# The McTaggart's Paradox, a door behind the flow of time?

McTaggart's paradox is, similarly as the Russel's Paradox known from the set theory, one of the most fascinating problems lying somewhere on the boundary of philosophy and science. It witnesses that both disciplines have the same origins. And that good philosophy is not far from science and vice versa.
The paradox of John Mc Taggart is very often interpreted as an (controversial) argument for a conclusion that "there is no time at all" or "time is unreal". I don't think that this is a correct interpretation, and also its less controversial inference, that the temporal order of things is (somehow) illusory, which seems to be correct in the light of the Einstein's Theory of Relativity, does not express its full message or information. So, let me to recall it's principle, with help of some mathematical formalism.
Let G be some class of events, and I think that in fact there is no reason why G could not be a set. Further, let M be a set of properties (or attributes, in other words), in particular, M contains, at least, the following elements: p stands for "Past", n stands for "Now" and f stands for "Future", and it also may contain some other elements. So {p,n,f} is a subset of M. There can be also some incidence relation between the sets G, M, which is (in Formal Concept Analysis) usually denoted by I. So I is a subset of the Cartesian product G x M. The membership set relation will be denoted by e.
Now we will consider three (potentially different) incidence relations P, N, F (in place of a general relation I) between the sets G, M. Again, P stands for "Past", N stands for "Now" and F stands for "Future", but in a slightly different sense that the "small", uncapitalized letters. (Since I am not a native English speaker, I intentionally don't want to use the grammar terminology and speak about various "tenses".)
If (a,b) e P, it means that "a had the property b" in Past,
if (a,b) e N, it means that "a has the property b" Now, and
if (a,b) e F, it means that "a will have the property b" in Future.
Further, if (a,b) e P, it also gives us the information, that (a,p) e N, that is, in "Now" the event "a has the property to be in Past" or "it happened in past".
Similarly, if (a,b) e F, it also gives us the information, that (a,f) e N, that is, in "Now" the event "a has the property to be in Future", so "it will happen in future".
Beside this, if (a,b) e N, it also gives us the information that (a,p) e F, that is, in "Future" the event "a will have the property to be in Past", so "it happened in past", and
also (a,f) e P, so in "Past" the event "a had the property to be in Future", so "it will happen in future".
Now we may conclude that for any (a,b) e G x M,
(a,b) e N => (a,p) e F => (a,f) e N
and
(a,b) e N => (a,f) e P => (a,p) e N,
which together gives
(a,b) e N => (a,f) e N and (a,p) e N.
Finally, taking a special property b e {p,n,f} we get
(a,n) e N => (a,f) e N <=> (a,p) e N
I think that it is very a important fact, that the conclusion has the form of an implication. It says, that if we can say "Now" that the event "a has some property b", then the event "a" is also "Past" as well as a "Future" event. But is there really any "Now"? And if so, if we admit that the "present moment" is not illusory, that it is not a some kind of missinterpretation of the nature of time, are we still able to check, at the "present moment", that the event "a has some property b"?
Perhaps the following conclusion could be a better, alternative interpretation of the McTaggart's paradox:
The "Now" is either only an illusion or it coincides with "Past" and "Future". We can choose. If time "flows", there is no "Now". If it does not flow, "Past", "Now" and "Future" are the same. By the way, there is a related Zen story, a koan. Without any claims for the correct and complete answer, I only reproduce the story below:
An old Zen master asked his acolyte, "What do you see?" The apprentice looked up and said, "Oh! The wild geese are flying." He saw the wild geese flying. This answer sent the old Zen master into a rage, and he gave the apprentice's nose a painful squeeze. Then he asked again, "What do you see?" The student replied, "Oh, they have flown away." [audience laughter] The old Zen master raised up his hand and brought it down hard on the apprentice's head. (From the True Buddha School Net)
I would also like to note that some people have an experience from their meditation, which they describe as a state of consciousness, in which the time "stops" flowing. And perhaps also God (if He or She exists, of course - I am a mathematician), can see everything "at once".
What is your opinion of this?

## Popular Answers

James Grindeland· University of North GeorgiaI appreciate your project, but it seems that you haven't yet gotten to the "logical core" of McTaggart's argument.

1. Getting to the "logical core" of McTaggart's argument requires accepting his definition of time. He defines time as requiring, at least, direction and change. Your formulation doesn't mention these properties.

2. "Now" is essential to your formulation, whereas in McTaggart's argument "now" is part of an A-series, but not necessarily part of a B- or a C-series. So, your formulation doesn't capture his arguments that B- and C-series can't be time series.

3. Your formulation doesn't capture McTaggart's argument against A-series time either; for that would require looking for change in an A-series, but not finding it in its A-series aspect of moving from future to present, or from present to past. (There should be a dilemma about how "nowness" is determined, where on one horn there is no change, while on the other horn there is an infinite regress.)

Yet I know that you are also interested in figuring out the nature of time, regardless of what McTaggart says about it, and thus that you are willing to consider a critique of McTaggart's argument. It seems to me that McTaggart goes awry right from the start in assuming that A-, B-, and C-series are the only potential time series. For A-, B-, and C- series appear to be eternal series, like "fixed rods," whereas an alternative understanding of time -- indeed, the common sense understand of time -- is that the universe's history grows. On this common sense understanding of time, the future doesn't already exist, let alone get pulled into the present; it gets added. Indeed, on a growing, dynamic model of time, "nowness" can be defined as the edge of the universe's growth, or the most recent addition to the universe's history. This is consistent with time as being tacked on in discrete increments. It is also consistent with "change" in McTaggart's sense without any kind of infinite regress. I even think it's consistent with relativity theory, which I say in my video on this topic: http://www.youtube.com/watch?v=zUB7d8MnPvM