The starting point of the most recent metaphysics on time can be shown by arguments by McTaggart. He viewed that events and times can be order in two ways:
B-Series: the ordering of events and times into tenseless relations of being earlier than and later than.
A-Series: the ordering of events and in terms of the tensed properties of past, present and future.
McTaggart also viewed that B-series presupposes (or is built off of more fundamentally) A-series. His argument is that A-series is a contradiction and since B-series presupposes A-series he concludes that time is unreal.
There has been some scholarly debate about the interpretation of McTaggart’s argument, but here are the main themes without getting into the debate.
From B-series we have events e1 and e2, either e1 is earlier than e2, e1 is later than e2, or e1 is neither earlier than nor later than - but simultaneous with e2. An event or time has an unchanging position in this series. e1 being earlier than e2 will always be true and hold that relationship. It’s static and unchanging.
The A-series is a series that takes us from the distant future through the present and into the remote past. This series differs from B-series because it isn’t unchanging/static, it is dynamic. Events and times change. Events move from the future, into the present and finally ending up in the past.
As mentioned earlier, McTaggart has two particular arguments (1) that B-series presupposes A-series and (2) A-series is a contradiction.
(1) Why does McTaggart think that B-series presupposes A-series? His claim is that the items making up the B-series constitute that temporal framework only in virtue of being subject to the various A-determinations (past, present and future)
(2) McTaggart argues that the properties of past, present and future are incompatible with each other. An event in the future is not present nor past, an event in the present is not future nor past, and an event in the past is not future nor past. With this reasoning he sees how events travel through future, present and past - therefore a contradiction.
Since A-series is a contradiction and B-series presupposes A-series, therefore time is unreal.
Metaphysicians that view B-Theory as correct have two main responses to McTaggart’s argument. (1) that McTaggart fails to show that B-series presupposes A-series and (2) he fails to show that that the idea of events and times are subject to attributions of the various A-properties.
(1) B-theorists view the theory just like McTaggart’s argument of B-series. They see time as eternally fixed framework structured by the tenseless relations of being earlier than, later than and simultaneous with. In this view, time is a dimension along with the three spatial dimensions. B-theorists hold that all the spatial locations and their contents, the various temporal locations or times and the things they contain have the same ontological status. All times and their contents are equally real.
McTaggart’s main argument against this view is that if these events are real and unchanging for all time, it is impossible for something to gain a property or cease to have it - it always has it. B-theorists respond by saying this by saying that this is confusing time-indexed properties at a time t and the non-time-indexed property of just existing.
(2) If we take the following sentence, it snowed yesterday, we have a tense. B-theorists believe that such sentences can be captured in the tenseless by changing it to something like, it snows on December 24 2012. Another example is, it is snowing now, vs, it is snowing simultaneously to this utterance.
The big rebuttal from A-theorists is that time isn’t some fixed and permanent framework in which every time, event and thing has an unchanging or equally real position. A-theorists also disagree with the B-theorists rewriting of the sentences in the above (2) because the first sentence doesn’t exactly mean the same thing as the second.
There is another view among A-theorists that it isn’t the events and things that move from future, to present, to past. It is the present that moves along a road of events.
There are various views that come out of the A-Theory such as there being no such things that make up the future events and others that think the past has no more events. The only thing really living is the present.
The New B-Theory
The new B-theorists agree with the defenders of the old tenseless theory. They deny that tensed language can be translated into tenseless language. They reject the idea that the A-theorist’s claim that the ineliminability of tensed language shows that time itself is tensed.