The Roots of Hypertime

1 Introduction

The everyday space we inhabit has three dimensions: width, length, and height. The everyday time we inhabit has one: to specify a location in time, we need only one coordinate (e. g., ‘5:30pm’). Hypertime is a theory that postulates that time has two or more dimensions. Much of the groundwork underlying current theories of hypertime in analytic philosophy is generally attributed to discussions in the second half of the twentieth century – either in connection with the objection against the passage of time or as a means to resolve problems in the philosophy of time travel.^[1]

This paper demonstrates that the historical roots of hypertime extend much further back. Drawing on recently uncovered and currently unpublished archival documents, I will show that despite McTaggart’s famous rejection of multiple time series, early attempts at formulating multi-dimensional time, hitherto neglected by historians of philosophy, were made by philosophers decades before the interest in time travel took off. These early pioneers of hypertime were working on psychical research: the study of psychical phenomena such as telepathy, clairvoyance, or ghosts, widely popular towards the end of the nineteenth and the beginning of the twentieth century. Recent scholarship is beginning to appreciate the influence that psychical research had on twentieth-century analytic philosophy.^[2] I have recently argued that C. D. Broad held a theory of hypertime (Moravec 2025a). This paper shows that Broad was part of a much wider movement of hypertime theorizing. I will demonstrate that decades before discussions about time travel or the passage of time became widespread, three British philosophers actively corresponding with Broad began developing hypertime theories as solutions to problems entailed by the purported existence of precognitions.

This paper proceeds as follows. Section 2 provides an origin story of hypertime by looking at hypertemporalist themes in Bradley and McTaggart. Section 3 explores a decisive chapter in the development of hypertime, J. W. Dunne’s serialism. Sections 4, 5, and 6 explore the role of hypertime in Broad’s discussion with three overlooked philosophers interested in psychical research: H. F. Saltmarsh, H. H. Price, and H. A. C. Dobbs. Section 7 demonstrates that the uses of hypertime in contemporary debates about the flow of time and time travel were anticipated by these discussions. The conclusion assesses the pitfalls of neglecting the history of hypertime.

2 Bradley and McTaggart

Arguably, one of the first suggestions appealing to something resembling hypertime can be found in Bradley’s Appearance and Reality (1893), which postulated the possibility of multiple time series.^[3] Bradley says that “[w]e have no reason […] to regard time as one succession, and to take all phenomena as standing in one temporal connection” (Bradley 1893, 210). For Bradley, if these time series exist, they must be independent: “In these the internal events would be interrelated temporally, but each series […] would have no temporal connection with anything outside. […] [F]or themselves, [the events] would not possess any relations to other series” (Bradley 1893, 211). Of course, this is not hypertime proper. Hypertime postulates two or more series of time, that is, of the same time. If the series have no relation to each other whatsoever, then we cannot properly speak about hypertime. (Just as we cannot speak about three-dimensional space if we posit three distinct dimensions, each one describing a single one-dimensional object, but the individual objects bear no spatial relations to one another).^[4]

The idea that these series might be related forms the background of the argument for the regress in the A-series in McTaggart’s “Unreality of Time,” which briefly mentions Bradley’s suggestion of multiple time series (McTaggart 1908, 466). However, as McTaggart observes – having Bradley in mind here – the infinite-regress argument against the A-series would apply to each one of the series: “I am not, of course, asserting that there is no contradiction in the existence of several distinct A series. My main thesis is that the existence of any A series involves a contradiction” (McTaggart 1908, 466). And this, in turn, calls into question the entirety of Bradley’s supposition of multiple time series.

McTaggart’s argument against the A-series itself appeals to an initially plausible (but ultimately dysfunctional) idea about resolving the contradiction in the series itself by appealing to two time series that are distinct but that, nevertheless, both describe one and the same time. Perhaps, the suggestion goes, the contradiction that exists within the A-series (i. e., the fact that each event possesses the mutually incompatible relations of past, present, and future) could be resolved by appealing to a higher dimension of time in which these relations are possessed at different times. The problem for McTaggart was, famously, that such a move leads to an infinite regress. If hypertime implies hyper-hypertime, then hypertime itself must be rejected.

This section has suggested that there are already traces of hypertime in Bradley and McTaggart. This, however, is not proper hypertime, since the time series are disconnected. Furthermore, McTaggart ultimately rejected the possibility of multiple time series anyway. The possibility that perhaps we should just accept the reality of time qua infinite regress was defended by J. W. Dunne. The next section explores his theory of serialism.

3 Dunne’s Hypertime and Precognitions

At the beginning of the twentieth century, the evidence for precognitions (i. e., the ability to gain cognitive access to future events, particularly in dreams or visions) was fairly uncontroversially accepted as genuine data requiring philosophical analysis.^[5] The purported existence of precognitions raised an important problem for the philosophy of time. As H. F. Saltmarsh put it: “What we have to explain is how an event which, being still in the future, does not, apparently, exist, can enter into a relation of cognition, that is to say, a relation of known to knower” (Saltmarsh 1938a, 81).

Precognitions had puzzled psychical researchers more or less since the foundation of the Society for Psychical Research (SPR) in 1882. However, a crucial moment that rapidly intensified this interest was the 1927 publication of John William Dunne’s An Experiment with Time.^[6] Dunne not only offered an extensive catalogue of his own precognitive experiences but also provided a hypertime theory that was supposed to explain how they happen. Dunne called his theory ‘serialism.’

Serialism is perhaps best understood by analogy with the regress in McTaggart’s A-series. McTaggart argued that the A-series inevitably leads to an infinite regress and must therefore be rejected. Dunne, by contrast, simply accepted that the nature of time consists in this very regress.^[7] Dunne’s theory suggested that since time moves or flows, there must be an additional hypertime to describe this movement. But the same is true of this very hypertime; for hypertime to be truly temporal, there must exist hyperhypertime measuring its movement, and so on. The series go on forever. At its furthermost level, ‘at infinity,’ we find the final term containing all the series below, which makes it possible to observe whatever happens in the inferior time series (Dunne 1927, 150–151). When dreaming, we can gain cognitive access to this hyper-hyper-level and get a glimpse of future events.

