First, we must look at the word Self. The Sanskrit word that gets translated to Self in English is atman. Self is an unsatisfactory English equivalent. To show that Self doesn’t mean ego and in fact has a special meaning, it is often capitalized. The Sanskit term anatman is translated to English as no-Self, which is another unsatisfactory translation.
To answer the question, we must look at other ways atman can be translated. Atman can mean essence or soul. This represents an unchanging self.
In Buddhism, self is seen as conditioned. It is always changing. Therefore it is not atman or in Sanskrit, anatman.
If you watch your mind during meditation, it is going from one thought to another and one feeling to another. This is the changing self. When your mind becomes quiet, who are you? When your mind is quiet, there is no thought of I.
Rebirth is more dicey. Some people point out that rebirth and anatman are not found in the same sutras (Pali suttas), suggesting that they are unrelated.
Others I have read say that rebirth is a mundane or exoteric teaching for the lay Buddhist. Whereas anatman is a supramundane or esoteric teaching for monks and nuns.
Still others say that karma passes from one life to the next. Nothing material is passed; only information.
Then there are those that cite sutras that say the body breaks down into its “elements” and the constituents combine with similar elements floating in space which get recombined to make a new person. The recombined elements come from a mix of different dead bodies.
Since Buddhism was founded in the iron age, it has an iron age view of the world as being made up of air, fire, water and earth. I am not sure where the idea of them floating in space comes from. I find this very odd.
©2016 Stephen L. Martin
Painting: Samsara, painter unknown