The Static Versus the Dynamic Temporal

By Richard Gale

This section will consider the treatment of time in twentieth-century analytic philosophy, this being a generic term which includes logical atomism, logical positivism, rational reconstruction, and linguistic analysis (ordinary language philosophy). We shall begin our investigation by considering J. M. E. McTaggart's famous argument for the unreality of time, which was first published in 1908. McTaggart's discussion is a key to the views of time held by twentieth-century analytical philosophers, for one can detect in their writings a common underlying concern: almost all of them are attempting to answer McTaggart's paradox. This is not to say that all these writings mention. Mctaggart by name, or even that their authors always had him consciously in mind, but only that the problems they wrestled with were those bequeathed to them by McTaggart. A person can scratch a mosquito bite without knowing that it is a mosquito bite. Mctaggart's argument is fallacious, but it is fallacious in such a deep and basic way that an adequate answer to it must supply a rather extensive analysis of the concept of time, along with a host of neighboring concepts that are themselves of philosophical interest, such as change, substance, event, proposition, truth, and others. What we shall notice is that the answers proposed involve very different analyses of these concepts.

Mctaggart's paradox is deeply rooted in two fundamentally different ways in which we conceive of and talk about time. On the one hand, we conceive of time in a dynamic or tensed way, as being the very quintessence of flux and transciency. Accordingly events are represented as being past, present, and future, and as continually changing in respect to those tensed determinations. Thus what is now happening ceases to happen and becomes past as future events become present, so that past events become more past and future events less future. This process of temporal becoming is often referred to by various metaphors and aphorisms - the gnawing tooth of time; the river of time; time flies; here today gone tomorrow; gather ye rosebuds while ye may; enjoy yourself; it's later than you think; and the rest of them. The dynamic conception of time lies at the basis of the temporalistic view of man which is present in certain religions, philosophies and works of art, and finds expression in our tensed way of thinking.

Yet time, in which all things come to be and pass away, necessarily involves a static structure or order. It is, to use T. S. Eliot's phrase, "a pattern of timeless moments." The very same events which are continually changing in respect to their pastness, presentness, or futurity are laid out in a permanent order whose generating relation is that of earlier (or later) than. This is the static or tenseless way of conceiving time, in which the history of the world is viewed in a God-like manner, all events being given at once in a nunc stans. Here there is no gnawing tooth of time - no temporal becoming - but only a democratic equality of all times. The static conception finds expression in our tenseless way of talking, in which temporal relations of precedence and subsequence between events are described by timelessly true or false statements.

The central problem is to relate these two radically different ways of conceiving or talking about time. As we shall see, McTaggart's paradox rests on a seeming incompatibility between the two. Adequately to dispel his paradox, analysts have had to inspect the logic of our tensed and tenseless ways of talking and to see how these two different manners of speaking are related.

McTaggart's argument comprises both a positive and a negative thesis. The positive thesis contains an analysis of the concept of time that Mctaggart claims to be the only correct one. The negative thesis attempts to show that this analysis entails a contradiction. The assumption here is that any concept which is contradictory cannot be true of reality.

In his positive thesis, McTaggart analyzes the concept of time in terms of two different types of temporal facts. First, there are facts about temporal relations of precedence and subsequence between events, and, second, there are facts about the pastness, presentness, and futurity of these same events. Corresponding to the first type of temporal fact is a series of events, called the "B-Series," runs from earlier to later, its generating relation being earlier or (later) than; corresponding to the second type is a series of events, called the "A-Series," which runs from the past through the present and through the present to the future. The relation of earlier or later than will be referred to as a "B-relation, and the pastness, presentness, or futurity of an event as an "A-determination."

Events can never change their position in the B-Series. Plato's death, for example, cannot through diligence and hard work sneak up on Stalin's death, for if one event is earlier than some other event by so many time-units, then it is always the case that one is so many time-units earlier than the other. The only change that an event can undergo is a change in its A-determination. Plato's death once was future, became present, and is now retreating into the more distant past. Such change has been referred to above as temporal becoming. McTaggart's B-Series corresponds to what we have called the static temporal and his A-Series to the dynamic temporal.

