In the Buddha’s time it seems speculation around atta and anatta was thought to be wrong contemplation (ayonisomanasikara- MN2). This makes sense as we would contemplate through our own ignorance and find it difficult to see past it.
The approach to this seems to be by watching the five aggregates (those qualities most likely to be mistaken as the self) arise and pass away according to the four foundations of mindfulness.
with metta
Mat