McTaggart’s famous article “The Unreality of Time” in Mind (1908) begins with the following words:

This is a very curious claim indeed! What does it mean to prove that nothing existent can have the characteristic of being in time? Still we all know too well that many existent beings, including ourselves, are definitely existing in time, are subjected to time. Does McTaggart’s claim consequently mean that we and other beings subjected to time do not exist at all? Can we understand this claim as an argument for Parmenidean teaching that only One exists, while Many is just illusion, non-being? Does McTaggart play here the role of modern Zeno of Elea, arguing this time for his master Hegel instead of Parmenides? I think that this analogy is appropriate to a certain extent, however it is not my principal aim in this paper to go into McTaggart’s ontological background, considered from the historical perspective. Rather I would like to point out the queerness of the fact that the so-called McTaggart’s proof for the unreality of time has become one of the main entries into the modern analytic philosophy of time. I would like to put the question whether McTaggart’s logic is really so convincing that David Hugh Mellor is justified in saying: “To me it [McTaggart’s proof] seems beyond all reasonable doubt.” (Mellor 1981, Real Time: here quoted from Oaklander & Smith 1994, where Chapter 6, “The Unreality of Tense”, is reprinted, p. 165). My point is, on the contrary, that this proof is subjected to very reasonable doubt. I do not go so far as Charles Dunbar Broad (1938) who called McTaggart’s proof a “philosophical howler” (cf. Oaklander & Smith 1994, p. 157), for I concede that McTaggart’s proof is important for opening some essential questions concerning time in the modern analytic philosophy, nevertheless I think that its importance is limited to, we may say, heuristic purposes, especially for analyzing relations between logic and (temporal) being – but this “proof” cannot demonstrate the unreality of time in the proper sense, neither the impossibility of beings to exist in time.

In order to clarify my point, let us reconstruct McTaggart’s proof, following Nathan Oaklander, who analyzes it into three suppositions (one general and two concerning time), and the conclusion (cf. Oaklander, in: Oaklander & Smith 1994, p. 158):

1. If the application of a concept to reality implies a contradiction, than that concept cannot be true of reality.
2. Time involves (stands or falls with) the A-series and temporal becoming; that is, if the A-series involves a contradiction, then time involves a contradiction.
3. The application of the A-series and temporal becoming to reality involves a contradiction.
4. Therefore, neither the A-series nor time can be true of reality; thus time is unreal.

The critical point of McTaggart’s proof is usually taken to be the supposition (3). Oaklander states that:

Here, as we see, logic with its principal Law of Non-Contradiction (LNC) seemingly forces us to accept a very curious conclusion, contrary to most of our experiences and common sense, namely that time is unreal – quite similar as the ancient Zeno’s aporias were supposed to be philosophical arguments against the reality of movement and multiplicity. To see this point better, let us quote directly from McTaggart’s article:

As I said, in recent philosophical discussions about McTaggart’s proof, his critics raise objections mostly to the supposition (3), i.e., that A-series involve contradictions. (Mellor, Oaklander and other followers of the “new tenseless theory of time”, who in principle accept McTaggart’s proof, chose another way of understanding the ontological status of time: they negate supposition (2), claiming that the real time does not involve A-series and temporal becoming; I will return to this point later.) The most usual objection to the supposition (3) is that the apparent contradiction has an obvious solution if we specify the various times at which events have the properties of being past, present and future. So, instead of saying that E is past, present and future, we should say that E is future at time t₁ (or simply that E will occur in some future time), that E is present at time t₂ (E is occuring now), and that E is past at time t₃ (E has occurred in some past time). It seems that contradiction disappears, for the temporal predicates of pastness, presentness and futurity are not predicated to the event E at the same time, but successively, and that should preclude the formal, logical contradiction – however, McTaggart does not accept this objection, arguing that it leads into infinite regress (or vicious circle), as he says:

This McTaggart’s counter-objection to the simple temporal indexing of contradictory temporal “properties” as the way of avoiding the contradiction in (3), was formally elaborated and endorsed by Mellor in the already quoted chapter of his book Real Time. Critics of McTaggart and of his followers then again protest that even if the proposed temporal indexing involved infinite regress, there would be no need to enter into this vicious iteration, since there was actually no contradiction at the beginning. (Maybe this problem could be solved by taking into account the distinction between object-language and meta-language, or by discerning use and mention?) The issue whether we have here a contradiction or not has grown up to the present time into a host of sophisticated arguments and counter-arguments, and it is quite difficult to decide which side is right. I may quote two typical critics of McTaggart, Charles D. Broad and Quentin Smith. Broad wrote:

