Time, as is well known, is according to Augustine extensio animi, an extension of one's soul. Hence, it does not exist apart from it.
However, Sartre maintained that the most fundamental level of consciousness is pre-egological and Husserl supported (only) a transcendental ego –that is, one which does not appear as such in consciousness. Buddhist thinkers were explicitly non-substantialist, at least after Vasubandhu.
Does time-consciousness entail a (transcendental, at least) ego?
Husserl's claim that there is a moment of retention within every instant of experience, might help one in avoiding to postulate an ego and yet account for time-consciousness. However, one might object, such a retention is itself momentary and hence cannot account for long-term memory.
While dealing with such questions, Matt MacKenzie admitted that retention is one of the conditions of possibility of memory, and it is still not the depiction implied by memory. In order to get it, one needs to add an account of the sedimentation of retention-traces (in Sanskrit one would call them vāsanā or saṃskāra). This is the role of the depository consciousnessm the ālayavijñāna. A presentist (and at the conference on Self: Hindu Responses to Buddhist Critiques this role has been performed by Jan Westerhoff) could instead object that there are, in fact, NO RECORDS of the past. What appears as a record of the past is in fact a present cognition, which we misinterpret as relating to the past. In other words, it only "looks" as a record, but it exists in the present as something else.
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