# McTaggart's infinite regress

McTaggart argues that the A series (a series of events being past, present, and future) is contradictory because an event cannot be past, present, and future, yet any event in the A series will be all three.

His response to a possible refutation (from his essay, "The Unreality of Time"):

If we avoid the incompatibility of the three characteristics by asserting that M is present, has been future, and will be past, we are constructing a second A series, within which the first falls, in the same way in which events fall within the first. It may be doubted whether any intelligible meaning can be given to the asser- tion that time is in time. But, in any case, the second A series will suffer from the same difficulty as the first, which can only be removed by placing it inside a third A series. The same principle will place the third inside a fourth, and so on without end. You can never get rid of the contradic- tion, for, by the act of removing it from what is to be explained, you produce it over again in the explanation. And so the explanation is invalid.

I don't understand where the infinite regress comes from. He says that we are constructing a second A-series, but how so? I don't understand what there is to say after saying "M is present, has been future, and will be past."

• Sounds like word games to me. Mathematically you can have infinite ordered sets with a beginning and no end, an end with no beginning, or both, or neither. You can't use sophistry like this to understand the true nature of time in the universe. I never understand why this kind of thought is taken seriously, and by whom. Even the example you gave, which (if I have any idea what it says) is about placing sequences within sequences. Mathematically it's trivial. It tells you nothing about the real world. It's just stuff some guy typed in and other people take seriously for reasons I can't fathom. Mar 3, 2015 at 20:27
• ps -- I read this and I still don't understand it. Can this question be made comprehensible to me, or is this just one of those things you either get or don't? Mar 3, 2015 at 20:32
• Many people feel that way, that McTaggart is simply missing the point. But I'd like to understand what he's trying to say before looking at refutations. McTaggart is definitely saying something, even if a lot of philosophers (in my experience it's been a lot, at least- mind you, it's definitely not all) seem to think that his argument is rubbish. I, for one, want to know what the fuss is about. First step: what's the argument? Mar 3, 2015 at 20:32
• Is it that you don't understand what the A series and B series are? Mar 3, 2015 at 20:33
• I'm reading through the link I gave in my previous comment. Evidently there's a big argument as to whether the A-series or the B-series is true, and this goes back to and old argument between Heraclitus and Parmenides. Has to do with the block universe, which I recognize as an idea from physics. If reality is a set of points indexed by time, then in a sense everything exists at once. If I have y = x^2 I can think of that as a process, where I input each successive x and get x^2; or as a graph, where all the pairs (x, x^2) exist at the same time. This is as far as I understand any of this. Mar 3, 2015 at 20:40

You said "I don't understand what there is to say after saying 'M is present, has been future, and will be past.'" I think McTaggart might reply that the thing left to be said is exactly what you mean when you use those terms "is," "has been," and "will be."

When the objector says to McTaggart that the event M in question is present, has been future and will be past, all he is saying, at least according to the assertions of McTaggart's argument, is that "M is future" is past, "M is present" is present, and "M is past" is future. But of course, the three events to which those propositions correspond constitute a second A series. Once you see this, it is not hard to see why he insists that this process could continue indefinitely, since you have to explain each of them in terms of yet another A series, and on it goes. Whether you think he is right is another question, of course. I hope that was at least partially helpful, but I would be glad to elaborate or clarify if you need it.

• The original problem that McTaggart poses is that the same event M has three incompatible qualities (past, present, and future). But if we move onto "M is past" is future, "M is present" is present, etc. we no longer have three incompatible descriptions applying to the same thing. "M is future" and "M is present" are, for instance, two different, unequal statements. I guess that I'm having trouble coming up with what the following steps in this infinite regress would look like. ""M is future" is past" is ...? Mar 4, 2015 at 11:20
• Just to be clear, I can understand why one might say invoking the past, present, and future again is circular, but not how it leads to a regress. Mar 4, 2015 at 11:25
• My apologies - I've typed a lot, so this is going to take up a few comments. You are correct when you say "But if we move onto 'M is past' is future, 'M is present' is present, etc. we no longer have three incompatible descriptions applying to the same thing." For now, the objector has managed to solve the problem of these seemingly contradictory properties applying to the same thing. But, of course, that means that these properties now apply to different things: "M is future," "M is present," "M is past" (I'll call them Q, R, and S), Mar 4, 2015 at 19:33
• and that those things are arranged such that Q is past, R is present, and S is future. Then the series containing Q, R, and S, is an A series, and as soon as McTaggart points out that Q, R, and S each have the properties of being future, being present, and being past, you're back to where you started. So, the regress comes when the objector notices that his or her reasoning answers McTaggart's challenge to an A series by positing another A series (because, of course, McTaggart can just raise his challenge again to that new A series). So the steps will go like this: Mar 4, 2015 at 19:35
• "M is present" is an element of the original A series. To resolve McTaggart's dilemma, the objector says "'M is present' was future, 'M is present' is present, and 'M is present' will be past." But McTaggart asks what the objector means by "was," "is," and "will be," and we get the second A series: "'M is present' was future" is past, "'M is present' is present" is present, etc. Just to be clear, McTaggart is not strictly saying that the explanation is invalid because it posits an infinite regress, but that, because of this circularity, it never really manages to explain anything. Mar 4, 2015 at 19:41

I found the following explanation in Barry Dainton's Time and Space (specifically in section 3.2).

As has been already mentioned, the statement "M is present, will be past and has been future" translates into "M is present in the present, past in the future and future in the past." Here we have three second level predicates, but there are in fact nine second level predicates in total. They are:

1. M... is past in the past
2. M... is past in the present
3. M... is past in the future
4. M... is present in the past
5. M... is present in the present
6. M... is present in the future
7. M... is future in the past
8. M... is future in the present
9. M... is future in the future

I have bolded what would be the first level predicates. Combined with "in the X," we have formed 9 second level predicates. Some of these are compatible with each other, like 1, 2, and 3 (what happened yesterday was past this morning [in the past], is past right now [in the present], and will be past tomorrow [in the future]). 3, 5, and 7 were used to respond to the first paradox, and they're compatible as well.

However, some are incompatible, such as 2, 5, and 8 (successively, M is "past in the present", "present in the present," and "future in the present"). In order to solve this paradox, we must again say that events don't have these three properties at the same time (take an event E happening now, it had one property [8] in the past, has the second property [5] in the present, and will have the third property [2] in the future). Thus we introduce third level predicates. But these will again face the same problem. And hence we have an infinite regress.

McTaggart elaborates on his A-paradox in the second volume of The Nature of Existence (1927).