This point, namely that there is no contradiction to be avoided, is quite clear and convincing, however, accepting it in its full sense would mean that McTaggart’s “proof” is indeed a “philosophical howler”, as Broad named it. Quentin Smith is more cautious, in principle he admits the possibility of a vicious circle in “tenser’s” objections against McTaggart, still his opinion concerning the initial contradiction is quite similar to Broad’s:

In this dilemma, whether there is or there is not a contradiction in the supposition (3) of McTaggart’s proof, I am more inclined to Smith than to Mellor (however, this is not my principal point yet). Smith’s position “that there is no contradiction to begin with” could be supported also by claiming that the temporal discourse is not in the domain of validity of the Law of Non-Contradiction (LNC). This can be true in spite of the fact that temporal formal logic – which validates LNC – was proposed by A. N. Prior and others. If we interpret temporal logic as a kind of modal system (as Prior in fact does), we can require, from the semantic point of view, consistency (i.e., validity of LNC) only inside each separate possible world, and not between true propositions in different worlds. (For example, given the set of worlds W, Mark is bald in the world w₁ and is not bald in the world w₂ without any contradiction, without violating LNC.) So, my opinion is that the best and the simplest way to reject McTaggart’s supposition (3) is to say that LNC is not – at least not without specifications – applicable to propositions which express temporal becoming, that is, to A-series. Actually this point is essential for all classical logic which was already at its beginnings in opposition to “temporal arguments”, such as the famous “Master Argument” of Diodoros Cronos. Aristotelian, as well as modern formal logic cannot be logic of temporal discourse in the strict sense – formal logic is essentially timeless, it is constructed as a synchronic, not as a diachronic system, the same as mathematics. (Who would object to a mathematician that two different tokens of a term in some formula are inconsistent, because the first token is prior in the formula, while the second token is posterior, claiming that these two “predicates” of the same term are inconsistent? That would be nonsense from the mathematician’s point of view.) Therefore, we may say, contrary to McTaggart: just because pastness, presentness and futurity are successive “predicates” of events, there is no initial contradiction between propositions which assign different times to the same event. LNC is not violated here, since its unconditioned domain are only “timeless” propositions. Temporal becoming a priori escapes from the strong grip of LNC.

Here something must be said about the possibility of the reduction of tensed to tenseless discourse. It is well known that the early “detensers” (following Bertrand Russell) claimed that all tensed discourse can be in principle reduced to tenseless, logically more transparent formulations. This belief was later mostly abandoned; the so-called “new theory of time”, developed in the last two decades by new “detensers” (Mellor, Oaklander, C. Williams and others, see: Oaklander & Smith 1994) concedes to “tensers” (Prior, Smith and others) that we have to take into account tensed discourse, however, as Smith points out:

Mellor’s strategy in the “new theory of time” is first to reduce truth-conditions of tensed sentences to a tenseless account, and then to claim that time itself (“real time”) has to be conceived tenselessly, i.e., that time is sufficiently determined by McTaggart’s B-series of events (events ordered in series by time relation before and after). This claim actually rejects McTaggart’s supposition (3), precisely its first part: temporal becoming (A-series) is considered not to be necessary for the concept of time. At first let us look more closely to the truth-reduction. Mellor says:

As I have mentioned above, the idea of such a truth-account which tenselessly evaluates truth or falsity of tensed beliefs was already proposed by Russell, so that Mellor could just complete it in the following “token-reflexive” scheme:

This account is called “token-reflexive”, because it includes a token sentence which is itself a part of its own truth-condition. Mellor uses it for “solving” McTaggart’s paradox by denying any ontological relevance of A-series (temporal becoming of events), i.e., for rejecting the supposition (2). For him, tenses have only a descriptive role, they are indispensable in our temporal discourse, but ontologically they do not denote anything real. Mellor writes:

If we put aside the objection that McTaggart would probably not agree that “the A-series is a myth”, since the supposition (2) of his “paradox” is taken to be true – we may say that Mellor’s “real time” follows from McTaggart’s conclusion, since Mellor conceives real time like an eternal, or better, timeless net, woven of B-series only, where events are like strings of beads, which were, are, and will be there timelessly. The metaphor of a net is appropriate here because it takes into consideration the relativistic features of time, its dependence of observers and relativity of simultaneity. And it is surely true that Mellor’s “tenseless theory of time” is compatible with Einstein’s theory of relativity, although the appropriate philosophical interpretation of the latter is still an open question. However, this question is out of the scope of this paper.