While time essentially involves both the A- and B-Series, both a dynamic and a static aspect, McTaggart claims that the A-Series is more basic, in that B-relations between events can be reduced to the A-determination, just as harmonic relations can hold only between notes having an absolute pitch. Without the A-Series, the B-Series is no longer a temporal series. Therefore, if it can be shown that the A-Series is unreal the unreality of time will ipso facto have been established.

In his negative thesis, McTaggart attempts to demonstrate the contradictory and therefore unreal nature of the A-Series,  thereby proving the unreality of time. His main argument is as follows. Every event in the A-Series, assuming that there is no first or last event, has all three mutually incompatible A-determinations - past, present, and future - and therefore involves a contradiction. We might try to explain away this seeming contradiction by saying that no event has more than one A-determination at the same moment of time. Rather it is the case that an event, such as M, has three A-determinations successively: for example, M has been future, will be past, and is now present. But to say this, McTaggart claims, must mean that M is future at a moment of past time, is past at a moment of future time, and is present at a moment of present time, respectively.

But this reply will not do, since it involves either a vicious circle or a vicious infinite regress. What we have done is to explain away the contradiction of an event in the first-order time-series having all three A-determinations by claiming that it has these determinations successively at moments of time in a second-order time series, its members, which are moments of time, must also form an A-Series, which means that evey moment of time has all three mutually incompatible A-determinations. Therefore, we have explained away the contradiction inherent in the first-order A-Series only by introducing a second-order A-Series. And this is to reason in a vicious circle, since we must presuppose a second A-Series to rid the first A-Series of contradiction.

If we should try to remove the contradiction in this second-order A-Series, owing to all the moments of time in it having all three A-determinations, by saying that these moments of time are successively future, present, and past at moments of time in some third order A-Series, we are merely transferring the contradiction to the third order A-Series. We are launched on a vicious infinite regress, for at any point at which we stop we are left with a contradictory A-Series. The curse of contradiction pursues us down the infinite regress like a sort of baton that each A-Series passes on to the next.

The obvious opening move to make when confronted with an argument for the unreality of time is to appeal to common-sense facts. G. E. Moore pointed out that if time is unreal then there are no temporal facts; nothing is past, present, or future, and nothing is earlier or later than anything else. But, plainly, it is false that there are no temporal facts, for it is a fact that I am presently inscribing this sentence and that my breakfast yesterday preceded my lunch. Since the conclusion of McTaggart's argument entails a statement known to be false, it follows by the rule of modus tollens that his conclusion is false. Therefore, his argument contains either a false premiss or a non sequitur.

Valuable as this opening move is, it is of course nothing but an opening move, for it fails to locate and correct the source of McTaggart's error. This task of the philosopher is not just to remind us that we were born and that our breakfast precedes our lunch, but to give a coherent account of what we mean by these expressions. The account McTaggart gives seems to result in the absurd conclusion that time is unreal. What must be done is to replace McTaggart's account of time by a more adequate one that will not involve this absurd result. The serious answers to McTaggart's paradox are those which attempted to do just that.

Analysts have given three different types of serious answer: (1) The B-Series alone is sufficient to account for time; (2) the A-Series alone is sufficient to account for time; but they must not be confused with each other, otherwise paradoxes arise. Answer (1), to be called the "B-Series Answer," attacks McTaggart's positive thesis because it denies that the the A-Series is necessary for the reality of time. Answer (2), to be called the "A-Series Answer," agrees with McTaggart's positive thesis that the A-Series is both necessary and fundamental, but denies his negative thesis that the concept of the A-Series is contradictory. Answer (3), to be called the "Either-Way-Will-Work Answer," attempts to show that, whether we affirm or deny McTaggart's positive thesis, we can give an adequate account of time. Each of these answers will now be considered separately, with particular attention to the competing analysis of time contained in the first two.

The B-Theory Answer

This answer to McTaggart, along with the theory of time contained in it, which will be called the "B-Theory," has been popular with those analysts whose approach to philosophy has been made from the side of mathematical logic and theoretical physics, which includes most logical atomists, logical positivists, and rational reconstructionists. The father of the modern version of the B-Theory is Betrand Russell and among his followers are: R. B. Braitwaite, C. J. Ducasse, A. Grunbaum, A. J. Ayer, W. V. Quine, N. Goodman, D. C. Williams, J. J. C. Smart and R. D. Bradley. Most of these philosophers would agree to the following tenets, which together constitute the B-Theory of time:

      (1) The A-Series is reducible to the B-Series since A-determinations can be analyzed in terms of B-Series between events;
      (2) Temporal becoming is psychological since A-determinations involve a B-relation to a perceiver;
      (3) the B-Series is objective, all events being equally real; and
      (4) Change is analyzable solely in terms of B-relations between qualitatively different states of a single thing.

