哲學功課: Problems of McTaggart and the unreality of time

In this essay I will criticize the unreality of time proposed by McTaggart. First I will outline the arguments on the unreality of time by McTaggart. Then I will reject his premises and deductions one by one to show McTaggart has failed to conclude that time is unreal.

First we have to understand the A-series, B-series and C-series description of time proposed by McTaggart. Let’s start with C-series, which is not a temporal series. The C-series specify the order of events and the time between the events. The B-series adds the notation of direction of time to the C-series. In a B-series, each event is expressed in term of earlier than or later than other events. The A-series adds the notation of the present moment of time to the B-series. In an A-series, each event is either in past, at present or in the future. McTaggart stated that we can only observe time through the forming of either A-series or B-series.

McTaggart then said B-series is not sufficient to describe time. Events in a B-series indicate permanent relations. The earlier and later relationship of events in the B-series cannot describe changes, which is essential for time to exist. Therefore, we are only left with A-series to describe time. McTaggart then claimed that if the A-series is unreal, then time must be unreal. He answered two objections to the removal of A-series will destroy time. The first one deals with imaginary time-series, such as a time-line inside a novel. He dismissed it by claiming time only belongs to existent. The second objection deals with multiple time-series. He dismissed it by claiming the different time-series with multiple moment of present should be rejected because it is incompatible with the A-series.

Next, McTaggart went on to show A-series cannot exist by arguing the A-series is contradictory. He argued that the past, present and future of an event are incompatible determinations. Each event can be in all three incompatible states depending on the verb-from of the event. However using verb-form to explain the states of event induce a vicious circle of infinite A-series. Since A-series has no valid explanation, it is a contradiction and therefore time is unreal. McTaggart’s argument can be summarized in the following table.

  1. Time can only be observed by forming B-series and A-series
  2. Time involves changes, so B-series is out
  3. If A-series is unreal, then time is unreal
  4. A-series is invalid, so it is unreal
  5. Therefore, time is unreal.

Traditionally, there are two camps of philosophers trying to rejecting McTaggart’s claim by two different approaches. The B theorists think that B-series alone is sufficient to describe time. The A theorists accept McTaggart’s claim that A-series is necessary for the existence of time, but reject his claim that A-series is contradictory. Both A theorists and B theorists has their problem dealing with McTaggart, mostly due to they are trapped by framework defined by McTaggart when discussing time. In this essay, I will use a different approach. I will first examine and reject each line of McTaggart’s argument, from step 4 down to step 1 in the table above. In the process, I will uncover some fundamental errors in the McTaggart’s construction of the A-series and B-the series, and provide a new framework of time based on the scientific theories of time.

In step 4 of McTaggart’s argument, he claims that the A-series is unreal because it involves an endless regression of A-series. I am going to reject his claim in three different ways. 1.) An infinite series can also be a real series. All we have to do to take the integration. In mathematics, there are real numbers with endless regression, such as π, e, and irrational numbers. We can only claim that the A-series is not precise in describing the states of an event, but we cannot deduce A-series is unreal from the fact that it merely has infinite circles. 2.) McTaggart tried to solve the problem of time using verb-form is limited by semantic constructs of his language, English. There exist languages with verb-from common to all past, present and future, such as Chinese. The timing relationship of an event in such language is specified explicitly by a time qualifier, such as today, tomorrow, 3 hours ago, last year, etc. 3.) In Dummett’s article, he suggested that using token-reflexive expression, such as now, may refute McTaggart’s argument. He then subsequently claimed the token-reflexive expression of the observer introduce another time-series, hence the endless regression problem still exists. I would answer this by stating that the now event does not require a mind to be an observer. A computer can objectively apply the token-reflex expression to resolve A-series without any existence of mind, thus the now event is real instead of being subjective. Therefore with the help of a real now event, the infinite regression of A-series can be collapsed into a single real A-series with the now event at present.

