The Buddha's silence on the subject of the Self and his stress on the impermanence of the world was negatively interpreted and blown up to its full potential by early Buddhist logicians resulting in the doctrine of momentariness or kshanikavaada. There's nothing permanent - everything is transient. Two brilliant philosophers who expounded this doctrine were Naagasena and Buddhaghosa.
The Bactrian Greeks who after the advent of Alexander occupied some parts of North Western Bhaarath, found Buddhism an easier faith to relate to and adopt, than the bewildering and culturally distinct Hinduism with its various Gods and Goddesses. The Milindapanha or the "Questions of King Milinda" is a beautiful work of prose in Paali, narrating a philosophical debate between the Buddhist dialectician Naagasena (100 BC) and the Greek king Menander, Indianized to Milinda.
Buddhaghosa (400 AD) was a learned brahmin from Andhra of the Patanjala Yoga school, who in the customary manner of his lot traveled around Bhaarath challenging and defeating heretic philosophers in debates, till he met his match and was converted to Buddhism. He wrote commentaries on the four great Nikhaayas and his greatest work is Visuddhimaggaa or the Path to Purification. His is the greatest name in Paali Buddhist scholasticism and his Atthashaalini is a valuable commentary on the Dhammasangani.
In Naagasena we find one of the earliest negative interpretations of the Buddha's silence. Buddhist thought is torn away from its ancestral stem answering to the religious needs of man and planted in a purely rational soil. The immortal Soul is dismissed as an illegitimate abstraction and projected as the product of the five skandhas (form, feeling, perception, intellect and pre-dispositions). There's no being - only becoming. The logical results of the philosophy of becoming are drawn out with rigour.
For Naagasena, the self is an unceasing stream of ideas. This stream possesses
a common character and this common element is mistakenly called the Self or
Atman. If we take a chariot, the individual parts - the axel, the wheels,
the rope, framework - are not the chariot. All the parts are not the chariot.
It's only on account of the coming together of all the parts in a particular
form, it comes under the generally understood term "chariot". It's just an
appelation, a name but in the absolute sense there's no chariot. We just imagine
something underlying the properties. Even so do we imagine a Self underlying the
mental states. Buddhaghosa explains in the Visuddhimaggaa :
"Just as the word chariot is but a mode of expression for axle, wheels and other constituent members, placed in a certain relation to each other, but when we come to examine the members one by one, we discover that in an absolute sense there's no chariot. Just as the words house, fist, lute, army, city, tree are only modes of expression for collections of certain things disposed in a certain manner, in exactly the same way the words living being and ego are only modes of expression for a complex of bodily and non-bodily constituents".
As body is a name for a system of qualities, even so the Self is a name for the sum of the states which constitute our mental existence. "Just as it is by the condition precedent of the co-existence of it's various parts that the word 'chariot' is used, just so is it that when the skandhas are there we talk of a 'being'". Naagasena likens the Self to the ever changing flame of a candle which burns through the night. "One element is always coming into being, another is always ceasing and passing away. Without beginning, without end, the change continues". Buddhaghosa elaborates : "The being of a past moment of thought has lived, but does not live nor will it live. The being of a future moment will live, but has not lived nor does it live. The being of the present moment of thought does live, but has not lived nor will it live."
But if the Self is just a stream of ideas how do we have the sense of continuity of our individuality? How do memory and recognition function?
Aniruddha's Abhidhammattha Sangaha comes out with an ingenious explanation for this :
"Each mental state is related to the next in atleast four different modes of relation : proximity, contiguity, absence and abeyance. Each mental state on expiring, renders service to the succeeding mental state, by passing on the whole of its energy. Each successor therefore has all the potentialities of its predecessor and more. Thus the principle of recognition or perception in each of the mental states, with all its heritage of the past, is a recognition under favorite circumstances, in the image reproduced of the original object by the very marks which were observed by its predecessors in a certain intuition or reflection".
Though the present Self may not be the past, it's yet the outcome of the past, the resultant of the series. There's persistent continuity as well as unceasing change.
Nirvaana is described by Naagasena as : "a kind of existence devoid of egoity, a timeless existence, fully of confidence, peace, calm, bliss, happiness, delicacy, purity and freshness." Though Naagasena seems to have thought of Nirvaana as something inherent in man, he desists from speculating further about its nature.
A humorous dig at Naagasena's theory of the Self is found in the Jaataka tales :
The Boddhisatva said to the pilgrim : "Will you have a drink of Ganges water fragrant with the scent of the forest?"
The pilgrim replied : "What is the Ganges? Is the sand the Ganges? Is the water the Ganges? Is the nether bank the Ganges? Is the further bank the Ganges?"
The Boddhisatva retorted : "If you except the water, the sand, the hither bank and the further bank, where can you find any Ganges?".