How does Buddhism explain consciousness if there is no self? One major differing point between Hinduism and Buddhism is the understanding of the self. Buddhist reject the Brahminical notion of an eternal, non-material soul substance that is distinct from the mind, body and sense organs. How then, is consciousness explained? Acts of cognition must occur from a cogniser, a subject that knows, because consciousness does not belong to the body or the mind. Could it not be therefore inferred that this cogniser exists as the self - a non-material soul? How can Buddhism explain  consciousness?
Acts of cognition do not require a "cogniser, a subject" that knows (apart from the mind itself), because consciousness belongs to the body &amp; mind.

The original question contains an implicit assumption that is invalid. 

Cognition results from consciousness; just as a mirror reflects without a self.

Buddhism explains there are five aggregates (khandha) that compose a human life. SN 22.81 explains the idea of 'self' is ignorantly created by the 'sankhara khandha' (mental forming aggregate) and not the 'vinnana khandha' ('consciousness aggregate'). SN 22.59 clearly states each aggregate is 'not-self'. The sankhara created 'self' is a temporary product of ignorance (SN 22.81) &amp; suffering (SN 5.10). 

Despite ideas contained in later-day Buddhism about 'relinking' or 'stream of consciousness', the Pali suttas report the Buddha taught there can be no arising of consciousness without sense organs (MN 38), without other aggregates (SN 22.53) and without a mind-body (SN 12.67). 

Also, the suttas do not explain a 'cause' ('hetu') of consciousness, i.e., the parts or sub-elements that create consciousness (similar to how water, clay &amp; pain are the parts used to make a cup or how ignorance, craving &amp; attachment mix together to create suffering). The suttas only state consciousness has a requisite 'condition' ('paccaya'), which is the mind-body ('nama-rupa') &amp; sense bases ('salayatana').