Basically he starts of explaining ontology, starting with Descartes and cogito ergo sum and the ball of wax and gives a pretty decent explanation of classical rationalism. i.e. "taking nothing as certain" until you can have "a clear and definite picture" of reality. However if you don't take his ontological explanation of God's existence any further than you can throw him (which you shouldn't, it's almost as bad as Anselm's) you're left with only one definite conclusion: something -- probably you -- exists. Well that's good; let's have a round of applause for the rationalists shall we? Come on even Plato got past this point and it's kind of annoying because my objections about the arbitrariness of this had to wait about a century for Berkley.
Well -- says the anthropomorphized Western philosophical tradition -- maybe we should only question things bit by bit (local skepticism,) because we need some way of appraising reality which contains our tools of analysis. We can't undermine everything, our naive view of existence might be perfectly alright and we'd never know. So we'll make a few assumptions.. we know that we're making assumptions, everything's under control. Otto Neurath's very elegant (which doesn't mean that it's correct obviously) comparison of a ship at sea to our picture of reality, is quite reasonable. In fact it flows directly from Hume's empiricist view.
Hume's idea was that: you can't doubt everything, you can't establish anything definite that way. What you need is observation; you can't just use your head, you've got to use your eyes and any other applicable senses (incidentally, 'common sense' was according to Aristotle the unifying sense that allowed us to interpret the input of all 5 senses..) Positivism is generally represented as the pro-scientific philosophical view and takes that -- as well as the better parts of Descartes' work -- into account.
So we've established that we're going to use the scientific method, because it beats twiddling our thumbs or doing nothing (ok at least I have.) But wait! We've got a problem: what if people don't see the world the same way you or I do? What if they're zombies? What if we live on a planet where we call this liquid thing water, where it freezes at 0 degrees celsius (which is epistemically objective even though the measurement is arbitrary and observer-dependent) were we drink it like water and it hydrates us like water with
Descartes suggestion (he was actually brilliant, hated by middle-schoolers everywhere for inventing algebra as we know it) was that our soul exists separately from our body.
Cartesian Dualism concerns dualism of substance and not merely appearance. Locke (in one of his duller moments) suggests that the sensations are "annexed" to a certain experience, they're arbitrary or are there "because God says so." That my dear children is called occasionalism (basically anyway, i'm not too clear on the details.) Liebnitz (*sighs besottedly*) decided that there must be some reason: 'if you're god, you should work smart and have the universe do it for you..' 'why should we get rid of cause and effect when the concepts have served us so well in the past' (assuming that we have survived the vagaries of childhood, learned which animals want to eat us and which pretty mushrooms aren't good to eat.) So -- Leibnitz says -- we experience things in the way that we do because of how we're constructed, sure sometimes things don't work that way and then people bring up qualia -- which is fine if that's your thing -- but usually people work the same way and feel the same way and so respond the same way.
But now we have another problem: if everything is determined by the physical constraints of the system, do we have a choice, any free-will? Sure.. I think I had an apple because I wanted an apple, but was I really free to choose an orange just as easily? Or was my "choice" of an apple as predetermined as the trajectory of a given rock or the size of the Milky Way? I think I chose, I can imagine myself choosing differently.. I have chosen differently under different circumstances, but I can't be sure. It brings up Schopenhauer's picture of the water, which is equally "free" to be a waterfall, rolling ocean or bubbling stream but 'prefers to rest quiescently in a pond right now thank you very much.' The saving grace of the book is that it actually explains compatibilism; compatibilist thought is basically determinism that makes a small amount of sense. Which is basically what I tried to say in another post except I didn't realize that I was trying to say it, so as a result it made no sense. The idea is that everything is determined by the laws of the system, but the laws of the system allow for other people trying to affect each other's actions. i.e. having speed limits: some people still speed but there are consequences which alter the parameters that affect what us automatons will "choose" to do. Which is not intellectually satisfying, but I'll admit is possible. Cartesian dualism suggests that something outside the natural world affects the physical world for us, which is called interventionism. Which I have to admit, doesn't sound much better... even to my ears. The bit God or a universal observer seeing you at a later point doing something meaning that it's all set up ahead of time is ridiculous too, a choice has to be made -- so of course you're going to see the result -- it doesn't change the decision. I'd rather believe in a weird 4d universe thanks.
There was more, but it didn't make a great impact a) because i was tired and didn't have the sense to just leave it for another day and b) he didn't have anything original to say. But it was about cool stuff like consciousness, probability and stuff that for some inexplicable reason makes most people's eyes glaze over.
All of this ends in a sort of circuitous way with him talking about universals, he keeps everything that's convenient about relativism and still reserves the right to tell you what's objectively good and bad.. or at least 'functional' and 'useless.' Which I do understand, I just don't agree with.
He has a thorough understanding of the subject (which i guess you should expect for a professor of philosophy) which helps him choose the most applicable source material from a given philosopher that answered opposing points of view. Other than that he's a bit of a jerk. I used to think that people talking about philosophers and some sorts of academics like stuck-up idiots was just because they were rednecks or jealous. But the thing is: it's actually true. As soon as you learn a little bit (insert appropriate snobby Alexander Pope quote here,) you end up thinking that everyone else is stupid. It's a really difficult sort of elitism to avoid. This weirdly synced with my podcast on the philosophy of society which is better than this book, especially because the lecturer was at Berkeley during the Free Speech Movement, so his lectures had some historical content as well.