Is there a defensible argument for the non-existence of time?
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"In the B-series, however, events are fixed in time-location. It was always true, for example, that my birth is 422 years after the birth of Galileo. Events are arranged in terms of earlier and later, but there is no present, past or future; there is no reference to a 'now.' A spatial analogue exists to further illustrate this distinction: a fixed street map on a road, with an arrow saying 'you are here,' is analogous to the A-series; it is only a true representation when looked at in one location; statements such as 'Oxford is further away from here than Cambridge,' are possible. On the other hand, a portable map, which has no reference point and merely shows the relations between the places on the map, is analogous to the B-series; the only statements possible are those which does not involve a concept of 'here,' such as 'Oxford is further away from London than Cambridge." Is that clear?"
"Yes. Exactly as I would have phrased it," I replied with a smile. "Now that we understand that distinction, can you go on to outline the argument?"
"For you, Will, anything. Essentially, McTaggart's is a three premiss and single conclusion argument, though of course each premiss is separately argued for. Thus the overall argument is of the form:
1. Change is necessary for Time
2. The A-Series is necessary for change
3. The A-Series is impossible
And from that he moves to the conclusion:
4. Therefore, Time does not exist/is unreal/is impossible.
Do you agree that this argument is valid?"
"Of course, if the premisses are granted, one cannot help but grant the conclusion. But what are the arguments for each premiss?"
"McTaggart notes that time is 'universally admitted' to involve change -- indeed, it is something of a truism that change is necessary for time..."
"But what about Shoemaker's argument in his essay 'Time without change,' where he outlines a counter-example showing that it is at least logically possible that people could have justification in thinking that time had passed even though nothing in their universe had changed (1993: 63-79). The example itself is long and complex and I feel that outlining it would be an unnecessary digression, though it does seem, to me at least, to be convincing. But you must accept that it is at least possible, logically, for time to pass without any change occurring in the world.
"Perhaps in the everyday sense of the word 'change,' where, for example, if a chameleon is green at one moment and red the next then we would say it has changed. However, McTaggart in this argument is defining change in very narrow terms, merely referring to relational change. When we speak of change in everyday parlance we refer to something having a certain property at one time and a different property at another: we think of an object as changing if its properties change over time. Relational change, on the other hand, is, as the name suggests, a change in relations between objects. For example, if my brother has a baby, in a sense I have changed: I am now an uncle when before I was not. In this sense, given the A-series, everything changes all the time: every event is constantly either becoming more past or less future: its relation to 'now' is changing."
"But is it fair to define change merely as relational change in this way? There are many other accounts of change..."