Dunne’s theory was almost universally rejected by academic philosophers.^[8] A rejection of Dunne’s theory, fairly representative in its selection of the weaknesses of Dunne’s book, was Martha Kneale’s (1909–2001) contribution entitled “Time and Psychical Research” delivered at the International Symposium organized by the Parapsychology Foundation at St Paul de Vence (20–26 April 1954).^[9] Kneale rejects Dunne’s theory because, she claims, it is not really a theory at all, merely a misunderstanding of a metaphorical use of language. Dunne was misled by the metaphorical talk of time ‘flowing’ into thinking that it literally has to ‘move’ within a higher time dimension, just like water moves in the riverbed. But the more severe problem, according to Kneale, was Dunne’s simultaneous postulation of an infinite regress of series and at the same time a point ‘at’ infinity from which the observation of the levels below can happen.

Although Dunne’s serialism was rejected, his book put precognitions at the center of attention of an entire generation of philosophers interested in time and psychical research. Most philosophers committed to the existence of precognitions attempted either to correct Dunne’s theory – this was the case of Broad (1935) – or to develop alternative theories of time of their own that would be able to explain precognitive access to future events. Dunne’s book crops up in all major discussions about the relationship between precognitions and time until the late 1950s.^[10] One of the few philosophers to have taken Dunne seriously was Broad. He explicitly argued that “Mr. Dunne might be right to the extent that it is necessary to assume a series of at least two terms for the special purpose of explaining Precognition” (Broad 1935, 168, emphasis original).

The possible existence of multiple dimensions of time formed the core of Broad’s discussion about precognitions with H. F. Saltmarsh, whose work is the topic of the next section.

4 Broad and Saltmarsh

This section provides an overview of H. F. Saltmarsh’s explanation of precognitions and demonstrates how his thought about multiple time series paved the way for later, more robust theories of hypertime in Broad, Price, and Dobbs.

H. F. Saltmarsh (1881–1943) was a psychical researcher mostly known for his work on survival after death and precognitions. He published two volumes on these topics, Evidence of Personal Survival from Cross-Correspondences and Foreknowledge, as well as several papers on psychical research (see Saltmarsh 1940). He joined the SPR in 1921 and conducted influential experiments with the medium Warren Elliott (Saltmarsh 1930), extensively discussed in Broad’s 1962 Lectures in Psychical Research.^[11] The focus of this section will be on three sources: Saltmarsh’s 1934 paper “Report on Cases of Apparent Precognition,” his 1938 Foreknowledge, and correspondence with C. D. Broad.^[12]

Saltmarsh rejected Dunne’s serialism. Apart from a general reluctance to accept an infinite series (Saltmarsh 1938a, 86–87), Saltmarsh attacked the claim that the passage of time entails a higher dimension of time within which this time passes. In doing so, he anticipated one of the most powerful arguments against the flow of time as such, the so-called ‘no-rate’ argument. This argument states that “time cannot literally flow or pass because it cannot be assigned any meaningful rate of flow or passage” (Mazzola 2014, 158). Dunne tried to articulate his belief that time does flow by making it move or flow in a higher dimension. One unit of time, in his view, was supposed to flow per one unit of hypertime. The problem with this suggestion, Saltmarsh says, is the following:

We can intelligibly speak of speed, or rate of change, when one of the factors is non-temporal, e. g., so many feet per second, or the change from optimistic self-satisfaction to pessimistic depression during the course of a day; but to speak of a speed of so many hours per hour seems, on the face of it, to be absurd. (Saltmarsh 1938a, 88)

Having rejected Dunne’s serialism, Saltmarsh suggests his own explanation for precognitions by appealing to what he calls the “subliminal specious present” (Saltmarsh 1938a, 94–102; 1934, 74–93). Saltmarsh’s starting point is the standard version of the doctrine of the specious present: “It is a commonly accepted principle that the present moment, of which we have experience, occupies a certain length of duration; it is not a point which has position and no magnitude” (Saltmarsh 1938a, 95). Because the specious present is extended, it can be co-present with events which are themselves successive in time: “it may be that more than one event is contemporaneous with it, and that those events are not contemporaneous with each other, but successive.” (Saltmarsh 1938a, 96)

Now, if we suppose that two different observers can have specious presents of different lengths, then some events in the specious present of one observer may be past or future in the specious present of another. To mobilize the specious present as an explanation of precognitions, Saltmarsh combines this insight with an ingredient from psychical research: the ‘subliminal mind’ or ‘subliminal consciousness.’ The ‘subliminal mind’ was a concept developed by F. W. H. Myers (1903) and referred to a level of consciousness below the conscious threshold that was responsible for phenomena like telepathy and communication with spirits of the dead.^[13] Many psychical researchers developed their own theories about this, but the particular definition of the subliminal self that Saltmarsh accepts is the following:

[I]t is a region, normally cut off from ordinary consciousness by a threshold, wherein events take place, events which, even if they are not identical in character with those of the supraliminal mind, are of an analogous nature. (Saltmarsh 1934, 79 n1)

Saltmarsh then fuses the subliminal self with the specious present:

Suppose now that we substitute for the second observer [with whose specious present my specious present overlaps] a stratum of my own subliminal mind. It follows that if the specious present of my subliminal mind be longer than that of my normal consciousness, events which are present to the former may be future to the latter. (Saltmarsh 1938a, 97)

The idea here is the following. Suppose we have a successive series of four points in time, t₁, t₂, t₃, and t₄. Although my specious present might only extend from t₂ to t₃, its subliminal correlate can stretch from t₁ to t₄ (and possibly beyond). In precognitive experiences, some of the information from this subliminal specious present (that includes future events contained in the interval t₃ to t₄) can be transmitted to the specious present of the normal mind, stretching from t₂ to t₃. In the case of some people, Saltmarsh argues, the subliminal specious present can perhaps even extend “over a period of many years” (Saltmarsh 1938a, 98) and “there seems to be no particular reason why it should not extend indefinitely” (Saltmarsh 1934, 85).

Many of Saltmarsh’s views about time built on the philosophy of C. D. Broad, with whom he corresponded extensively from at least 1932 onwards.^[14] A specific worry that Broad raised was that Saltmarsh’s theory of the subliminal specious present is unable to explain how information can pass from the subliminal level to the supraliminal level. In a letter from June 1933, Saltmarsh provides a highly evasive response: “What the mechanism of transference may be I cannot imagine, but then we know very little about the normal passage through the [subliminal] threshold. […] Still I cannot see that there is any inherent impossibility in such a transference.”^[15] The same ambiguity makes it into the published paper on the cases of apparent precognition from 1934, where Saltmarsh tries to argue that since the transmission of information from the subliminal to the supraliminal level happens regularly in dreams or in the cases of hyperaesthesia, there is no reason why the same could not be the case with the transference between the two specious presents (Saltmarsh 1934, 82–83).

