Science is great when it comes to discoveries and studies about the physical world. It requires lots of work and dedication, analytic skills to test various hypotheses, and a wealth of creativity to figure out how to conduct experiments to tell the merits of one explanation from those of another. For all of that, however, and without implying any denigration, it's also somewhat easy because you have the physical world itself to check your results against. If you think dropping heavy objects will float, the universe itself will let you know you're wrong...
Philosophical research, on the other hand, is more difficult because the object of our studies is concepts, and concepts will not smack you upside the head when you're wrong. Take one simple example for comparison: in science, you might study how something changes, and you can easily imagine the set of tools you might need to do the job. In philosophy, you'd study the nature of change itself. How on earth do you do that???
And the investigation of change is one of the philosophical questions par excellence, tracing its history all the way back to Heraclitus and Parmenides. In this final lecture, Professor Millican explores the question of personal identity: assuming that you do exist, what does it mean to say that your past self and your present self are the same person? How can it be the case that something that changes is still the same thing? That sounds like a logical contradiction, and yet pre-reflectively at least, this is what we all assume to be true.
Click here to see the course slides
And more awesome stuff on this and related questions, check out the Brainspotting tag.