggest you research.