"There is no self." This is a teaching one hears frequently in current non-duality circles. This teaching comes from the Buddha, only in the cases to which we are referring, it is, in general, not being correctly understood.
Categorically stating "There is no self" is an idea, a concept in the mind - albeit a very subtle one. A person clinging to this idea - because it is so subtle - does not easily recognize what they are doing. However, others will observe and sometimes experience the rigidity that comes along with fiercely clinging to any idea.
But let us consider why this idea is so subtle. Firstly, the idea "There is no self" is correct from an Absolute perspective. There is no separation. There is only the Self. brahman (God) is one-without-a-second.
Nonetheless, no genuinely realized person outside of or inside of any tradition, including Buddhism, will state "There is no self" in a categorical way. This is because Reality is viewed as non-dual. If we look at the Sanskrit word "advaita" we see that "a" means "not" and "dvaita" means "two". So the term is indicating that what appears to be two is not. Here we can ask, "What two are not two?" These are vyavahAra and paramArtha, which is to say, the relative and the Absolute.
Secondly, once it has been categorically stated that "There is no self" the dimension of the relative is seemingly undercut - but from a subjectivist point of view, which maintains there is no ontological existence. Rather than categorically stating "There is no self", genuine non-duality situates the relative within Consciousness. This relative existence is considered to be mithya, underscoring that name and form are neither Real not unreal.
Name and form are not Real because they are not the Real, since the Real is by nature abiding and permanent. Simultaneously name and form are not unreal because they do have ontological existence, if only temporarily.
Instead of saying "There is no self", great vedAnta RRiShi-s and sages have taught that there is only the Self. This Atma, this Self, this Reality is not devoid of appearances; It is full of them. And emptiness is only one of those appearances. When we consider how emptiness is objectively verifiable (as in the case of seeing nothing in a cup), we are able to understand how stating "There is no self" is tantamount to saying existence is comprised entirely of one objective substance. It is like saying, for example, that Reality is stone.