If we return to possible solutions of McTaggart’s paradox, we may state that Mellor’s type of solution by rejection of the supposition (2) is quite different from Smith’s type of solution by rejection of the supposition (3); these two ways are characteristic for “detensers” (or B-theorists of time) and “tensers” (or A-theorists of time) respectively. Each of the two ways has its problems: A-theorist is subjected to the objection of a vicious circle (or infinite regress), while B-theorist meets two general counter-arguments, pointed out by A-theorists:

(i) How can we, if we accept Mellor’s idea of the “real time” – which is actually timeless (or at least tenseless) – explain our obvious experience that time flows, that everything, including ourselves, is changing and passing away, like the river of Heraclitus? If reality is timeless, what is the cause or origin of change, of temporal becoming in its broadest, Aristotelian sense? And what does becoming ontologically mean at all, in case the reality is timeless? Is the river of changes just an illusion, maya of Indian philosophy, non-being of Parmenides? Mellor does not go so far, instead of that he argues that change can be conceived by B-series alone:

Again McTaggart would probably not agree with Mellor’s reduction of A-series to B-series, on the contrary, he insisted that B-series, if taken as time series, necessarily involve A-series, and so “test for temporality” of “real B-series” fails. This objection is quite convincing, since what is indeed temporal in Mellor’s B-series – temporal order of them? But without recurrence to A-series, i.e., to pastness, presentness and futurity of temporal becoming, temporal order of B-series remains only an abstract, formal order which is isomorphic with, for example, order of natural numbers with regard to the relation “bigger than” (or “smaller than”); there is nothing specific temporal in such an order.

The second objection, met by B-theorist from the side of A-theorist, is the following:

(ii) How to explain, from the point of tenseless “real time”, our evident and “clear” experience of the present time, the actuality of NOW, in comparison with past times which are fading away from us, remaining only possibly “present” in memory, and on the other hand in comparison with future times which are “not yet here”, which are, as all except strict determinists would agree, a realm of possibilities? And how could we explain our relief when some unpleasant event is over – when we say “Thank God it’s over!” – in case past times were ontologically as real as present time? It may be also asked, what kind of ontology we have in mind, if we do not distinguish our present and past (or future) experiences? And what “universal mind” is the subject of such an ontology?

It is really difficult to answer the questions (i) and (ii) from the point of Mellor’s tenseless “real time”. Concerning the question (i), one of the possible and among B-theorists quite popular answer is that time actually does not flow, but we have just the impression of its flowing, when we move “through time”, in analogy of moving through space. The idea of “spaciousness of time” has its origin in the modern space-time physics, but it is only a possible interpretation of relativistic and quantum physical theories, an interpretation which does not follow from them by necessity. Symmetry between space and time is not to be conceived as complete equivalence of spatial and temporal dimensions (cf. Sklar 1993). That’s why the following Oaklander’s argumentation for the tenseless (B-theory) of time cannot be conclusive. He writes:

It is interesting that Nathan Oaklander, B-theorist who in general agrees with Mellor, concerning the tenseless theory of “real time”, introduces the consciousness in his argumentation. Following this line, Oaklander thinks that “the detenser has a reasonably good response” also to the question (ii), i.e., the explanation of our evident experience of the present time (“now”). He proposes an answer by appealing to the focus of the individual consciousness as the “phenomenological fact”. He says that “for an individual, every experience he or she is conscious of is one known to be present” (Oaklander, op. cit., p. 345), and he maintains that:

Unfortunately, the ontological problem of the actuality of present time is not solved by this reduction to our conscious experience, but it is only transposed and transformed into the more basic ontological problem of consciousness. Indeed philosophy cannot be satisfied with the statement that our experience of the actual present time is “nothing more” than focusing our consciousness to what is presently happening – for the problem of time is in such a way only displaced to even heavier ontological question what is consciousness; it is transposed from “objectivity” of temporal becoming to “temporality of consciousness” which is one of the main topics of phenomenology. If we simply exclude consciousness from the external, “real world”, it turns us back to “naïve positivism” which – so I am convinced – cannot be a suitable ontological frame for the modern philosophy of time.