It might, nevertheless, be objected that Saltmarsh is not talking about hypertime at all. Hypertime requires two orthogonal dimensions, such that any specification of whatever happens in time requires two temporal coordinates. What Saltmarsh has in mind is rather that the objective description of time operates in one type of series, while our temporal experience operates in another. His emphasis on the specious present (traditionally discussed within the domain of temporal experience) makes this look even more likely. To make things worse, Saltmarsh’s theory strongly resembles that of David Lewis (1976), who distinguishes between ‘personal’ and ‘external’ time in an attempt to do away with multi-dimensional time altogether.

There are several reasons why I think that this interpretation should be resisted and why Saltmarsh deserves a place in the history of hypertime.

The first is that for most early twentieth-century authors (particularly those operating outside of academic circles, like Dunne or Saltmarsh), the distinction between temporal experience (or subjective time) and objective time was non-existent. They just wrote about time, though whatever they said about it was heavily informed by temporal experience (see Moravec 2023). The distinction that Lewis (who, weirdly enough, also mentions precognitions; see Lewis 1976, 78) makes would have most likely seemed unintelligible to Saltmarsh. Where temporal experience is co-extensive with time, and someone talks about two times, we are justified in reading the resulting theory as hypertemporalist.

The second reason why Saltmarsh’s theory should be considered as an early version of hypertime is that the two parallel time series have distinct ontologies that – unlike Bradley, for example – nevertheless describe the same reality. (This, of course, seems implausible. How can the same event have two different ontological states, depending on whether it is considered in one of the time series or the other? This is exactly the problem that will immediately get picked up by Broad and Price; see below). The first series is eternalist and contains the events in the subliminal mind: “the future exists now in some way, and may be accessible to my consciousness under certain circumstances” (Saltmarsh 1934, 72). The second series, by contrast, has a growing-block structure. It has a distinguished specious present into which, in cases of precognition, enter contents of the eternally existing subliminal mind:

It might seem at first sight that my theory implies that a future event, meaning thereby an event which does not yet exist, can exercise a causative influence on the present. This is obviously impossible, for non-existence cannot exercise a causative influence. But my suggestion is that the event which is the object of a precognition is not future in this sense; it already exists in the present of the subliminal. It is future only in the sense that it is temporally located later than the events which are in the present of the supraliminal. (Saltmarsh 1934, 86)

The fact that Saltmarsh thinks of the two series in hypertime terms is apparent from a set of illustrative diagrams he provides in his 1934 paper. Each one of these diagrams operates with two parallel timelines (Saltmarsh 1934, 80–85), the top one describing the sequence of specious presents, the bottom one containing the events existing eternally in the subliminal mind.^[16]

The third reason is that Saltmarsh’s theory has an important affinity with Dunne’s serialism. True enough, Saltmarsh rejected Dunne’s postulation of an infinite sequence of time series. However, he did accept the inference to the first one of them. This is explicitly stated in a typescript entitled “An Alternative to Professor Price’s Hypothesis”: “We can suppose that the ordinary spatial and temporal limitations might be relaxed in various ways. There might, for example, be more dimensions than the usual three of space & one of time, […] If there be other dimensions of time, an event which is past or future for the normal might be in the present of the second or third dimension.”^[17] Dunne and Saltmarsh also share the attempt to hold together temporal becoming (i. e., the coming of events into existence) and their ‘already’ existing as the objects of precognitions – in a higher time series in the case of Dunne, in the subliminal mind in the case of Saltmarsh. For example, the illustration that Saltmarsh uses to explain the subliminal specious present theory is remarkably similar to Dunne’s serialism:

Imagine a bundle of wires or threads all running roughly parallel to each other. You are looking at the bundle through a narrow slit across its length so that you can see only a short section at any one time. […] Not only can you see through the slit, but you can also touch the wires through it. Some of the wires are flexible and elastic, others rigid and movable. […] The wires that are capable of being moved have this peculiar property that after the slit has passed over them they become rigid, so that the whole bundle astern of the slit is fixed and immovable. […] The bundle of wires represents a strand of history, the slit the specious present of the observer. The screen in which the slit occurs is the threshold between the supraliminal and the subliminal.^[18] (Saltmarsh 1934b, 89)

This description is structurally identical to the insight that led Dunne to postulate hypertime. According to Dunne (1927, 97), temporal events are spread out like notes on a sheet of music. This sheet of music, however, is incomplete. For the description of reality to be complete, we require an additional time series timing the movement of the ‘now’ across the sheet to indicate which note is being played presently. Dunne then claimed that the same applies to the series of positions of the ‘now’ itself. Saltmarsh does not go that far, but his illustration above commits him to two time series with different ontologies: the first in which the events are all existent and which is somehow accessible to the subliminal self (Saltmarsh 1934, 91), and the second, which describes the movement of the present (or the slit in the example above) over them.

As a matter of fact, it is precisely the postulation of two time series that leads Saltmarsh to observe a specific ontological problem that can also be found in Dunne. This might be called the problem of the ‘double existence’ of events, which will play a key role in the disagreement between Broad and Price in the next section. The problem is this. On the one hand, future events must exist (in the subliminal self in the case of Saltmarsh; or in the higher time series in the case of Dunne) to be able to feature as content of precognitions. But, on the other hand, in order for temporal becoming to be real – something that both Dunne and Saltmarsh (Saltmarsh 1934, 75) seem to affirm – events must successively acquire existence. So the future ones cannot exist yet. Dunne’s serialism (at least in the version presented in the Experiment) is highly ambiguous on this issue and slides back and forth between future events being “real enough to be experienced as pre-presentations” (Dunne 1927, 91) and their being “partly real – less real, for instance than are past events” (Dunne 1927, 91). The same problem troubles Saltmarsh: “It may seem plainly repugnant to common sense to suggest that a future event may exist in any sense and yet be subject to change” (Saltmarsh 1934, 92). The awareness of the ambiguity around the ontological status of future events is clearly on Saltmarsh’s mind when he asks: “[T]he future exists now in some sense. Can we form any idea of the manner in which it exists?” (Saltmarsh 1934, 89, emphasis original). His answer on the pages that follow is extremely ambiguous. In the end, Saltmarsh concludes: “That there are difficulties I do not deny, but then ontology is always difficult” (Saltmarsh 1934, 90). We will return to this problem in the following section, as it forms the core of the disagreement between Broad and Price.

