William James postulated a "stream of consciousness" that presupposes temporal continuity. The neuronal mechanisms underlying the construction of such temporal continuity remain unclear, however, in my contribution, I propose a neuro-phenomenal hypothesis that is based on slow cortical potentials and their extension of the present moment as described in the phenomenal term of "width of present". More specifically, I focus on the way the brain's neural activity needs to be encoded in order to make possible the "stream of consciousness." This leads us again to the low-frequency fluctuations of the brain's neural activity and more specifically to slow cortical potentials (SCPs). Due to their long phase duration as low-frequency fluctuations, SCPs can integrate different stimuli and their associated neural activity from different regions in one converging region. Such integration may be central for consciousness to occur, as it was recently postulated by He and Raichle. They leave open, however, the question of the exact neuronal mechanisms, like the encoding strategy, that make possible the association of the otherwise purely neuronal SCP with consciousness and its phenomenal features. I hypothesize that SCPs allow for linking and connecting different discrete points in physical time by encoding their statistically based temporal differences rather than the single discrete time points by themselves. This presupposes difference-based coding rather than stimulus-based coding. The encoding of such statistically based temporal differences makes it possible to "go beyond" the merely physical features of the stimuli; that is, their single discrete time points and their conduction delays (as related to their neural processing in the brain). This, in turn, makes possible the constitution of "local temporal continuity" of neural activity in one particular region. The concept of "local temporal continuity" signifies the linkage and integration of different discrete time points into one neural activity in a particular region. How does such local temporal continuity predispose the experience of time in consciousness? For that, I turn to phenomenological philosopher Edmund Husserl and his description of what he calls "inner time consciousness" (Husserl and Brough, 1990). One hallmark of humans' "inner time consciousness" is that we experience events and objects in succession and duration in our consciousness; according to Husserl, this amounts to what he calls the "width of [the] present." The concept of the width of present describes the extension of the present beyond the single discrete time point, such as, for instance, when we perceive different tones as a melody. I now hypothesize the degree of the width of present to be directly dependent upon and thus predisposed by the degree of the temporal differences between two (or more) discrete time points as they are encoded into neural activity. I therefore conclude that the SCPs and their encoding of neural activity in terms of temporal differences must be regarded a neural predisposition of consciousness (NPC) as distinguished from a neural correlate of consciousness (NCC).