Consider a waterfall. One moment of a waterfall is not a waterfall, given only a single moment we can’t tell whether it is a waterfall or not, it is part of the essential nature of a waterfall that it be different from moment to moment*. But not just arbitrarily collection of subsequent moments can be a waterfall, they must bear the correct relation to previous moments; they must have the right kind of similarity. So why are we considering waterfalls? Because some things are, by their nature, spread out through time like waterfalls, and you can’t study those things by asking what properties at any moment define them, you must ask what kind of sequence defines them. It is my claim that consciousness is one of these things.
Of course you shouldn’t take my word for it. Is consciousness something that must be spread out in this way? Perhaps your experience of thinking is somewhat like speaking, such that parts of the thought, like parts of the sentence, occur at different times, and thus, like the sentence, it can only be understood as a temporally extended whole. I admit that this is possible, but it doesn’t seem especially likely. For example, we know that when speaking at least the majority of the sentence is complete before verbalization begins, so even if one thinks through “inner speech” it seems possible that the thoughts may be completely formed, and that we only think of them as extended over time because we are so used to verbal communication. Of course it is unlikely that thoughts simply appear in the mind, perhaps they go through a process of “coalescing” into their final forms, but even if this is the case it wouldn’t seem impossible to understand the thought, and hence consciousness, in the moment that it becomes part of experience alone, without the need to reference previous mental moments.
Let us approach the problem from a different angle. Essentially consciousness is defined by the existence of experience and a first person perspective. Is experience / the first person perspective something that can exist in only a single moment of time? Before I go further allow me to bring into this discussion some of my analysis of the first person perspective, which I developed here. I argued that the first person perspective was created by the structure of experience, not something extra. To avoid possible problems with circularity I introduced the concept of proto-experiences, which are exactly like experiences except they aren’t necessarily experiences for some first person perspective, and consequently aren’t necessarily part of any consciousness. What a proto-experience is, versus what it is not, is something that I have developed only minimally, and is not something I plan on expanding upon here. Thus I will assume that proto-experiences can be said to exist in a single moment of time, and thus if consciousness is to be something that can only be understood only as a sequence, and not as a property of some moment, proto-experiences aren’t the reason why.
This puts the burden solely on the first person perspective. I think, intuitively, it should be clear that for a first person perspective to exist it must exist over some period of time, since it is impossible to imagine being something that exists only for a single moment. To have experience, to be a first person perspective, is to live through some time, however short. I would be unhappy though if my claim was supported by intuition alone, so let me explore a bit more how experience creates a first person perspective.
If a first person perspective is to be created it must be consistent. One part of experience can’t be structured as belonging to subject A and another as belonging to B. (Actually something like this might happen for patients with multiple personalities or a split brain, but in such cases we generally say that there is more than one consciousness, reinforcing my point.) This structuring is itself accomplished by the incorporation of self-information (information about the experiencer) into the experience. Seeing a hand as my hand also involves some awareness of who the “my” is. Even in people who have lost all of their memories, and are unable to form new lasting ones, the “I” in experience can at least be presented as the experiencer of the current experience, and of the immediately previous experiences. It is this consistency requirement that forces us to look at more than one single moment of experience to know that a first person perspective exists (just like we must look at more than one moment of the waterfall to properly know that it is a waterfall). For a first person perspective to exist it must have certain degree of stability. If we wanted to know if an object had some stability in shape we would have to look at several moments in order to know that the shape wasn’t fluctuating wildly. Likewise, we must look at several moments of experience in order to know that the first person perspective isn’t fluctuating wildly, since first person perspectives must have more stability than this, and so such fluctuations would mean that there really wasn’t a first person perspective at all, even though a particular moment of experience indicated that one could potentially exist.
Admittedly stability is a vague requirement. A waterfall is only a waterfall if the succeeding moments are of the right type, not the same as previous moments, but falling within some range of possible future moments, if the object observed is to be thought of as a waterfall. It is reasonable to expect that the stability required of the first person perspective can be defined more rigorously as well, and must be if we wish to understand consciousness. Obviously I don’t plan on tackling such a large project today, but it is a gap that I must point out. Another gap is obviously the nature of proto-experiences. It is possible (likely) that they too have a temporal component to their existence as well, meaning that proto-experiences too must be understood as a certain kind of sequence of states. Well, as they say in textbooks, I leave these problems as an exercise for the reader.
* Although you could probably make a fairly good guess. My point is that you can’t know for sure, some of the information required to draw a definite conclusion can only be found in other moments.