Philosophy to come up with the right argument and psychology to make it stick
Unfortunately, philosophy is very far from coming with the right argument. I took a philosophy course in college, to "broaden" my outlook, and it had the exact opposite effect. Read any text by a philosopher, and in the end you'll get to the conclusion that perhaps there could be one or two good ideas there, if it had been written in a hundred words instead of a hundred pages. That's why sometimes a philosopher seems so smart to the uninitiated, they have read only the aphorisms and quotations, they have never had to pore through a full book written by a philosopher.
IT is a field for many different specialists. In the most common forms, what is needed is an expertise in human interfaces, we need graphics designers to create the screens and writers to create the documentation. In that sense, yes, it's all about expertise in the humanities. The vast majority of IT work in development is about personal and corporate software, of which data input and presentation is the bulk of the thing.
Logic and mathematics, although it's behind every software, is a very small part of the development job. However, it cannot be totally disregarded, because it's an essential part.
There's the dilemma we face. We cannot just exempt people working in IT from training in the essential parts most of them will never use, because we never know when those skills will be needed.
Those programmers who say "I've never used a differential equation" are people who slept through their calculus courses and cheated at the exams. If you are simulating pitching a ball or you are calculating the profits from an investment fund you are using differential equations, and you should know how to do the job. Unless you work for a big company, you cannot be assured that the only things you'll ever need to do is drawing screens and writing manuals.