As someone with a degree in philosophy and mathematics but who has earned his bread & butter doing QA, coding, network and sys admin I feel that I have a lot of inside knowledge that I can bring to this debate.
I could fill an essay myself in response to Paul's post but I'll keep it brief so as not to bore anyone.
This: "Philosophy doesn't really have a subject matter in the way math or history or most other university subjects do. There is no core of knowledge one must master. The closest you come to that is a knowledge of what various individual philosophers have said about different topics over the years. Few were sufficiently correct that people have forgotten who discovered what they discovered."
The subject matter of philosophy is the world of abstract ideas. Some call them universals, they are to be contrasted with cold hard facts, stuff we can reason scientifically about. It is not that "few were sufficiently correct" but rather (as Kant for one pointed out) that metaphysical claims like the famous "Gods exists" or the "universe is infinite" can be asserted to be true while at the same time there opposite can be asserted to be true! "God does not exist". "The universe is finite". Now, does that make everyone wrong? No, of course not, a wiser person just digs deeper.
And this: "But did studying logic teach me the importance of thinking this way, or make me any better at it? I don't know."
The thing is, as I've come to realize (from thinking about it long and hard!) is that logic is not a part of philosophy. Yes they go hand-in-hand but logic is really a cross-disciplinary tool with applications in many disciplines, mathematics, computer science, philosophy and so on. Just because it has traditionally been very closely associated with philosophy can mislead us into thinking that logic is part of philosophy. And so to blame philosophy because learning logic didn't benefit you in the way you thought it would is a category error at the very least in my opinion.
I'll stop here but I have to say, I would love if Paul were a bit more humble and a bit less arrogant and realize that there's a reason philosophy is so difficult. It's not because it's all smoke and mirrors and sophistry - though there is some of that, and you need the mental tools to sort the wheat from the chaff. You know Richard Rorty has said that philosophy is merely a branch of literature! And he was one of the leading philosophical figures of the last century! Think about that for a moment...
I would argue that mathematics itself does not have a subject matter. It started with counting and geometry, then became applied to physics, and slowly developed applications to probability, then computing. It seems to me that if we can reason in a rigorous and general way about any subject, the study of that reasoning is a discipline within mathematics. Philosophy, on the other hand, seems to me to in fact have a subject matter, or rather many subjects. Philosophical conversations always center on something, be it the existence of abstract ideas or the foundation of moral choices. (If you think that having a multitude of subjects constitutes having no subject, then one might make the same charge that science has no subject since it investigates sounds as well as heat flow, as well as cancer...) What I think separates philosophy from other disciplines is not the kinds of subjects it investigates, but the kinds of answers to them that it seeks: completely precise, general, and unquestionably true.
From what I know of the audience here, I think a lot of people would be interested in reading a well-reasoned response to one of pg's essays. Even if it's long.
http://www.paulgraham.com/philosophy.html