Each of these tenets is vigorously defended in the paper by Donald Williams reprinted below. We shall consider each separately and then chow how collectively they contain an answer to McTaggart's argument.

      (1) The A-Series is reducible to the B-Series since A-determinations can be analyzed in terms of B-relations between events. The main contention of the B-Theory of Time is that events are not past, present, and future, simpliciter, but are merely earlier than, simultaneous with,¹ and later than other events. Another way of stating this position is that "is present," "is past," and "is future," grammatical appearances to the contrary, are really tenseless two-place predicates that take event-expression as their arguments. Nelson Goodman has attempted to reduce A-determinations to B-relations in this manner:

The "past", "present", and "future" name no times. Rather the "is past at", the "is present at", and the "is future at" are tenseless two-place predicates that may respectively be translated by the tenseless predicates "is earlier than", "is at", and "is later than".²

If such a reduction of A-determinations to B-relations is sound, then the A-Series is reducible to the B-Series.

An event is not intrinsically past, present, or future; it is merely earlier than, simultaneous with, or later than some other chosen event. The chosen event is usually either a linguistic event consisting in the utterance of a tensed statement about the events in question or a mental event consisting of a memory, perception, or expectation of it. The first method of reducing A-determinations to B-relations will be called the "Linguistic Reduction"; the second will be called the "Psychological Reduction," and will be be considered under tenet (2). The aim of both reductions is to show that the A-Series can be reduced to the B-Series and that furthermore the A-Series is subjective, since A-determinations involve a reference to a subject as either a language-user or a preceiver. If there were no language-users or perceivers in the world there would still be a B-Series; however, there would be no A-Series. We shall now consider the Linguistic Reduction.

¹ We are counting simultaneous with as a B-relation. Our justification for this is that simultaneity (a) expresses a permanent temperal relation between events, as does earlier than, and (b) is needed in the construction of the B-Series, since earlier than relates classes of simultaneous events.

² N. Goodman, The Structure of Appearance, Cambridge, Mass., 1951, p. 295. Goodman's use of "is at" is synonymous with "is simultaneous with."

The first step in this reduction is to point out that A-statements, that is, statements asserting that an event has a given A-determination,³ are, as Williams contends, situational in that they reveal the speaker's temporal relation to the event reported by his statement. To say that an event occurred or will occur simply means that it occupies a time earlier or later than my statement about it. More precisely, an A-statement such as "M is past" means "M is earlier than this utterance," in which "this utterance" refers to the occurrence of the sentence within which it occurs, a token being a pattern of sounds or ink marks, etc. For this reason A-statements are said to be "token reflexive."⁴ The second step in the Linguistic Reduction is to claim that the sole function of tense is to express a B-relation between the reported event and the occurrence of the tensed sentence token that reports the event. Therefore there is no reason why we cannot translate the A-statement into a B-statement, that is, a timelessly true or false statement describing a B-relation between two events, which makes the relation explicit. "M is present (past, future)" can be translated without loss of meaning into the B-statement "M is (timelessly) simultaneous with (earlier than, later than) the utterance of 'M is present (past, future).'" This statement is made through the use of a sentence that is freely repeated, since it makes a statement having the same truth-value whenever it is used. Notice that it mentions rather than uses the tensed sentence "M is present (past, future)." Thus this statement does not assert that either M or the linguistic event consisting in the utterance of a tensed sentence, "M is present (past, future)," is now present (past, future); it merely describes a timeless B-relation between M and the tensed utterance about M.

A more common technique for translating A-statements into B-statements is to eliminate in the tenseless rendering all reference to the original tensed statement and instead

³ For a more precise definition of an A-statement, see pp. 295 ff of my introduction to Section IV.