The fourth reason why Saltmarsh’s precognition theory is a prototype of hypertime is that towards the end of the 1938 volume, Saltmarsh surprisingly affirms the possibility of multiple dimensions of time in connection with the survival of bodily death: “If, as has been suggested, precognition implies a second dimension of time […], it seems possible that a man might die and cease to exist in one temporal direction, yet survive in another” (Saltmarsh 1938a, 114–115). And in the typescript entitled “An Alternative to Professor Price’s Hypothesis,” Saltmarsh explicitly connects the multi-dimensionality of time with the theory of the specious present: “[I]f time be multidimensional, X. Y.’s death may be in the past of normal time, yet in the future in some other dimension. Or if the specious present […] be of a longer duration for the subliminal mind, it might cover a period which, from our normal standpoint, would go back beyond the date of X. Y.’s death & thus permit of telepathic transmission.”^[19]

The fifth piece of evidence for Saltmarsh’s commitment to hypertime comes from his treatment of McTaggart. In a letter to Broad from March 11, 1933, he says that he had been extensively studying McTaggart’s Nature of Existence and that the sections of McTaggart’s book which deal with time have a direct impact on his own theory of precognitions. In the letter, Saltmarsh rephrases the illustration with the bundle of wires (see above) using the language of A- and B-series: “In terms of my illustration, the A series is the bundle of wires, the B series the series of views of the wires through the slit.”^[20] This identification of the bundle of wires with the A-series and the views of them with the B-series is surprising. One would expect exactly the opposite. However, for Saltmarsh, the reason for identifying the bundle of wires with the A-series lies in free will: the changing location of the present in the A-series corresponds to the change in the separation between the wires that are rigid (the past) and those that might still be changed through free action (the future). The relative location of these positions themselves in the series (and their apprehension by the mind) is then understood using earlier-later relations.^[21] Unlike McTaggart, however, Saltmarsh clearly thinks that the A- and B-series are both equally real. In his views on McTaggart, therefore, we can again see Saltmarsh’s commitment to hypertime.

Saltmarsh’s writings only contain a tentative commitment to hypertime. Judging by today’s standards, we might really just have here a distinction between a series describing objective time and another series describing temporal experience. However, Saltmarsh’s bifurcation of these two series (whatever they apply to) ultimately led to a fully-fledged articulation of hypertime as we know it today. The next steps towards this took place in a widely-referenced discussion between C. D. Broad and H. H. Price about precognitions. This discussion, in which Broad tries to respond to some of the ontological problems with hypertime raised by Saltmarsh, is the topic of the next section.

5 Broad and Price

In 1937, Broad published a paper entitled “Philosophical Implications of Foreknowledge,” in which he responded to various objections against precognitions. The published text was immediately followed by a paper entitled “Philosophical Implications of Precognition” that records his discussion on the topic with H. H. Price. This second paper contains a sustained discussion of multi-dimensional time that became the focal point for an entire subsequent generation of philosophers exploring hypertime as a potential solution to precognitions.^[22]

H. H. Price (1889–1984) was Wykeham Professor of Logic at Oxford between 1935 and 1959. He published extensively on both philosophy (particularly philosophy of perception) and psychical research. He served as president of the Aristotelian Society (1945), the Mind Association (1945), and the Society for Psychical Research (1939 and 1960).

Broad’s first paper responds to three objections against precognitions: epistemic, causal, and fatalistic (Broad 1968, 188–194). The objection that motivates him to speculate on the possibility of multi-dimensional time is the causal one. The objection states that an event cannot have causal descendants until it has happened. Precognitions violate this since the precognized event causes the precognition that comes before it (Broad 1937, 190). Or in other words, precognitions seem to violate what Broad calls one of the ‘basic limiting principles,’ namely, the “general principle of causation […] [that] [i]t is self-evidently impossible that an event should begin to have any effects before it has happened” (Broad 1949, 293). It is this objection that motivates Broad to “go in off the deep end” (Broad 1937, 199) and to suggest the possibility of an additional time series, using an analogy with different directions on the compass:

A point which is east of another point may be either north of, or south of, or in the same latitude as the latter. Suppose that “east of” corresponds to “later than” in the only temporal dimension that we ordinarily recognize. And suppose that there were a second temporal dimension, and that “later than” in this dimension corresponds to “north of” in the case of points on the earth’s surface. Then an event which is “after” a certain other event, […] might be either “after” or “before” or “simultaneous with” this other event in the second temporal dimension which persons who accept a prehensive analysis of foreseeing would have to postulate. (Broad 1937, 200, emphasis original)

Broad, however, is skeptical as to whether this “fantastic suggestion” (Broad 1937, 203) should be accepted. He warns that “it ought not to be lightly admitted into society merely on the dubious claim to kinship with perfectly respectable hypotheses about additional spatial dimensions” (Broad 1937, 203) and that, after all, it “may be simply nonsensical” (Broad 1937, 203).

Price’s reply focuses almost exclusively on Broad’s suggestion of multi-dimensional time, “the most interesting and exciting part of his whole paper” (Broad and Price 1937, 214). Similarly to Saltmarsh’s specious-present suggestion, Price relativizes the meaning of ‘future’ to one particular temporal dimension. The precognized event is “not merely future. It is future in one dimension of time, but it is past in another” (Broad and Price 1937, 214). Although Price seems to be on the whole sympathetic to Broad’s suggestion, he raises a number of objections. One of the objections is that although two-dimensional time might be able to cope with the problem of the ordering of cause and effect, it does not seem particularly successful at explaining the exact nature of their relation:

Can we suppose that a future event emits a light ray which finds its way into my present eyes? To be sure, the event is past in the other dimension of Time. But can light rays travel in that dimension? […] [T]he suggestion seems very queer. (Broad and Price 1937, 218)

Price suggests his own solution to this problem. Perhaps we have to get rid of physical causation altogether. Perhaps the content of precognition is not the event itself, but the mental content of other people perceiving the event. In that case, telepathy might come to the rescue:

[W]e can now say that the pre-presentative datum is produced telepathically. Of course we don’t in the least understand what telepathic causation is. But there seems to be very strong evidence for the occurrence of telepathic causation, and there are at least some grounds for thinking it to be a purely psychical process, which does not involve the passage of any sort of physical radiation through space. And if once an extra dimension of time is introduced, it becomes possible that telepathy should occur between minds living in widely different periods of ordinary Time. (Broad and Price 1937, 218 emphasis original)

