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In The Nature of Existence [Volume II: Reality - 1988 paperback edition, p.10] McTaggart distinguished between two senses of time:

The A-Series, to 'that series of positions which run from the far past to the near past, to the present, and then to the near future, and to the far future, or conversely'.

And to the B-Series, which runs from 'earlier to later, or conversely'.

I'm having some difficulty in distinguishing these two senses; and the unhelpful names do not help either, other than exemplifying that they are series ie ordered.

I'd suggest that the A-Series identifies the present, and then from the present identifies the past and the future; this is generally how we identify time in our daily life ie

I will meet you tommorow

Or

later, man, later

And

Did you watch the game yesterday?

And that the B-Series is like the mathematical notion of time in that the whole of time is there, in a sense; and we can identify one event from another as being earlier or later, or even simultaneous; and this is the time generally used in history

in 1789 the French Revolution happened

In 1831 the Indian Act was signed

Of course, historical time does not extend to the future; as events haven't happened yet; but some of course are planned

The Football World Cup of 2020 will take place in ...

Are these the correct interpretation of McTaggarts two senses of time; and what was the problematic the identified?

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    Interestingly McTaggart suggested there were three views about time. The A and B theory are ones that he rejected. The C theory is an idealistic one that does not exist (plato.stanford.edu/entries/mctaggart). – virmaior Jul 17 '15 at 12:31
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Regardless of what one thinks of McTaggart's conclusions about the unreality of time your analysis is correct!

As you say, the A-series identifies the present. To reword, the A-series chooses or picks out a moment (or position as McTaggart says) in and marks that as the present moment. From there, relative to that present moment, the near past and near future and the distant past and distant future, are constructed.

So let us call the A-series the relative conception of time. (the term subjective might also work but relative is probably better because it fits with relational theory in physics.)

The B-series relies on the fact that If /M/ is ever earlier than /N/, it is always earlier. (a bit further up the page). McTaggart characterises the distinctions of this class using the term permanent and the other class as not permanent.

But let us go with calling the B-series the absolute conception of time. (The term objective might also work but as we're going with relative let's choose absolute.)

This is why your use of standardised Gregorian dates is correct in your last three examples and why their absence is correct in your first three.

I'm not sure why you are having difficulty in distinguishing the senses because you have distinguished them reliably and in the manner in which McTaggart has.

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