The Connection Principle
There's a necessary connection between consciousness and mentality. All thinking—as a form of mentality—is a least in principle accessible to consciousness. Even unconscious thoughts involve consciousness, as they can potentially become conscious.
Searle's belief that California is on the West Coast, for example, may be unconscious when he sleeps, but it is at least potentially conscious in that it can be brought to consciousness if he is asked for directions to California.

John Searle (1991a).
Artificial Intelligence »Artificial Intelligence
Can computers think? [1] »Can computers think? [1]
No: computers can't be conscious [6] »No: computers can't be conscious [6]
Consciousness is necessary to thought »Consciousness is necessary to thought
The Connection Principle
Mental states have aspectual shape »Mental states have aspectual shape
Connection principle is merely definitional »Connection principle is merely definitional
The Connection Principle Dilemma »The Connection Principle Dilemma
The consciousness-pill thought experiment  »The consciousness-pill thought experiment
The water-seeker thought experiment »The water-seeker thought experiment
Unconscious and conscious states aren't identical »Unconscious and conscious states aren't identical
Unconscious intentional zombies »Unconscious intentional zombies
John Searle »John Searle
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