One of the major aims of the first half of the Enquiry is to question the justification of out beliefs about the world. This is not a particular pet peeve of Hume's, it's just good epistemology. Hume's conclusion will be that we don't have any good, philosophically respectable justification for most of our supposed knowledge of the world.

What is his argument?

First, Hume makes the point that most of our beliefs about what the world is like are based on causal reasoning. Analytic knowledge (relations of ideas) can't tell us anything about what the world is like. In order to know about the world, we have to be directly aware of something, and then be able to reason from that thing to something else in the world. For example, when I read a letter form my friend, I am immediately aware of the white sheet of paper, and the black ink marks, and infer that my friend is in France, because I infer that my friend is causally responsible for the fact that there is a letter in my hands now that says things like "In France -- wish you were here."

When I read history books, I come to believe that Caesar crossed the Rubicon because I have faith in the reliability of the causal mechanisms which start with historical events, and end up with history books being printed. (Perhaps it was something like this: A Roman soldier saw Caesar cross the Rubicon, and this caused him to write about it in his diary, and then years later, a historian read that diary, and wrote an article about Caesar and the Rubicon, and then someone else read this article, and this caused him to believe that Caesar crossed the Rubicon, and when he wrote a history book, etc. The real chain of events is much more complicated, of course. But the reason that I come to believe that someone did something 2000 years ago, an event that I could never have any direct evidence for, is that I have confidence in the causal mechanisms that lead from events to their expression in certain kinds of books. If this causal machinery broke down: suppose things that look just like history books, but with random evens written in them, popped into existence all the time, and I knew that this happened, then I would no longer come to believe that Caesar crossed the Rubicon just because I read it in a book. If you think about it, you should be able to convince yourself that almost everything you believe about the world -- past present and future -- you believe only because you have a tremendous amount of faith in the reliability of certain kinds of causal mechanisms.

So now the question is: can we justify our faith in these causal mechanisms? Well, first we need to ask why we believe that there is a certain kind of causal connection between two types of things, A and B, in the first place, say fire and heat (this is just an example, the same reasoning applies to all other causal mechanisms). Hume argues that this knowledge can't be analytic. We can't just look at something and tell what caused it, or what it will cause. Again, this seems fairly plausible. So, Hume concludes what seems plausible anyway, that we learn that there is a causal link between As and Bs because we have seen As cause Bs before.

OK. At this point, what we know is that in all the cases that we have observed, As cause Bs. So if we can then justifiably conclude that ALL As will casuse Bs, then we could use this piece of causal knowledge to extend our knowledge from what we directly observe to what we don't. How? Next time we see an A, we would be able to justifiably come to believe that a B will be caused, either in the future, or somewhere nearby. For example, I have seen many examples of moving myself, and maybe objects, around in sunlight and causing shadows. If I then could KNOW, justifiably, that there was a causal link between all sunlit objects an shadows I would be able to extend my knowledge in various ways outside the realm of what I can directly observe. For example, if I see the sun shining on my from the front, I can know that there is a shadow behind me, even though I don't now see it. If I see a shadow move across a wall, I can know that there is something moving nearby that is causing it, even though I can't see this thing, for example.

So this is where induction comes in. In order to use knowledge of causation to extend my knowledge beyond what I can immediately perceive, I must know that the causal principle holds not just for the things I have observed, and on whose basis I have come to believe the causal principle. I must be able to know that the same causal link holds between even those objects I have not yet observed, or between those pairs of which I have observed only one. So, for example, though I have observed say 200 cases of an object casting a shadow, I need to know that that principle holds of all sunlit objects, even the ones such that I have not yet observed them together with their shadows. Only if I know this will I be able to deduce that there is an object when I see a shadow, or deduce that there is a shadow when I see a sunlit object.

So now the question is: Can we justify induction, the principle that things which have not yet been observed will be similar to the things which have been observed? Hume's point is that there is no justification for this principle. All supposed justifications either simply fail, or are circular, and hence fail. Almost all of the initially plausible arguments boil down to something like "Induction always worked in the past, and so it will continue to work in the future." This clearly begs the question, as the premise only follows if in fact the unobserved (the future) works the same way as the observed (the past, when induction did in fact work).

For those of you who don't see why circular arguments are bad, dig: An argument starts with some set of premises, statements, call these P1, P2, P3, etc., and attempts to reason from those premises to some conclusion, C. Now a circular argument is one in which C itself shows up as a premise. Circular arguments fail to justify their conclusions, because they assume what they try to prove. You can prove ANYTHING if you are allowed to assume that thing as a premise.

Anyway, Hume's point is that all the arguments people might pose for their belief in induction are circular, and hence worthless. And as we discussed in class, even 'practical' arguments such as 'assuming that induction is legitimate is better than not assuming it' are circular as well. If you simply assume that induction is legit, things will only work out better for you if in fact the future resembles the past. (Or more generally, that the unobserved resembles the observed.)