In answering the question i think we can look to the Anattalakkhana Sutta by Mahasi Sayadaw which can be found here.
In here the 5 aggregates are discussed, how they are formed and why they are not-self.
All of the 5 aggregates are suffering because they are subject to the 3 signs of existence: impermanence, unsatisfactoriness & not-self.
I think this philosopher Dan Dennett does not go to the deepest level of reality - Paramattha Sacca, the ultimate reality. Here designations such as "we, us, brain" does not exist. They are only conventional truths that humans have constructed in order to be able to communicate with each other.
If one looks at the ultimate level of reality there are only 4 things that can be said to be ultimately real according to the Abhidhamma. These 4 things are: Mind, Mental concomitants, Materiality and Nibbana. When Dan Dennett talks about "us and the brain" he speaks only of conventional reality.
There is no "us". The human being is a comming-together of the 5 aggregates. When these aggregates are working together as a physio-psychological machine the idea of an "I" is formed. But this false idea of an "I" is really just one of the 52 mental states, contained in the 4th aggregate of mental formations. This is said by Dr. Walpola Rahula on p. 19 in his book "What the Buddha taught" .
I think that a philosopher like Dan Dennett would get much intellectual knowledge out of reading the Anattalakkhana Sutta and The Abhidhamma but he will never truly understand consciousness or anything else if he does not engage in insight meditation.
To my knowledge even Modern psychology, limited as it is, has finally come to the conclusion that the "Self" is merely a construct. Although they only deal with it at a conventional level.
Buddhism have been dealing with this on an ultimate level for 2500 years while modern psychology have just begun to scrath the surface in the last 100 years. Although modern psychologists are actually beginning to understand more about how buddhist psychology is really what they are now "rediscovering".
I am here quoting Dr. K. Sri Dhammananda as he writes in his book "What Buddhists Believe" on p. 109:
"... The analysis of the nature of the mind given in the Abhidharma is not available through any other source. Even modern psychologists are very much in the dark with regards to subjects like mental impulses or mental beats (Javana Citta) as discussed in the Abhidharma. Dr. Graham Howe, an eminent Harley Street psychologist, wrote in his book, THE INVISIBLE ANATOMY:
In the course of their work many psychologists have found, as the pioneer work of C.G. Jung has shown, that ‘we are near to [the] Buddha. To read a little Buddhism is to realise that the Buddhists knew two thousand five hundred years ago far more about our modern problems of psychology than they have yet been given credit for. They studied these problems long ago, and found the answers too. We are now rediscovering the Ancient Wisdom of the East.’..."
I hope i have understood the above mentioned correctly. If im wrong about something feel free to correct me.