Notwithstanding this bizarre solution, the main problem that Price identifies in Broad’s suggestion concerns the ontology of the two-dimensional theory. This is the problem of ‘partial becoming’ that we already encountered in Saltmarsh:

I think [if we commit to two-dimensional time], we are also committed to the even more curious notion of Partial Becoming. Suppose that I precognize an event which is to occur next Saturday. In one respect this event has not yet come into being: it is still future, and does not yet exist. But in another respect it is past, and so has come into being. It is so to speak half-real; it has partially become but not wholly. When next Saturday arrives, but not before, it will receive its second instalment of being. (Broad and Price 1937, 224–225 emphasis original)

Broad conceded that he has no answer to the problem of ‘partial becoming’ (Broad and Price 1937, 240). Nevertheless, he expressed his hope that these problems might one day be resolved: “Prof. Price has shown that [two-dimensional time] would have such interesting applications, if only it could be made intelligible, that one is encouraged to try to make it so” (Broad and Price 1937, 239).^[23]

The problem of partial becoming already shows up in the correspondence with Saltmarsh leading up to Broad’s presentation of the paper. In a letter to Broad from March 11, 1933, Saltmarsh raises the question: “What happens when an event happens?”^[24] Supposing that the universe were completely determined (and its determinedness might allow us to precognize events), what ontological significance, Saltmarsh asks, can be attached to the claim that an event ‘happens’? In the letter, Saltmarsh suggests that ‘becoming’ should be analyzed by appealing to free will: it consists of the ‘rigidification’ of the wires in his earlier analogy. He thus seems to suggest a reductio: without free will, we would not be able to give meaning to temporal becoming. But we must be able to give meaning to temporal becoming. So there must be free will.

The discussion between Broad and Price (which he reviewed for the SPR; see Saltmarsh 1938b) and its suggestion of two-dimensional time also had a significant impact on Saltmarsh’s writings after 1937. In a letter to Broad from June 12, 1937, he mentions having read Broad’s “Philosophical Implications of Foreknowledge” and expresses his appreciation for the two-dimensional theory.^[25] He even writes that he had made a similar suggestion in a paper entitled “Ambiguities on the Question of Survival,” but that it was not accepted for publication in the Proceedings of the SPR or the Hibbert Journal.^[26] In the letter, Saltmarsh again re-articulates the problem of the ontological status of becoming that he had raised in his letter five years earlier.^[27]

The discussion between Broad and Price also made it into Saltmarsh’s Foreknowledge (Saltmarsh 1938a, 89–94), where he connects Broad’s analogy of different world directions with the postulation of a subliminal mind. Suppose we think of our ordinary time series as running from north to south and the additional time series as running from east to west. Saltmarsh says:

With one dimension we must think of an event as a line, having length but no breadth; with two dimensions, we may picture it as an area, having both length and breadth. […] Any area which lies in the sector from north to east will then be absolute future, i. e., future in both dimensions; an area in the sector from south to west will be absolute past; but in the sectors from south to east and from north to west, an area lying therein will be past in one dimension and future in another. […] [S]hould we gain subliminal knowledge of the westerly part of an area, lying in the north-west, it would appear to our normal consciousness as precognition, because the northerly dimension in it is our normal future. (Saltmarsh 1938a, 92–93)

The suggestion of multi-dimensional time, made by Broad, Price, and – first tentatively, later more explicitly – by Saltmarsh was very bold for its time. Most scholars active during this period assumed that if you postulate a single additional time series, an infinite series inevitably follows, just like it does in McTaggart’s argument or Dunne’s serialism. For example, Alexander Gunn, in one of the earliest reviews of Dunne’s book, states: “Any second time […] can only lead to the absurdities of an infinite regress of Times, a doctrine which vitiates Dunne’s book” (Gunn 1928, 74 emphasis original).

We have seen that Saltmarsh’s hypertime possibly confused time and temporal experience, and that Broad’s ‘fantastic suggestion’ ran into insuperable ontological problems. H. A. C. Dobbs, another one of Broad’s correspondents whose hypertime we turn to now, tackled both of these problems head-on.

6 Broad and Dobbs

The scholarly consensus is that Broad’s final theory of time is the one he presented in his 1938 Examination of McTaggart’s Philosophy.^[28] This theory seems to try to affirm both an absolute becoming of events and at the same time their eternalist existence. I have recently suggested (Moravec 2025a) that this commits Broad to a hypertime theory. In 1938, Broad’s commitment to hypertime was only implicit. However, in the years that followed the publication of his Examination, Broad became intensely occupied with further thoughts on multi-dimensional time and expressed its potential plausibility much more explicitly. The main evidence of this involvement is his correspondence with H. A. C. Dobbs, who boldly worked out a multidimensional theory in the late 1940s and early 1950s.

Henry Adrian Conway Dobbs (1914–1970), son of H. R. C. Dobbs (Foreign Secretary to the Government of India and later High Commissioner and Consul General for Iraq; see Wilks 2023), studied Moral Sciences at Trinity between 1933 and 1937.^[29] He spent most of his life working for the Colonial Office,^[30] after a lecturership in Colonial Administration at Oxford between 1945 and 1948,^[31] while publishing on psychical research and the philosophy of science, particularly on time and quantum mechanics (Dobbs 1971). Broad (1970, 394) indicates that he retired from the Colonial Service in 1957 and accepted a job offer “from an extremely ‘hush-hush’ branch of the British Government Service.” He joined the SPR in 1957 (Broad 1970, 396) and was involved in several parapsychological experiments the Society conducted in the 1960s.^[32] He gave the Tarner Lectures entitled ‘The Concept of Time’ at Trinity College in 1962 and corresponded with Broad on topics in science, time, and psychical research. The two “used to meet fairly often in Cambridge and have long talks” (Broad 1970, 396). Broad also published an obituary for Dobbs in the Journal of the SPR (Broad 1970) and the Broad papers at Trinity contain a horoscope that he made for him.^[33] Dobbs’ private office at his home contained key sources on psychical research, including Myers’ Human Personality and Its Survival of Bodily Death (1903) and books by J. B. Rhine.