⁴ For a fuller and more critical account of this see pp. 296-97 of my introduction to Section IV.

tenselessly to ascribe a date to the event reported by the original tensed statement; for example, "It is now raining" is rendered by "Rain is (tenselessly) at June 24, 1966." When we tenselessly ascribe a date to an event we show a timeless B-relation between this event and the event which serves as the origin of our calendar. In mathematical logic a date is one among sundry predicates that are tenselessly ascribed to something. The characterizing copula as well as the quantifier is tenseless. When a logician says, "There is a sea battle, which is at June 25, 1966," he is not saying that either the sea battle or the date in question is now present; for both the "is" of the existential quantifier ("There is a") and the "is" of the characterizing copula are tenseless. Quine has claimed that the tenseless mode of existential quantification fits in well with the tenseless space-time talk of Minkowskian geometry employed in relativity theory. In relativity theory, supposedly, a thing is represented as a four-dimensional worm consisting of three-dimensional cross sections strung along the fourth dimension in time. The physicist speaks in a tenseless mode about these spatial cross sections, saying, for example, that a certain cross section is tenselessly earlier or later than some other cross section. Williams' "manifold theory of time" is largely derived from such considerations. The assumption here is that what is good for physics is also good for logic and metaphysics.

Regardless of which technique we use for translating A-statements into B-statements, we are left with tenseless propositions about B-relations that are true or false once and for all, even if the original A-statement was about a contingent event in the future. The fact that lanaguage can be detensed without loss of meaning shows that A-determinations are not intrinsic to events.

(2) Temporal becoming is psychological since A-determinations involve a B-relation to a perceiver. The Psychological Reduction can be viewed as a supplement to the Linguistic Reduction. To the claim that A-determinations indicate B-relations between reported events and utterances, the Psychological Reduction adds the claim that A-determinations also express the characteristic state of belief of the utterer - whether he remembers, perceives, or anticipates the reported event. Russell has argued that A-determinations are notions derived from psychology, since to understand them references must be made to consciousness. To understand what is meant by "past" we must make one of our past experiences an object of experience, while to understand the meaning of "present" we must refer to one of our sensations. Thus, in a world devoid of sentient organisms there no more would be A-determinations than there would be pains. And since A-determinations are psychological it follows that temporal becoming is also. The temporal becoming of a physical event is analyzable in terms of its bearing different B-relations to a series of mental events consisting of an expectation, perception, and memory, experienced by a single mind. Whether becoming is mind-dependent will be one of the major themes in Section IV on Human Time.

(3) The B-Series is objective, all events being equally real. What is objectively real is the B-Series. The A-determinations of events are subjective in the sense of being relative to our temporal perspective as either utterer or perceiver. However, there could be B-relations in a world devoid of language-users or perceivers, since these relations do not involve reference to a subject; they are objective relations between events, neither of which need be a mental or linguistic event. Corresponding to our timeless B-statements describing B-relations between events is a timeless series of events - the B-Series. All events of history form a totum simul. As Williams says, past, present, and future are equally real and determinate by a necessity of logic, since we can formulate timelessly true or false propositions about B-relations between events.

(4) Change is analyzable solely in terms of B-relations between qualitatively different states of a single thing. It is claimed that the B-Series alone is sufficient to account for (i) changes of time, that is, changes in the A-determinations of events, and (ii) changes in time, that is, qualitative and quantitative changes of things. The first type of change is temporal becoming, and we have already seen how it is analyzable in terms of B-relations between events, in which one of the relata is either a linguistic event (the Linguistic Reduction) or a mental event (the Psychological Reduction).

Qualitative and quantitative change - change in time - is analyzed by Russell solely in terms of the B-Series as follows:

Change is the difference, in respect of truth or falsehood, between a proposition concerning an entity and a time T and a proposition concerning the same entity and another time T', provided that the two propositions differ only by the fact tht T occurs in the one where T' occurs in the other.⁵

In expounding this position, Braithwaite said that change in time "consists in the fact that a different relation holds between the thing (a substance in the ordinary sense) and a certain property at one of the times than holds at the other time."⁶ An empirical thing or substance is reducible to a certain series of successive events, such that the members of any one such series are intimately interconnected by certain spatial and causal relations that do not interconnect members of any two such series. What we mean by the change of thing in time is a sequence of successive events all regarded as states of one thing. Such changes are analyzable solely in terms of B-relations between events comprising the history of a single thing without invoking the becoming of these events. This view of change underlies Williams' claim that time is nothing but a certain ordered extension of events.

