If you're arguing that the scientific method is our best known way of investigating consciousness, I don't think anyone disputes that. If we assume the existence of an external world (as common sense would dictate), we have a great deal of confidence in science. My concern is that it's hard to investigate consciousness without a good definition.

Any definition ultimately depends on undefined concepts. Let's take numbers. For example, "three" is a property shared by all sets that can be put in one-to-one correspondence with the set { {}, {{}}, { {{}}, {} } } (to use Peano's construction). A one-to-one correspondence between two sets A and B is simply a subset of the Cartesian product A x B that satisfies certain properties. So numbers can be thought of in terms of sets. But what is a set? Well, it's a collection of objects. We can then ask what collections are and what objects are, etc. At some point we have to decide upon primitive elements that remain undefined and build everything up around those. It all rests on intuitions in the end. We decide which intuitions are the most trustworthy and go from there.

So, if we want to define "consciousness", we are going to have to found it upon some elementary concepts. The trouble is that, since our consciousness forms an important part of all our perceptions and even our very thoughts, it's difficult to get a good outside perspective and see how the edifice is built.