Dobbs’ most influential contribution to the discussions about hypertime were two papers published in the British Journal for the Philosophy of Science, the first of which was published with a “logistic analysis of the two-fold time theory” by Broad (Dobbs and Broad 1951; Dobbs 1951). However, Dobbs already mentioned the idea that “there are 2 and not 1 time dimensions” in a letter from September 14, 1946 to the artist John Napper.^[34] The main aim of Dobbs’ paper is to “elucidate the phenomenon known in psychology as ‘the specious present,’ by postulating a two-dimensional theory of the extensional aspects of time” (Dobbs and Broad 1951, 122). His suggestion relies on the distinction between the ‘extensional’ and the ‘transitory’ aspect of time developed by Broad (1938, 267–277).^[35]

There are two aspects to every process in time, […]. The transitory aspect is the one involved in the general fact that any events which we can think of as happening at a certain particular time, must begin by being “future” […], then become “present” […], and finally become “past” […]. This aspect has also been called the “becoming” of events in time. It is clearly different from […] [t]he extensive or extensional aspect of time. […] This is the aspect representable graphically by means of stretches of points on lines, the positions of such points of time having an ordinary relationship describable in terms of the elementary relation “earlier (or later) than.” (Dobbs and Broad 1951, 129)

These two aspects of time correspond to two distinct time series:

Our assumption of a second time-dimension implies that there exists a second way of ordering the constituents of a temporal process, by means of a relation similar in structure to the relation of “before (or after)” or “earlier (or later) than.” The two time-orders thus generated would have the same complete logical independence, or mutual orthogonality, as the three extensive aspects of space-relations, commonly described by three orthogonal cartesian coordinate axes. (Dobbs and Broad 1951, 129–30)

Dobbs thinks that the reason why scholars have been reluctant to accept multi-dimensional time has been the tendency to accord both of its series the same metaphysical nature – that is, to assume that both series either have to have an extensional aspect, or that both have to have a transitory aspect.^[36] Dobbs specifically accuses Price’s response to Broad of having committed this confusion:

It has been supposed (for instance by Professor Price) that a two-dimensional theory of time must involve a twofold becoming of events; that is to say, a “double now.” […] Such a double-now conclusion rests essentially upon a confusion between the “extensive” aspects and the “becoming” aspects of time. Once the distinction is properly grasped, there is no […] reason to think that two separate fluxes of becoming must flow independently. (Dobbs 1951, 184)

With this machinery set up, Dobbs tries to explain how the two time series relate to each other in the specious present. Specifically:

[B]ecause two distinguishable event-phases, one of which precedes the other in phase-time, can yet be compresent in one speciously present moment of transition-time, we must clearly realise that a phase of an event can precede another phase in one dimension of time, while yet the two are compresent together in another time order.^[37] (Dobbs and Broad 1951, 132)

Although Dobbs’ paper mentions Price’s discussion, the two papers in the BJPS do not explicitly discuss the links between precognitions and hypertime. Nevertheless, the connection was made elsewhere. For example, C. W. K. Mundle (1916–1989), highly active in psychical research circles around the middle of the twentieth century, rejects Dobbs’ claim that the specious present requires the postulation of a second time series, but – referencing Broad and Price’s discussion (Mundle 1954b, 334–35; see also 1954a) – emphasizes that the main motivation for accepting two-dimensional time is that it can explain precognitions. The reason he gives is the same as the one that motivated Broad in the first place: the precognition might precede the precognized event in one dimension, but can be preceded (and caused by it) in another. Similarly, in “A Note on Multi-Dimensional Time,” C. T. K. Chari (1909–1993) explicitly links Dobbs’ theory with that of Dunne and Broad (Chari 1957, 155–156). Chari closes his article with the following sentence: “At a recent International Conference at St Paul de Vence, France, Pascual Jordan discussed the new trends in physics and said that the hypothesis of a multi-dimensional time is worth careful study” (Chari 1957, 158). Chari decided not to mention that the full title of the conference at St Paul de Vence was the International Parapsychology Conference and that Pascual Jordan (1902–1908) was particularly interested in the implications of physics for parapsychology.^[38] The links between Dobbs’ theory and psychical research are also emphasized in a critical discussion note by G. W. Scott Blair, who calls for further details about how Dobbs’ theory might help to explain precognitions, and explicitly states that multi-dimensional time originates with Dunne (Scott Blair 1952, 82–83).

More importantly, Dobbs himself later provided his explanation of how two-dimensional time explains precognitions. This appears in his extensive study “Time and Extrasensory Perception” published in the Proceedings of the SPR in 1965. The goal of the paper is to see “whether certain developments in the concept of Time in physics can help throw light on the concept of Precognition” (Dobbs 1965, 249). The paper develops a sophisticated theory of two-dimensional time and, combined with a theory of probability, applies it to the problem of precognitions involving mediums predicting whether a coin will fall heads or tails with a higher-than-expected probability.^[39]

A full exposition of Dobbs’ theory, which blends quantum mechanics with probability theory and psychical research, is beyond the limits of this paper, but what is note-worthy here is that Dobbs’ paper seems to be one of the first (with the exception of Dunne) to diagrammatically represent the two time series by two axes at right angles to each other, which later becomes the norm in discussions about two-dimensional time in the philosophy of time travel (see for example Meiland 1974, 158).^[40] This is radically different from the hypertime we get in Saltmarsh (where the two time series somehow run parallel to one another) or in Price’s discussion with Broad (which at least implicitly seems to assume the same). Dobbs, by contrast, emphasizes that the two lines need to be thought of as representing two different degrees of freedom with respect to the temporal coordinates of each event, since “there are now two degrees of freedom instead of one for the movement of the representative ‘now’” (Dobbs 1965, 279). Dobbs also thought that this could respond to the problem of partial becoming that troubled Broad and Price. According to Dobbs, “in a two-dimensional spatial model of the extensive aspects of time we have to represent the transitory aspect as the resultant locus of intersection of two lines” (Dobbs 1965, 280 emphasis original). Becoming can apply to both dimensions of time – if reality grows at the same rate on the x-axis as it does on the y-axis, then “the locus of P [the now-point] will be a straight line, bisecting the angle of 90 ° between the two time axes” (Dobbs 1965, 281). One can see how this might alleviate Price’s worry. If one thinks of the two dimensions of time as two parallel train tracks, each with its own ‘now’ represented by a train moving on it, then one cannot avoid thinking that the train on one of the tracks will have to re-reach a point that the train on one of the others has already reached. If, by contrast, the (single) now is understood as consisting of the intersection of two different temporal dimensions at right angles to each other, no such problem appears. Unlike Saltmarsh’s theory, which raises questions about the relationship between temporal experience and objective time, this is clearly hypertime proper.

