In chapter 4 it is pointed out how advances in modern external observation can work with internal introspective observation in the study of the perception processes. Today cognitive science has made progress up to the brain with many instruments measuring, scanning, and piercing the brain but research seems to end there. Further progress requires introspection research to study how we build up objects by referring concepts to things.

4-11 I am in a position to follow the processes taking place in my organism up to those in the brain, even though my assumptions become more and more hypothetical the closer I come to the central processes in the brain. The method of external observation ends with the brain processes, more precisely, it ends with what I would observe if I examine the brain with the help of the instruments and methods of Physics, Chemistry, and so forth. The method of inner observation, or introspection, begins with the sensation and extends to include the construction of things out of the material of sense-data.

Trains of Thought - Inner and Outer Observation
Hi Tom,
This is an interesting point you raise - I think this is a weak point in our everyday world-view that Steiner highlights clearly throughout the Philosophy of Freedom.
Our thinking is so thoroughly trained to think in terms of externally perceived objects that we easily persist in trying to reduce all human experience into these terms. It's like a train (train of thought) that we get on board that will take us to certain places (places of certainty) but cannot ever travel off its designated track. But we all know in the case of trains that there are many many other destinations we can travel to or must travel to without their help.
In many cases we could travel to a town on the train, then walk, drive, ride, fly or sail on to our destination. In this broader picture we still rely on thinking and observation but observation now includes inner observation. This allows us more freedom in reaching certainty.
In this example travel is any path of thinking and observation - train travel is the path of thinking that believes that only the path of thinking and external observation (i.e. travel to destinations connected by train tracks) can lead us to truth, to a belief we can be certain of.
The interesting fact is that no real person actually travels on this "train" all the time in their life - even the most materialistic scientist needs to be able to observe and review their own thoughts and those of others objectively in the light of observed evidence to reach conclusions. This activity itself is one that cannot be carried out on the "train" - it involves inner observation, a capacity for judgement, memory etc. The view of life adopted by someone who believes stricly in the sole validity of truth arrived at by these means is similar to that adopted by someone travelling to work on the train every day who believes that train travel is the only "real" method of travel while ignoring the plain fact that they also along with many others walk, run and utilise other means of travel every day.
For example - if we travel on the "train" we may believe that thinking is nothing but a firing of neurons in the brain (the firing of neurons being something that can be measured via scientific instruments and the results perceived externally). This seems a reasonable belief only so long as we do not follow the path of thinking and observation outlined in Chapter 3. Then we start to perceive and experience thinking directly as something that is completely known and surveyable as our own activity that is also filled with life and meaning.
Or as another example - there are numerous reports of near-death experiences freely documented and available nowadays - however these are all clearly the result of inner observation by an individual (the reports in each case cannot be verified directly by another individual), so many travelling on this "train" of thinking and external observation believe the similarities between them must be due to some externally perceptible cause, e.g. a peculiarity in physical brain function when the human organism approaches death and so on.
The thought that a human individual could continue to exist in a form that is not externally perceptible is "off the tracks" as it were for obvious reasons - to follow that thought to its conclusion we have to get off the train once again at some point to determine for ourselves the place of what we call "inner" or "subjective" observations in reaching a destination of truth.