Answer to McTaggart's Paradox. McTaggart, in arguing for the necessity of the A-Series, claimed that change, without which there could not be time, required the A-Series. It is logically impossible for any features of the B-Series to

⁵ Bertrand Russell, The Principles of Mathematics, Cambridge, 1903, p. 469.

⁶ R. Braithwaite, "Time and Change," Aristotelian Society Supp. Vol. 8 (1928), p. 169.

change: there can be no increase or decrease in its membership, no change in the qualities of any event included in it, and no change in the B-relations between its members. Therefore, by a process of elimination, the only possible change is change in the A-determination of an event. The B-Theory claims that McTaggart considered only changes in events and thus overlooked one possible candidate for the title of change, namely changes in things. And in tenet (4) of the B-Theory it argued that such changes in things - changes in time - require only the B-Series. Therefore, the reality of time does not require that there be an A-Series. McTaggart's reply to this way of countering his argument is contained in the passage from his Nature of Existence that is reprinted in this section.

While the B-Theory denies the necessity of the A-Series, it still cannot countenance McTaggart's claim that the A-Series is contradictory; for in tenet (1) it claims that the A-Series is reducible to the B-Series. Such a reduction would not be possible if the A-Series really harbored a contradiction. Therefore it behooves B-Theorists to answer McTaggart's main argument main argument to the effect that the A-Series is contradictory because every one of its members has all three mutually incompatible A-determinations. The B-Theorists' way of explaining away this alleged contradiction is to claim, in accordance with their Linguistic and Psychological Reductions, that the A-determinations of past, present, and future that there is an event being earlier than, simultaneous with, and later than. A contradiction would emerge only if an event had two or more of these temporal relations to one and the same event; but this McTaggart has never shown to be the case. By the Linguistic Reduction it is shown that an event is past, present, and future only in the elliptical sense of being respectively earlier than a tensed statement that it did occur, simultaneous with a statement that it is occurring, and later than a statement that it will occur. And by the Psychological Reduction it is claimed that an event has these three A-determinations only in virtue of its being respectively earlier than a memory of it, simultaneous with a perception of it, and later than an expectation of it.

The A-Theory Answer

Another answer to McTaggart is based on what we shall call the "A-Theory of Time." The A-Theory of time received its most articulate formulation in the work of C. D. Broad, which is reprinted in this section, and it has prevailed among those philosophers whose main concern is to clarify ordinary language by studying the way words are used in various contexts. Among those holding views in some way similar to Broad's are L. S. Stebbing, J. Wisdom, P. Marhenke, A. N. Prior, D. Pears, W. Sellars, S. Hampshire, P. F. Strawson, and J. N. Findlay. As these men have far less in common than the defenders of the B-Theory, it is more difficult to abstract a set of common tenets from their writings; but I believe that the following four are representative of their work:

      (1) The B-Series is reducible to the A-Series since B-relations can be analyzed in terms of A-determinations;
      (2) Temporal becoming is intrinsic to all events;
      (3) There are important ontological differences between the past and the future; and
      (4) Change requires the A-Series.

Each of these tenets is either the contradictory or the contrary of the B-Theory tenet of the same number. As before, we shall discuss each tenet separately and then show how together they constitute an answer to McTaggart.

(1) The B-Series is reducible to the A-Series since B-relations can be analyzed in terms of A-determinations. The defenders of the A-Series is both necessary and fundamental. Their arguments attempt to show B-relations are temporal relations only because their relata have A-determinations and change in respect to them.

One argument, which is contained in the Broad selection, states that what makes the B-Series a temporal series is that its members form an A-Series and change in respect to their A-determinations. In the course of his argument Broad makes two claims, one highly controversial and the other acceptable even to those holding the B-Theory of Time. The non-controversial claim is that a temporal series differs from a spatial one in that, while both have an intrinsic order, only the temporal series differs from a spatial one in that, while both have an intrinsic order, only the temporal has an intrinsic direction or sense. The controversial claim is that the direction of a temporal series is due to the fact that its members undergo temporal becoming.

