The "conventional" self - in what way can it be accepted? Buddhist writers, such as Joseph Goldstein and Thupten Jinpa, say that although the self is not intrinsically real, that we still accept the "conventional" idea of self. For example:


  If we arrive at the knowledge that the self at which we grasp is empty, we may imagine this means that we as individuals with personal identities do not exist.
  But of course this is not the case--our own personal experiences demonstrate that we as subjects and agents of our own lives, we certainly exist.
  So how then do we understand the content of this insight into absence of Self?
  What follows from this insight?
  We must be very clear that only the self that is being grasped as
  intrinsically real needs to be negated. The self as a conventional
  phenomenon is not rejected.
  This is a crucial aspect of the Buddha's teaching on emptiness.
  Without understanding this distinction, one cannot fully understand the meaning of no-self.


If we believe anatta, then how, specifically, can the "conventional" self be accepted? Do they mean we only pretend that the illusion of self is real in order to talk to people in everday language? Or is there some part of the concept of self that even Buddhism cannot reject?
The usage of the word 'self' in a conventional sense is the same as the usage of the word 'chair'. There's nothing intrinsic in the material it is made of that makes a chair a chair. But the usage of concepts are useful in day to day life for the purpose of identifying functions.