From reading this question on Hume, having read the first seven sections of the Enquiry Concerning Human Understanding (which covers the relevant section), a further question hit me. Hume dismisses the occurrence as "singular ... scarcely worth our observing", yet he brings the counter example up instead of others. Why does he bring up a counterexample which he himself dismisses as trivial? Is it to bolster his argument by suggesting that the only counterexample so important as to be worth mentioned is itself highly trivial? Or is it merely because its the only concrete, simple counterexample Hume conceived of? Responses with links to Hume scholars would be appreciated.
Hume's thesis is that all of our ideas are copies of our sense impressions. That is, Hume is saying any mental representation we have of some real or imaginary thing must derive in some way from our experience.
But what does it mean to say our mental representations are derivable from experience in this way? The missing shade of blue objection is important because it shows that Hume thinks about this requirement about derivability from experience in a broad, and plausible way. To see what Hume is up to, consider the differences between the following different versions of the derivability requirement.
Strong Derivability You might initially think that Hume thinks we could only think about things we have actually, personally witnessed, touched, heard, etc. Strong derivability is very implausible though. I think about lots of things that I personally have never seen. (Unicorns, for instance.) So if what Hume meant was that all of our mental representations were strongly derivable from our experience, his thesis would be false. It is pretty clear just from Hume's explicit words though that this isn't his view, since he often uses imaginary beings as examples of things we have ideas about.
Moderate Derivability is the view that we can think about things whose mental representations are composed of pieces or parts, which are things that we have personally witnessed, touched, heard, etc. On this view, there would be no problem with my thinking about a unicorn, since I have personally seen both horses and horns and I am capable of combining those two separate representations into a new representation of a thing which is a horse with a horn on its head.
Now the person who is challenging Hume about the missing shade of blue is assuming moderate derivability is Hume's view. So, the objection is that moderate derivability is still too strong a requirement, because I can think about things that I never experienced at all. For example, there are lots of shades of blue. Imagine them all next to one another on a color wheel. It is certainly possible that there are three adjacent shades of blue on the color wheel, blue1, blue2, and blue3 such that I have personally experienced blue1 and blue3, but not blue2. Nevertheless, the objector says, I can form a very clear and definite idea of what blue2 must look like, just by imagining what must come between blue1 and blue3. Now if that's the case, then it looks like I have a (simple) idea of something that I never experienced, and hence it looks like the moderate derivability requirement is false.
Now Hume responds to this that he is quite happy to acknowledge that we can come to think of blue2 in this way, without ever having directly experienced it. All I am committed to, Hume might say, is a thesis much weaker than moderate derivability.
Weak derivability If I have a mental representation of X, then there is some thing Y (not necessarily identical to X) which I have personally experienced, such that my idea of X can be derived from Y.
Notice that the missing shade of blue objection doesn't tell against weak derivability because my ability to think of blue2 is still dependent upon my having had experiences of other things that were blue1 and blue3. Hume is considering the objection, because it helps him make clear that his thesis is only this far weaker (and therefore, more plausible) claim.