A linear spatial order of one dimension has an intrinsic order, because, given any three members of this order, one of them will appear to be between the other two regardless of what position they are viewed from. This order, however, does not have an intrinsic direction because whether one does not have an intrinsic direction because whether one member of it is to the right of another will depend on the position from which they are viewed. An observer in the orchestra will see Warren standing to the right of Tibaldi, but an observer backstage will see Warren to the left of Tibaldi. A linear spatial order has a direction only in reference to the right and left hands of an external observer; thus its direction is extrinsic to the order itself. The spatial relation to the right of is triadic, since it involves a relation to some third position from which one object is to the right of another. In a linear spatial series there is no asymmetric dyadic relation intrinsic to the series.

Like a spatial series of one dimension, a temporal series has an intrinsic order, but in addition it has an intrinsic direction; since its generating relation - earlier than - is a genuine dyadic relation. Max Black, who has made an analysis of temporal relations similar to Broad's, states that temporal relations, unlike spatial ones, are not incomplete relations, since they do not involve reference to some third term.⁷ If we say that X is earlier than Y we do not have to specify some third position from which X and Y are viewed, as we do when we say that X is the right of Y. When we are told

⁷ M. Black, "The 'Direction' of Time," Analysis, 19 (1959), 60.

that Warren's singing of a rousing aria was earlier than his dropping dead we do not ask from what third position these events were viewed. Broad claims that temporal betweenness is not fundamental (as is spatial betweenness) because it is definable in terms of the genuinely dyadic relation of earlier than taken twice over.

The controversial claim made by Broad is that becoming, what he calls the "transitory aspect of temporal facts," is of the very essence of time, and that without it a temporal series would not have an intrinsic direction, thereby being indistinguishable from a spatial order. It is because and only because the events comprising a B-Series undergo temporal becoming that we can distinguish a B-Series from non-temporal series. We cannot do this solely in terms of the logical properties of the generating relation of the B-Series - its being asymmetric, transitive, and irreflexive - since there are non-temporal relations, such as larger than, which have the same logical properties: and yet we know that a number series is basically different from a time-series. It is temporal becoming that causes all analogies between space and time to break down. When we represent time by a line we cannot account for the direction of a time-series. If direction is to be introduced into a one-dimensional spatial order this must be done extrinsically, either by reference to motion along the line (and therefore including time, since motion takes time), or by reference to the right and left hands of an external observer. The intrinsic direction of the B-Series is therefore essentially bound up with the temporal becoming of its members.⁸

This argument of Broad's, if it can be called such, will not convince any B-Theorist. He would agree with Broad that earlier than is a dyadic relation and that time-series is sui generis, but would deny that these two facts are dependent upon temporal becoming. What makes a time-series unique, he would contend, is that its generating relation is a temporal relation. Certain empirically minded B-Theorists would argue, as does Adolf Grunbaum in his article on "The Status of

⁸ C. D. Broad, Scientific Thought, London, 1925. pp. 55-58.

Temporal Becoming" in Section IV, that what bestows a direction on a time-series, what makes it irreversible or anisotropic, are certain physical asymmetries, such as an increase of entropy, which are intrinsic to the B-Series of physical events. The efforts of such theorists to explicate the direction of time make no reference to temporal becoming, being concerned only with law-like asymmetries and/or boundary condition asymmetries between earlier and later times.

The second argument presented by Broad and other proponents of the A-Theory of Time for the necessity of the A-Series is that B-relations are definable or analyzable in terms of A-determinations. In addition to showing the necessity for the A-Series, this is an argument for the fundamentality of the A-Series, since it attempts to show that the B-Series is reducible to the A-Series. This argument claims that the meaning of "M is (tenselessly) earlier than N" is "When M is present N is future and when N is present M is past."

Since B-relations are analyzable or definable in terms of A-determinations, it follows that A-statements cannot be translated without loss of meaning of B-statements, that is, freely repeatable statements that describe a B-relation between two events. The main difficulty with all such translations is that the B-statement does not assert, as does the A-statement of which it is a rendering, whether the reported event is past, present, or future. There is an asymmetry in information between A- and B-statements. When I tell you that X is present and Y is future I have already told you that X is earlier than Y; but if instead I had asserted the latter B-statement I would not have told you the X is present or that Y is future. Attempts to detense language by the use of dates fail for the same reason.

