I would recommend: Selves & Not-self: The Buddhist Teaching on Anatta, by Ṭhānissaro Bhikkhu
There are many philosophies on self. In Buddhism there is a concept called not self. This book covers this aspect.
"He demonstrates how the properties of self-referential systems, demonstrated most famously in Gödel's incompleteness theorems, can be used to describe the unique properties of minds." — (https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop)
I recommend I Am a Strange Loop by Douglas Hofstadter.
May I suggest 'The Essentials of Zen Buddhism' by D.T. Suzuki, or any number in the series that Suzuki's written about Zen?
In my opinion Zen is about the pinnacle of both Western and Eastern thought in this area, and I can tell you that Suzuki has a way with words on the subject.
It's not as much about the self explicitly, but rather the lack of one and ...
I think it's fascinating from both recent Western accounts and older Eastern philosophical investigations which are still as relevant as ever. Sometimes the two are intertwined, depending on the tradition. In terms of a Western approach, Susan Blackmore has a really good introductory book called Consciousness: An Introduction. I like Dennett's Consciousness ...
You will get a summary from this:
And this book deals its details:
Answer to a possible doubt:
Blackburn's book is very readable but as a stereotypical 'Western' thinker he has little to say other than to describe the state of academic philosophy.
The entire literature of the Perennial philosophy or 'Wisdom' literature is about the self, and there are so many good books you won't be able to miss them.
One book that comes to mind is Sri Ramana ...
It seems like we can conceive of self contradictory things that can exist. e.g. the proposition expressed by "this sentence is false" is self contradictory but I don't seem to have any trouble understanding the sentence. e.g. Lazerowitz says that there it is straight-forwardly true that self contradictory propositions "exist" if we mean "declarative sentence"...