Further evidence for sustained interest in hypertime by Broad and Dobbs can be found in two currently unpublished manuscripts by Dobbs and in correspondence with Broad on the content of these texts.

The first typescript is entitled Two-Fold Time, and sections of it formed the basis of the two BJPS papers. It was submitted for consideration by Cambridge University Press in 1950,^[41] though Dobbs had been working on it as early as 1945.^[42] He had earlier also sent it to Price,^[43] who, based on what Dobbs says in a letter to Broad from July 6, 1947, thought the manuscript was worthy of publication.^[44] In April 1951, the Press Syndicate considered reports on the manuscript by Broad and H. Dingle, pending advice by R. B. Braithwaite.^[45] On May 4, 1951, the Press decided not to publish the book, but to inform Dobbs that if he did not manage to find a publisher for it in the US, the Press would consider it again.^[46] The Press Syndicate Minute books also mention that in April 1953, the Press again declined to publish the book, on the report of E. Schrödinger.^[47] The typescript of Two-Fold Time currently only exists in one copy as part of the Adrian Dobbs Papers. Around eighty pages of Broad’s notes on it are available in the Broad Papers at Trinity College, and Dobbs repurposed some of its contents for publication in the two papers mentioned above.^[48]

Two-Fold Time applies the machinery of hypertime to explain various problems in physics and temporal experience, including the problem of the specious present and the “relativity time-paradox [which] entails that, for a large class of pairs of events, some observers would be justified in asserting that one event E1 say preceded another E2; whereas other observers […] would say they were simultaneous, and yet a third set of observers would be equally justified in affirming that E2 preceded E1” (Dobbs ‘Two-Fold Time,’ 2 emphasis original). In the very final pages of the typescript, where Dobbs extensively discusses Dunne’s serialism, he specifically mentions that one of the many applications of two-fold time (beyond its use in quantum mechanics and relativistic physics) is that it can explain “the so called ‘psi-phenomenon,’ the contents of para-normal perceptions” (Dobbs ‘Two-Fold Time,’ 169) and explains how Dunne’s theory can be re-interpreted in light of Dobbs’ two-dimensional theory. Dobbs explicitly says that “Dunne’s multi-dimensional time theory does provide a remarkably plausible explanation of ostensible precognitive experience, once his theory has been purged of its mistaken, infinitely regressive, postulation of an infinity of time dimensions” (Dobbs ‘Two-Fold Time,’ 171). The infinite regress, Dobbs thought, can be stopped in its tracks by keeping becoming out of the hypertime series and confining it to the normal time series.

An even wider application of two-dimensional time can be found in Dobbs’ 1962–1963 Tarner Lectures, The Concept of Time, the typescript of which is also contained in the Adrian Dobbs Papers. After Dobbs’ death in 1970, Broad (who died less than a year later), together with the psychical researcher Rosalind Heywood (see below) and Dobbs’ relatives were trying to get the manuscript published in Routledge. Unfortunately, despite positive peer-review reports, on April 18, 1974, Routledge decided not to publish the manuscript.^[49] The lectures further clarify some of Dobbs’ earlier considerations about multi-dimensional time in relation to topics as wide-ranging as “Circadian Rhythms in living structures” (Dobbs, ‘The Concept of Time,’ 408) and the “reversibility of time” (Dobbs, ‘The Concept of Time,’ 126).

The discussion about two-dimensional time between Dobbs and Broad continued into the late 1960s (they had been corresponding from as early as 1940). At the time of writing, around half of the letters are in the Broad Papers at Trinity College, the other half in the Adrian Dobbs Papers. These include numerous references to Broad’s discussion with Price,^[50] further suggestions that a two-dimensional theory of time might help with some additional problems of precognition,^[51] or discussions about the directions of time in each one of the two series,^[52] specifically whether time or causation run in the opposite direction “in the paranormal route.”^[53] In one of the letters Dobbs also discusses the possibility that time may run at different rates in the two dimensions and that some paranormal effects might require causes to travel faster than the speed of light.^[54] In a letter from April 26, 1966, Broad provided further comments on the two-dimensional theory he defended in his discussion with Price:

[A section of your paper] refers to a suggestion about 2-dimensional time (very different from yours) which I very tentatively put forward in Supplementary Vol. XV of the Proceedings of the Aristotelian Society. I shall not be concerned with this at present. What I am concerned with here is only the suggestions discussed by you [in ‘Time and Extrasensory perception’] on pp. 263–267. […] Now my latest thoughts on these lines have not as yet been published. They are contained in a typescript which I completed on June 6^th 1965, and sent to Mrs Heywood for a collection of essays which she is editing, and to which you also are, I believe, contributing.^[55] […] My suggestions certainly presuppose a conventional one-dimensional view of time; though, as you know from other writings of mine, I am in no way committed to that. You, of course, have various reasons, quite independent of my suggestions about ostensible precognition, for the particular form of 2-dimensional time-theory which you develop in your paper.^[56]

In a letter from January 28, 1967, Dobbs fittingly summarizes their earlier discussions about two-dimensional time thus:

It is interesting that some physicists are now becoming obsessed with questions about time and “meta-time” – clearly another dimension of time – as evidenced in Nature, Scientific American etc in recent months. I believe 2-dimensional time may be ‘respectable’ scientifically before we are dead.^[57]

This section has demonstrated a sustained interest by Broad and Dobbs in hypertime that goes beyond what is considered to be Broad’s final theory of time in the Examination. The aim of the following section is to show that many of the problems that troubled philosophers interested in psychical research anticipate later questions in the philosophy of time to which hypertime is supposed to be a solution.

7 Flow and Time Travel

Broad, Saltmarsh, Price, and Dobbs were some of the first thinkers to have introduced the idea of multi-dimensional time into analytic philosophy. They have done so despite McTaggart’s skepticism about multiple time series and despite a general academic skepticism about Dunne, who became associated with them. This section aims to show that two key concerns of contemporary philosophy of time were anticipated by discussions about precognitions in psychical research. The first are discussions about the flow of time. The second are discussions about time travel.