We are not able to assimilate tensed existential statements to the tenseless mold of existential quantification, as the B-Theory demands. Ordinary language, as Strawson and Hampshire have argued, is an irreducible tensed-substance language because of necessity it must contain referring expressions, and only tensed statements can refer successfully to unique objects and events. In order to single out and describe some object in our immediate environment we must speak in a tensed mode, using ourselves as centers of spatio-temporal orientation. When we ask about objects (or events) in ordinary contexts the question of whether they exist (or occur) now is always relevant. For this reason the method of existential quantification employed in mathematical logic cannot do justice to ordinary language.

(2) Temporal becoming is intrinsic to all events. A similar argument can be employed against the Psychological Reduction, which said that events have A-determinations only in relation to a perceiver. But once again this does not reduce A-determinations to B-relations, because the series of mental events that runs concurrently with the series of physical events forms an A-Series. I am sure that my own mental events temporally become. If the mental acts of an observer are intrinsically past, present, and future, then the objects of these acts, which are contemporaneous with them, must likewise be intrinsically past, present, and future. Becoming cannot be intrinsic to one series of events without being instrinsic to the other. Grunbaum attempts to refute this argument in his piece on "The Status of Temporal Becoming."

(3) There are important ontological differences between the past and future. The A-Series is objective, not being dependent upon a language-user or perceiver. Several defenders of the A-Theory have gone on to claim that because temporal becoming is objective there are significant ontological differences between past and future events, consisting in the fact that the future is open, a realm of possibilities, while the past is closed, a realm of actualities. This ontological difference reveals itself in certain logical asymmetry in our ways of talking about the past and future in that (i) statements about the future must be general in logical form while statements about the past can be singular, and (ii) all statements about the past are either true or false while some statements about the future are neither true nor false now. These matters will be discussed at length in Section III.

(4) Change requires the A-Series. The B-Theory analyzed change in time in terms of B-relations between events or states belonging to the history of a single thing. The A-Theory challenges this analysis this analysis, for in tenet (1) it claims that B-relations are dependent upon A-determinations. From this it follows that (a) since change in time necessarily involves B-relations between events and (b) since B-relations depend upon the A-determinations of the events related, that there can be no change in time without the A-Series. Thus the claim that there can be no change in time without the A-Series is a corollary of tenet (1). Only if B-relations were independent of A-determinations could change in time be explained solely in terms of B-relations between events.

Broad claims that change of time - temporal becoming - is sui generis and that any attempt to represent it in terms of change in time is vicious. Though a thing exists both before and after it undergoes some qualitative or quantitative change, an event does not exist both before and after it becomes present. When we represent becoming by analogy with motion along a one-dimensional spatial order we are reducing change of time to change in time. We think of the present as a spotlight that plays along a line of chorus-girl-like events; but this involves us in a pseudoproblem of how fast - how many seconds per second - the spotlight moves. All representations of becoming in terms of some kind of motion (or other change in time) involve a vicious circle, since motion (or any other change in time) presupposes becoming.

Answer to McTaggart. The A-Theory agrees with McTaggart's positive thesis concerning the necessity and fundamentality of of the A-Series, but disagrees with his negative doctrine that the A-Series involves a contradiction. McTaggart's inability to combine the static view of time exemplified in his B-Series with the dynamic view contained in his A-Series is due to his substantialization of the events in the B-Series, which causes him to represent temporal becoming as if it were some sort of motion, the A-Series moving up the B-Series. McTaggart substantialized events because he thought - mistakenly - that the events in the B-Series must always coexist since B-relations are permanent. The events in the B-Series are now treated like a line of chorus girls, who exist both before and after they do their brief bit in the spotlight of presentness. But that view involves us in the above difficulties of reducing becoming to movement. Broad claims that there is no incompatibility between becoming and the "permanancy" of B-relations between events.

The B-Theory explained away the contradiction inherent in each event's having all three A-determinations by showing that these determinations are reducible to B-relations. The A-Theory cannot avail itself of this way out, since it denies that such a reduction is possible. Rather it claims that since temporal becoming is intrinsic to all events, there is no contradiction to be explained away. A contradiction would arise only if in a single utterance an event was asserted to have two or more A-determinations, but there is nothing in our temporal experiences to warrant making such a statement. A-determinations are unanalyzable. "M is present" entails, but does not mean, according to Stebbing and Wisdom, "M is present at a moment which is present." McTaggart's infinite regress, it follows, is benign: it is a regress of entailings and not meanings. Therefore, there is no need to analyze statements predicating an A-determination of an event in terms of a moment of time in some second-order A-Series at which the event has this A-determination.