In step 3 of McTaggart’s argument, he dismissed the objection from the theory of a plurality of time saying it is merely a hypothesis. McTaggart assume time is absolute for all observers. However his viewpoint contradicts with Einstein’s relativity theory, which is a scientific fact. According to principle of relativity, time experienced by an observer is a function of the speed of the observer and the speed of light, which is a constant real value. The faster the speed of the observer, the slower the time he will experience. The relativity of time is confirmed by the 1962 dual atomic clock experiment. In the experiment, two pairs of very accurate atomic clock are mounted on the bottom and the top of a tall tower and it is observed one clock is running slower than another. There is also the famous twins paradox. One of the twins travels in a spaceship near the speed of light. When he returns, he will be much younger than the other twin staying on earth. Each individual has his own frame of reference in time that depends on his velocity and his location related to massive bodies. McTaggart concluded time is unreal because he mistakenly assumed time must be absolute. If time is relative, then there exist many A-series and many instances of present in the universe. Therefore rejecting the A-series alone is not sufficient to prove the unreality of time. Moreover, since the speed of light is real and the speed of the observer is also real, time as a function of those two must also be real.

In step 2 of McTaggart’s argument, he claimed that the B-series indicate permanent relations. Therefore the B-series cannot describe the nature of change in time. McTaggart has made an assumption about the deterministic worldview of time. The B-series is only capable of describing past events. The very last event in the B-series is the now event marking all the possibilities are lying ahead in the future. Take McTaggart’s own example, the death of Queen Anne. Before the event actually happen, there are all sorts of possibilities that Queen Anne could escape death. She could be adducted by aliens preserved as a frozen specimen or she could ascend into heaven like Jesus. If N is earlier than O and later than M, it will only be so if all three events have already happened. If O is in the future, then there is no guarantee this event will exist in the B-series. Therefore, a growing B-series is sufficient to describe time, at least time earlier than the present moment. The becoming of an event is described by its position relative to the now event in the B-series. In this sense, a B-series is equivalent to an A-series after we apply some transform function between the two series using now as the operator.

At last, in step 1 of McTaggart’s argument, he claimed that we never observe time except forming both A-series and B-series and he also claimed that time can be subjective which cannot exists independent of human mind. Let’s try to imagine the following scenario. There is a third world war and every man on earth is killed by nuclear weapons. The earth is heavily polluted and will be inhabitable for the next several thousand years. However, there is a great scientist come up a plan to save humanity. He builds a modern version of Noah’s art safe keeping DNA of every species on earth, including human. The art is controlled by a super computer, which monitors the atmosphere. When the earth becomes habitable, it will populate man and animals from the art’s DNA database through cloning. It is obvious that computer would also keeps track of the time between the last man is dead and the first cloned man is born. During this period, there exists no human mind to subjective perceive time and yet time exists. This thought experiment demonstrated time exists independent of human mind. Moreover, we can also describe time through forming paths in light cones instead of forming the A-series and B-series. The future light-cone is the path of a light pulse from an event and the past light cone is the path of all the lights pulse that will pass through an event. For an event A to be affected by another event B, event A has to lie within the future light cone of event B, since nothing can travel faster than light. Therefore time can be described by the path of lights passing thought the light cones of events. If we use the framework of quantum physics, events change is just a secondary property of time. An event happens on the moment all the probability of the quantum wave equations collapsed into certainty. Then the becoming of an event can derives the change of an event. Therefore, change is not essential to time, instead becoming is essential to time.

In conclusion, in this essay I have rejected every single statement in McTaggart’s argument on the unreality of time. Therefore we have no reason to believe time is unreal based on his arguments. On the other hand, there are plenty of evidence in modern science showing time is real. Hence as a rational being, we should accept the reality of time instead of the unreality of time. In the matter of facts, the questions about the nature of time should no longer be a metaphysical question. It should follow the example of gravity, which moved from the department of philosophy to the department of physics.

[1] J.M.E. McTaggart, “The Unreality of Time”
[2] Michael Dummett, “A Defense of McTaggart’s Proof of the Unreality of Time”
[3] Stephen Hawking, “A Brief History of Time”
[4] Stephen Hawking, “The Universe in a Nutshell”
[5] Wikipedia, “The Unreality of Time”, “Notes of McTaggart, The Unreality of Time”, “Philosphy of space and time”

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