According to McTaggart's famous paper, "The Unreality of Time," there are only two kinds of temporal order, namely the A and the B series, and all topologies must fall under these two classifications. Philosophers have not been able to find a plausible topology outside of those two series so on this account, McTaggart may be correct. The problem, as McTaggart pointed out, is that the B series are two-place relations (is before, is after) but that these relations cannot make sense of change which McTaggart believed essential to time.
The A series, however, does no better because it is incoherent. The reason is that the A series takes the past, the present, and the future to be genuine properties of times but that if the A series were true, all times would have all three properties at once and that is incoherent or contradictory.
I would like to concentrate on the growing block universe theory. Traditionally it has been thought of being described thus:
On this view, which we can call “The Growing Universe Theory,” the universe is always increasing in size, as more and more things are added on to the front end (temporally speaking).
However, why is the stuff always added on the front end?
Can't we think of time as receding away from the present? Instead of the past (especially the Big Bang e.g.) being the stationary reference point, why can't we see the present as such a point? Some may quickly respond and say that this view is clearly false because it seems that our subjective sense of time is of a "moving forward" into the future but what justification is there of that directionality? Can't we as easily see this as the past receding away from us? It would be analogous to people before Copernicus thinking that the sun and all heavenly objects revolved around the Earth when it was the earth that revolved around the sun. But here, there is no essential stationary reference point in modern astronomy.
(future?)<-----------Present --------->Big Bang (beginning of time?)
One of the major advantages of this view of time is that it jibes well with relativity and the expanding universe idea (which presentism has notorious difficulties with among other things). If space is expanding, time is probably as well as space and time are unified under general relativity. Eternalism seem to be also at odds with an expanding spacetime. Also, notice that the expansion I am thinking of can be thought of as symmetric (which growing block is most certainly not).
We can simply think of the expansion of time like the stretching of a rubber band. The space between any two points on the band expands. In the case of space, astronomers thought that expansion of space is more like a balloon being inflated with any two points on the balloon's surface getting further apart when the region (balloon's skin) between them expands. This explains the odd observation in the early 20th century by astronomers that every galaxy in the universe seems to be flying away from us and each other.
I think doing so would mean making this kind of symmetric growing block have certain decided advantages of presentism without some of its problems. First of all, it can make sense of change and thus has some of the advantages of the A series. Second, it has some of the B series advantages such as making sense of "truth makers" for the past and maybe future as well for assertive claims about the non present. The past exists under the B series and has the same ontological status as the present, thus a fortiori, facts about the past exist rendering assertive statements about the past true or false unlike presentism which claims (implausibly) that all assertive statements about the past are strictly speaking false or have no truth value. My idea also has the advantage of symmetry which we know that our best physical theories posit. The general theory of relativity, quantum mechanics and statistical mechanics all posit temporal symmetry.
I am agnostic about whether we are at the growing tip of one end of that expanding rubber band or in the middle somewhere. This has the epistemic disadvantage that we may not ever be sure of where we are in the temporal order of things which was argued by David Braddon-Mitchell and Trenton Merricks to be a fault with growing block. We could be anywhere except one end which is the point of the Big Bang (Merricks argued that it is far more probable that we are in the past if growing block is true than any-when else). But notice that in my rubber band topology, all points on the rubber band, corresponding to times, will seem alike to any other. So it may be that we are between some point in the future and past and yet we would have the same perspective as any other point on the band. Any point on the band will look "alike" from the perspective of those in it.
I do think that we have reason to think that we are at the end band opposite from the Big Bang because we seem to have better epistemic access to information from the past than the future. We are better informed of the past than the future and this asymmetry may suggest we are at one of the end's edge. This epistemic asymmetry between knowledge of past and future presumably is because the future does not exist relative to our position.
My idea is disadvantaged however by the fact that any point in the future, if it exists and we are not at the endpoint opposite the Big Bang, is rocketing away from us (much like points in space are getting further apart from each other). That may seem counter intuitive. A further oddity that may have to be explained is that while the expansion of the universe and the Ptolemaic world views mistakingly see our own position as privileged and stationary, in the case of time, why is it that we seem to see the past (or perhaps the Big Bang) as that privileged and stationary point?
I also have some ideas about the semantics of talk about the present (and past, etc) which my view of time seem to offer ways around traditional difficulties with the other viewpoints. More to come on that later. This is just a sketch of my hazy idea which I will call (unimaginatively) "rubber band growing block theory." I need to think about it more. Also, we may see the view advocated here not so much as a growing block but a dynamic eternalism with a finite temporal extension (if such a thing makes any sense) but I suspect that that is a terminological point.