The Either-Way-Will-Work Theory Answer

The third answer to McTaggart, which is put forth by J. N. Findlay and J. J. C. Smart, is based on a theory of time that claims that either the A- or the B-Series alone is a sufficient account of time and change, and paradoxes arise only if one is confused with the other. The essential tenet of this theory is that the tensed and tenseless modes of speaking are both equally workable and legitimate: everything sayable in a language containing only A-statements is sayable equally well in a language is sayable equally well in a language containing only B-statements, and vice versa. Herein the Either-Way-Will-Work Theory is closer to the B-Theory than the A-Theory is a denial that A-statements can be rendered without loss of meaning by B-statements.

Findlay points out in his article in this section that while the tensed and tenseless modes of speaking are both equally workable and legitimate, there nevertheless are certain practical advantages in speaking tenselessly, since our statements are then timelessly true or false independently of when they are made. The ideal of science is to eliminate tenses so that statements can be freely repeatable. In the tensed mode of speaking we must systematically alter the tense of our statement depending on our B-relation to the reported event. McTaggart's paradox results from the attempt to speak at one and the same time in both the tensed and tenseless modes. In certain "moods" we become enamored with the time-independence of our tenseless mode of speaking, and we attempt to apply this ideal to the tensed mode: we are then apt to think that there is something contradictory about tenses since we must continually change the tense of our statements with the passage of time. When McTaggart claims that the A-Series is contradictory, he is applying the ideal of the tenseless mode of speaking of the tensed mode. A contradiction results only if we expect tensed statements to have the same logical behavior as tensless ones, that is to be freely repeatable.

The brief paper by Smart defends a similar thesis. Smart distinguishes between an objectionable and an unobjectionable sense of spatializing time. In the objectionable sense we conceive of events as being in time in exactly the same way that ordinary empirical substances are in space. We must conceive of them as coexisting substances which endure in some meta-time. In the unobjectionable sense of spatializing time we treat time as a fourth dimension, as in the four dimensional space-time geometry of Minkowski. Herein time is a dimension in which the three-dimensional spatial cross sections are strung out in accordance with the timeless B-relations between them. A system of solid geometry, regardless of how many dimensions it deals with, has no reference to change of time. In a four-dimensional geometry we do not think of space or the network of spatial relations as enduring or lasting throughout some period of time. When we represent time spatially as a timeless network of B-relations we must not apply tensed concepts of enduring or changing to these relations. If we do, we are spatializing time in the objectionable sense, since we would then need a meta-time for this change or changelessness to be in. This is the start of the famous infinite regress of times changing or enduring with times.⁹

For a fuller and more critical discussion of the material contained in this introduction as well as the introductions to Sections III and IV, see my book, The Language of Time, Routeledge & Kegan Paul, London, 1967.

BRIEF BIBLIOGRAPHY (MAINLY OF SELECTIONS MENTIONED IN TEXT)

Broad C. D., "Ostensible Temporality" from An Examination of McTaggart's Philosophy, Vol. II. Part I. Cambridge University Press, 1938.

Findlay J. N. "Time: A Treatment of Some Puzzles" in Australasian Journal of Philosophy 19. (1941)

McTaggart J. M. E., The Nature of Existence, Volume II. Cambridge University Press, 1927, Book V, Chapter 33.

Smart, J. J. "Spatializing time" from Mind 64, (1955).

Williams, D.C. "The Myth of Passage" Journal of Philosophy, 48, (1951).

Additional Titles

Broad C. D. Scientific Thought Kegan Paul, Trench, Tubner. London. 1923.

Hornstein, N. As Time Goes By: Tense and Universal Grammar. MIT. 1990.

Ludlow, P. Semantics, Tense, and Time MIT. 1999.

Reichenbach, H. "The Tenses of Verbs," in Elements of Symbolic Logic. The Free Press. 1947.

J. Rosenberg, "Tensed Discourse and the Eliminability of Tenses," Phil. Quarterly, 16. 1966.

W. Sellars, "Time and the World Order," in Minnesota Studies in the Philosophy of Science. III. ed. H. Feigl, G. Maxwell, and M. Scriven. University of Minnesota Press. 1962.