"continuity of consciousness" is correct and usable in written English.
You can use it when discussing or writing about the idea that consciousness carries on from one moment to the next, sometimes over long periods of time. For example, "The continuity of consciousness allows us to remember events that occurred years ago."
Locke's proposal was that personal identity consists of continuity of consciousness.
What you need is an older man who can define the self through a continuity of consciousness and also survive the Great Plague.
The new person that he became had continuity of consciousness with his life as Jesus of Nazareth, an earthly life in which he had become fully human and fully divine.
Remarkably, the patients were conscious and cooperative throughout the procedure, and there was no interruption of the continuity of consciousness, despite the removal of vast amounts of cerebral cortex.
Although the Jamesian emphasis on the continuity of consciousness is widely viewed sympathetically, there are dissenters.
This sort of continuity of consciousness can span very short durations (such as the 'specious present').
William James is well-known for emphasising the continuity of experience – 'Consciousness, then, does not appear to itself as chopped up into bits.
James concludes by embracing a position that he had more tentatively set forth in The Varieties of Religious Experience: that religious experiences "point with reasonable probability to the continuity of our consciousness with a wider spiritual environment from which the ordinary prudential man (who is the only man that scientific psychology, so called, takes cognizance of) is shut off" (PU, 135).
What interests me in Buddhist thought, and what I experience in meditation, is its interest in a continuity between the space of consciousness and space at large.
Unlike Broad, Husserl addresses the Strong Continuity Thesis – albeit not in so many words – and has a good deal to say about the experiential relationships between neighbouring specious, relationships which (he believes) suffice to secure the kind of continuity in consciousness which actually exists.
By moving rapidly from one thought to another, Clive managed to secure a sort of continuity, to hold the thread of consciousness and attention intact — albeit precariously, for the thoughts were held together, on the whole, by superficial associations.
