What tradition(s) lies really at the roots of the Classical Indian Philosophy?
I recently read an article by R. Bhattacharya (AION 2007, just published!) and one by K. Preisendanz (Indian Journal of History of Science 2009) on the role of ancient Indian medicine and its place within Indian philosophy. K. Preisendanz accurately examines Vidyabhusana's view that the medical work Carakasaṃhitā is an earlier output of the same Ānvikṣikī tradition which later led to the composition of the Nyāyasūtra. She mostly focuses on the tradition of debate and offers many cogent evidences. Hence, can we safely assume that we owe Indian philosophy as it is to the Ānvīkṣikī tradition, as reflected in the Carakasaṃhitā?
Yes and no.
I have been working for years on the technical terminology of the Kalpasūtras and the way it is intertwined with the terminology of Mīmāṃsā and the one of Grammar. This work made me aware of how philosophical terms, such as prasaṅga, have a deep ritual background and can be better understood through it. Furthermore, the dialectical shape of most Indian philosophical texts has been fundamentally influenced by the succession of pūrvapakṣins and siddhānta as found in the ritual sūtras.
To sum up, the past is more complex than one might believe. There has been more than one root for what we now know as Indian philosophy and its dialectic attitude. Does not this just amount to say that the past was as complex and intertwined as the present?
On prasaṅga, see here, here and here (showing also the connection of Mīmāṃsā, Kalpasūtra and Grammar). On another example of such connections, see here (about the history of the classification of prescriptions).