It is interesting to note that Quentin Smith, a defender of the A-theory of time, explicitly proposes to include phenomenological insights into analytic philosophy of time:

I agree with Smith’s advice, especially with regard to the very illuminating phenomenological analysis of time by Edmund Husserl (Husserl 1928). This issue is connected with the fundamental question whether methods of the modern analytic philosophy, which were mostly established in the first half of 20th century as logical and semantic investigations of theoretical languages, can be decisive for solving basic ontological questions, among them the question of the ontological status of time and temporal becoming. My opinion is that the modern analytic philosophy, when dealing with metaphysical topics, should consider the following reflections:

1. For the further development of the analytic philosophy, it might be convenient to loosen often too restrictive formal approach of the classical logic, grounded on the absolute and unconditioned validity of the LNC, and eventually to introduce paraconsistent logic(s) for some philosophical contexts.
2. The analytic philosophy should always take into account the limits of its traditional “semantic ascent”, for after a century of its modern development it is quite obvious that not all problems of philosophy can be treated just with analysis of philosophical language.
3. The analytic philosophy should consider the essential role of consciousness in ontology and metaphysics. From this point of view, it seems to be natural to establish closer connections with phenomenology and with other “continental” philosophies seems to be natural.

Now let us return to the main topic of this paper, to McTaggart’s “unreality of time”. At the end of his famous article, he triumphantly concludes:

Is this triumph of timelessness a rational conclusion? Isn’t it something very curious, in fact quite repugnant to reason, that the presumed ontological negation of time is supposed to be demonstrated as an a priori truth, verified by logic alone? Statements like “Nothing really changes” and “Nothing is really in time” are considered by McTaggart and his followers to be necessary statements, derived from a priori “evident” premises. We know well that something must be wrong here. But the proof itself, analyzed by Oaklander into three suppositions and the “paradoxical” conclusion is formally valid. We have seen that McTaggart’s critics, A-theorists of time, try to undermine the supposition (3), but are exposed to the objection of the infinite regress. On the other hand, McTaggart’s proponents, B-theorists of time, try to “correct” his paradoxical conclusion by dropping the supposition (2), holding that B-series alone can constitute “real time”. Both ways meet difficulties – but is there a third way to solve McTaggart’s “paradox”? If Oaklander’s analysis is correct, only the general supposition (1) remains to be questioned. Let we repeat it:

This supposition seems to be evident, so that it has not been questioned in discussions about McTaggart’s proof. But what does it actually mean in this context? McTaggart himself did not formulate the supposition (1) explicitly, probably because he considered it too obvious. In Oaklander’s analysis of McTaggart’s proof, (1) can be implemented with the concept of time, meaning:

However, such a relation between the logical Law of Non-Contradiction (LNC) and ontological reality is questionable. If we take it as granted without any further condition, this relation would mean that LNC is a necessary – although not sufficient – condition that a concept in question denotes something existent. In case of the concept “round square”, for example, it is obvious that LNC is necessary and also sufficient condition to exclude existence of the round square, since a figure cannot be round and square at the same time. But what should we say about the concept “round square in time”, meaning that some figure is first round and later square? In this case the contradiction disappears, since this temporal concept is simply out of domain of LNC. It might be objected that “temporal concepts” are not concepts at all, namely that every concept is atemporal – yes, we agree that no concept as concept is temporal, but there are surely concepts which have temporal objects as their denotations, for example concepts like: “Beethoven’s 5^th symphony”, “bird’s flight over the garden”, “waiting for Godot” etc., up to the abstract temporal concepts like “change”, “duration”, “evolution”, “history”, as well as the concepts which constitute McTaggart’s proof: “temporal becoming” and “time” itself. If we succeed to demonstrate that these concepts (better, the propositions which include them) are contradictory with regard to LNC – let us say for a moment that we do succeed it in McTaggart’s style – that still does not mean they cannot have existent temporal denotations, but reveals only the limit of validity of LNC, considered as a criterion for ontological reality. So we may reply to McTaggart: even if the concept of time is contradictory from the formal logical point, with regard to LNC, this does not mean that time itself is not real. Time is real, but it is outside the scope of formal logic. On the other hand, timelessness of formal logic remains out of question, since we may well believe (as we usually do) that logical laws are not subjected to “temporal becoming”. But this is quite another question which reveals nothing new concerning the reality of time (unless only logic is real), for the timelessness of logic, in the contrary to the temporality of the world, was well known already to Aristotle.