Hypertime has usually been associated with discussions about the ‘flow’ of time. In his seminal “River of Time,” J. C. Smart argues against the idea that time flows:

[J]ust as we thought of the first time-dimension as a stream, so will we want to think of the second time-dimension as a stream also; now the speed of flow of the second stream is a rate of change with respect to a third time-dimension, and so we can go on indefinitely postulating fresh streams without being any better satisfied. (Smart 1949, 484)

One of the recent solutions to the problem of the rate of passage has been offered by Baron and Lin (2022), who argue that the problem of an infinite regress of dimensions is a result of the desire that either both time and hypertime have an A-theoretical structure or that they both have B-theoretical structure. Their model, which combines A-theoretical structure in one series and B-theoretical structure in the other, solves this problem. I have recently argued that their proposed model is identical to the two-dimensional time suggested by Broad and Price (Moravec 2025a). However, the connections between the flow of time and hypertime already existed in the psychical research circles that this paper has been looking at. One of the objections that Smart’s seminal paper poses against the claim that time ‘flows’ is that it invites questions about the rate at which it flows:

A connected point is this: with respect to motion in space it is always possible to ask “how fast is it?”. […] Contrast the pseudo-question “how fast am I advancing through time?” or “How fast did time flow yesterday?”. We do not know how we ought to set about answering it. What sort of measurements ought we to make? We do not even know the sort of units in which our answer should be expressed. (Smart 1949, 485)

But, as we saw earlier, the rate-of-passage objection had already been voiced by Saltmarsh nearly twenty years earlier and directed specifically against Dunne’s serialism, whose view, after all, is also briefly mentioned by Smart (1949, 483) himself.

The second area from which discussions of hypertime are typically seen as having originated is the philosophy of time travel. Goddu (2003, 25 n10), who defends a hypertime model of time travel, references Chari’s discussion of Dobbs’ multi-dimensional time. Around thirty years prior, Lewis (1976, 151) mentioned precognitions in his seminal “Paradoxes of Time Travel,” which rejected Meiland’s multi-dimensional time.^[58] But the links between psychical research discussions, hypertime, and time travel go much deeper. H. G. Wells, whose Time Machine was widely referenced by philosophers engaged in time travel discussions in the 1970s, was a close friend of Dunne.^[59] Dunne’s An Experiment with Time (Dunne 1927, 106–108) itself referenced Wells’ Time Machine and the links between Wells and Dunne (as well as Abbott, the author of Flatland) have been noted (see White 2018, 15–68, 169–196). Price’s suggestion of multi-dimensional time also mentions Wells’ Time Machine in the context of precognitions (Broad and Price 1937, 227) and Wellsian time travel was used as a paradigm by D. C. Williams (Williams 1951, 463), who elsewhere referenced Broad’s work on Dunne (Williams 2018, 151–153). Lewis’ earlier-mentioned “Paradoxes of Time Travel” tried to offer an account of time travel narratives that would not have to resort to multi-dimensional time. In that process, Lewis rejects the model developed by Meiland’s 1974 paper “A Two-Dimensional Passage Model of Time for Time Travel,” which offers an account of time nearly identical to the one we find in Broad and Price, namely, a “multi-dimensional theory of time […] as compared with the usual one-dimensional theory which represents time along a straight line” (Meiland 1974, 159). The diagrams Meiland uses, which draw the two time axes at right angles to each other, are structurally identical to those that first appear in Dobbs.

Before addressing the implications of these similarities, it is worth briefly noting that there even exists an interesting genealogy linking the earlier-devised solutions to the problem of causation in precognitions and in time travel. Antony Flew – who was also actively engaging with psychical research (Moravec 2025b) – addressed the question of backward causation in a symposium with Michael Dummett in 1954 and in his paper on Broad’s views on precognitions (Flew 1959, 433). Both Flew and Dummett mention precognitions in their discussion (Flew and Dummett 1954, 43, 45, 61–62; see also Black 1956, 52, 54–55) and the symposium is later referenced by Brier (1973), previously a research fellow at the Institute for Parapsychology at Duke University. Dummett’s seminal “Bringing About the Past” (1964), which draws on the earlier discussion with Flew, is then taken up by a number of canonical papers addressing the possibility of time travel.^[60]

8 Conclusion

The cases of the flow of time and time travel demonstrate two important lessons about psychical research for the history of twentieth-century philosophy of time.

First, insufficient attention to the role that psychical research played in twentieth-century British philosophy has created a misleading impression about Broad’s views on hypertime. Broad’s inference that the idea of a ‘flow’ of time leads to an infinite regress is frequently cited as an argument against hypertime (see, e. g., Baron and Lin 2022, 263). But the authors who use Broad in this way generally appeal to his critique of the moving-spotlight theory in Scientific Thought (Broad 1923, 59–60) or the claim that treating absolute becoming purely as a species of qualitative change leads to infinite regress made in the Examination (Broad 1938, 279–281). But, as we saw, paying attention to his later philosophy reveals much more sympathetic views about hypertime. A good example of this is his “Reply to My Critics” (1959) where he discusses “the theory of 2-dimensional Time” with a particular reference to the version which “has been put forward and argued in detail by my friend and former pupil, Mr. H. A. C. Dobbs” (Broad 1959a, 769). He specifically says that the theory of the specious present he defended in the Examination “becomes considerably clearer when stated in terms of 2-dimensional Time” (Broad 1959a, 772). Broad’s later, less dismissive views about hypertime were firmly rooted in his commitment to precognitions and predate the use of multi-dimensional time in discussions about the flow of time and time travel by several decades.

Second, contemporary metaphysicians should pay more attention to discussions about time in psychical research during this period. Many of the theories that dealt with ‘spooky’ problems and that derived from discredited evidence for precognitive events, were developed by leading philosophers of the time and might well be valuable in their own right, regardless of what they were originally designed to do. As we saw earlier, the models of multi-dimensional time developed by Broad and others, for example, were structurally identical to those in much more recent solutions to problems with the flow of time and in debates around time travel. They would probably have entered mainstream philosophy much sooner, had they not been articulated within the context of psychical research.^[61]

In some cases, there even appears to have been a conscious attempt to brush these discussions under the carpet. For example, Chapter 10 of the first edition of Swinburne’s influential Space and Time (1968) recommends the Broad and Price discussion for readers interested in the possibility of two-dimensional time (Swinburne 1968, 211). However, in the second edition from 1981, in the same place, the reference to Broad and Price has been erased, and Swinburne (1981, 175) instead instructs the reader interested in two-dimensional time to look at Quinton’s ‘Spaces and Times’ and § 7 of Lucas’ A Treatise on Time and Space. Scholarly as those two sources might be, many of the suggestions (e. g., about causation) that troubled Broad and his correspondents cannot be found in them.