Lowe on McTaggart's Argument for the Unreality of Time

Last night, Jay and I presented some material on McTaggart's argument for the unreality of time. What follows is part of what we talked about.

McTaggart’s Argument
1. Time essentially involves change.
2. Change can only be explained in terms of A-series expressions.
3. A-series expressions involve contradiction and so cannot describe reality.
4. So time is unreal.

Lowe wants to resist (4). He does so by denying (3). But his denial of (3) requires altering McTaggart’s account of (2) to explain how change can only be explained in terms of A-series expressions. Lowe’s argument can therefore be broken down into two parts. Part I: Denying that A-series expressions involve contradiction. Part II: explaining how change essentially involves A-series expressions.

PART I: Denying that A-series expressions involve contradiction

1. McTaggart’s argument for (3) involves the following claims:

a. The predicates “is past”, “is present” and “is future” all apply to all events

b. These predicates are inconsistent

2. An initial response: “past”, “present”, and “future” do not apply to all events at the same time.

3. Two versions of this response:

a. A-series version, second-level tenses: Event e is present (in the present), is future (in the past), and is past (in the future).

b. B-series version, indexing tenses to dates: Event e is present in 2006, is future in 1978, and is past in 2034.

4. Traditional problems with each response:

a. Traditional problem with A-series version (given by Dummett): The contradiction is not eliminated. Event e is not only present (in the present), it is also past (in the present) and future (in the present); or it is not only future (in the past), but past (in the past) and present (in the past). Each group of higher level A-series expressions is contradictory.

b. Traditional problem with B-series version: The contradiction is eliminated, but the A-series is reduced to the B-series. “Event e is present in 2006” is equivalent to “Event e is simultaneous with 2006”; “Event e is future in 1978” is equivalent to “Event e is after 1978”; and “Event e is past in 2034” is equivalent to “Event e is before 2034”.

5. Lowe’s new problems with each response:

a. A-series version: Higher-order tenses are incoherent (66). Tenses function like indexicals. Indexicals get their content from the context of utterance. The context of utterance cannot be shifted. David Kaplan says that attempts to shift the context in which indexicals get assigned their contents generate “monsters”. It doesn’t make sense to say that in the future, it is the present, just as it doesn’t make sense to say it is here over there or To you, I am you.

b. B-series version (Sorabji): Indexing A-series expressions to times is also incoherent, for the reasons just given. Saying “Event e is future in 1978” attempts to shift the context of utterance for “is future” back to 1978. But we can’t do that.

Jason worried that Lowe's intuitions about the incoherence of utterances like "In the future, 2006 will be past" were wrong. It seems perfectly possible to say something like, "Back in 1984, my college years were still in the future" without lapsing into incoherence.

PART II: Explaining how change essentially involves A-series expressions

7. McTaggart explained change in terms of future event e becoming present and receding into the past (68). But Lowe can’t use this explanation of change, because the idea of an event going from being present to being past is what generated the contradiction in the A-series. So how does Lowe explain change?

8. Lowe’s explanation of change in terms of sequences:

a. Lowe thinks he can show how change is essential to time in a way that it isn’t for space: “In all the possible space-time routes a person may take, the order of temporal positions will be the same, while the order of spatial positions may vary” (69).

i. A Worry: How does this show that change is essential to time, and not to space? It seems if anything it shows that change is essential to space, since the temporal sequences of the routes a person may take are always the same.

9. But granting that Lowe has shown that change is essential to time, why does he think that change essentially involves A-series expressions?

a. Lowe has explained how change is essential for time in terms of possible variations in space-time sequences: an active person may take sequence <(s1, t1), (s2, t2), (s3, t3)>, or a couch-potato may take sequence <(s1, t1), (s1, t2), (s1, t3)>, but both the active person and the couch potato will have sequences that must have the form <(-, t1), (-, t2), (-, t3)>. What about these sequences involves anything about the A-series? We could, for example, fill in the time variables with B-series dates: <(-, May 2, 2006), (-, May 3, 2006), (-, May 4, 2006)> (69). If the sequences that explain how time essentially involves change don’t essentially involve the A-series, then Lowe has rejected premise (2) in McTaggart’s argument, which he doesn’t want to do (63).

b. Lowe’s response: Routes are sequences of “spatio-temporal perspectives” (69). What does this mean? It means that routes can’t rely on anything like non-perspectival, non-tensed, non-indexical ways of specifying times (and locations?). Perspectival sequences would look like this: <(there, yesterday), (here, today), (there, tomorrow)>; <(here, yesterday), (here, today), (here, tomorrow)>.