Kaṅkhāvitaraṇa-visuddhi

kaṅkhāvitaraṇa-visuddhi is translated as "purification by overcoming doubt," "purification of crossing over doubt," etc. In the Pali tradition, kaṅkhāvitaraṇa-visuddhi is identified as the fourth of the seven stages of purification on the path to liberation, as presented in the Visuddhimagga.

Buddhism: One Teacher, Many Traditions states:

Purification by overcoming doubt (kaṅkhāvitaraṇa visuddhi) discerns the conditions of the mind and matter in the past, present, and future, thus eliminating doubts concerning them. By meditating on dependent arising, meditators view the present collection of aggregates as dependently arisen, conditioned phenomena, thus understanding their body-mind complex does not arise due to a transcendent creator, is not a manifestation of a primal or permanent cosmic substance, and did not appear causelessly.

Rupert Gethin states:

Having established a sense of experience as subsisting in the interdependence of mind and body, the practitioner moves on to the fourth purification, that of ‘crossing over doubt’. The practice at this stage is referred to as ‘comprehension of conditions’. In the previous stage the practitioner contemplated the interdependence of mind and body in any given experience; here he broadens the meditation to take in the past, present, and future. In other words, the practice moves from the contemplation of the particular to the general, and one begins to see that what is in operation is a universal ‘law’—the law of dependent arising; one begins to see that, just as mind and body are interdependent now in the present, so they have been in the past and so they must be in the future. One sees that mind and body, although existing, have not been created or brought into being out of nothing by some creator God. Thus there is no particular beginning to their existence and no end. The law of dependent arising alone is a sufficient explanation of their existence. Direct insight into this process is presented as deeply affecting the meditator. His outlook on the world is profoundly changed. His understanding of the teaching has ceased to be purely theoretical and become a matter of direct experience which cannot be denied. Thus the meditator is said to cross over doubt and thereby complete the fourth purification to become a ‘lesser attainer of the stream’.

Sources

• Buswell, Robert E.; Lopez, Donald S. (2014), The Princeton Dictionary of Buddhism, Princeton University 
• Dalai Lama; Thubten Chodron (2014), Buddhism: One Teacher, Many Traditions, Wisdom Publications 
• Gethin, Rupert (1998), Foundations of Buddhism, Oxford University Press