Abstract
Here I examine the issue of the spatialization of time, attempts to construe becoming in terms of a “moving now” or of changing relations to the ‘now’, and the “block universe” interpretations. I argue that McTaggart’s “A theory” and Russell’s rival “static” or “B theory” of time fail because they presuppose a time in which temporal relations could either change or stay the same.
World history consists of actual concrete happenings in a temporal sequence; it is not necessary or possible that happening should happen to them all over again.
— D. C. Williams (1951, 464).
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Notes
- 1.
For an succinct treatment of Whitehead’s philosophy of time , see (Hurley 1986).
- 2.
- 3.
In reporting this I do not mean to dismiss Hinton as some crank. Among the many merits of his book is his insightful discussion of rotations in higher dimensions. After a certain rotation in 4-space, he writes, “The dimension which appeared as duration before will become extension in one of our known dimensions, and a dimension which coincided with one of our space dimensions will appear as duration .” (Hinton 1887, 241). This is a remarkable anticipation of Hawking’s hypothesis of imaginary time, if we make due allowance for the fact that, in Minkowski spacetime, the signature of the four-dimensional metric is such that what is on a par with a dimension of space is time multiplied by the imaginary number i. Hawking hypothesized that the problem of the origin of the universe in time could be dissolved by allowing that the (imaginary) time dimension rotates to become a dimension of space as we extrapolate back to the beginning of the universe. See Hawking (1988, 136–141). This idea spatializes time in precisely the sense that Bergson criticized.
- 4.
Actually, in connection with the fourth dimension Wells specifically mentions Simon Newcomb (Wells 2001, 61), rather than Hinton. But as discussed by Nicholas Ruddick in his introduction to his edition of The Time Machine (Wells 2001, 22–24), Wells was indebted to Hinton’s essay for some of his ideas, as were both of them to Edwin A. Abbott’s Flatland (1884).
- 5.
- 6.
This criticism evokes, curiously, a similar criticism that Russell made of Bergson: “The whole of Bergson’s theory of duration and time rests throughout on the elementary confusion between the present occurrence of a recollection and the past occurrence which is recollected.” (Russell 1912, 342).
- 7.
The same point about Wellsian time travel was made eloquently by D. C. Williams: “Time travel, then, is analyzable either as the banality that at each different moment we occupy a different moment from the one we occupied before, or the contradiction that at each different moment we occupy a different moment from the one which we are then occupying—that five minutes from now, for example, I may be a hundred years from now ” (Williams 1951, 463).
- 8.
As David Wright has reminded me (private communication), Wells’s Traveller does return to the relative past from the far future of the blood-red dying sun, and would have fallen headlong into this paradox of changing the past if he had made good on his intention on the way back to save Weena from the Morlocks.
- 9.
- 10.
“It was the analysis of the notion of time as that enters into mechanics and physics,” he is quoted as saying, “which overturned all my ideas. I saw, to my great astonishment, that scientific time does not endure. This led me to change my point of view completely” (Encyc. Brit. article on Bergson).
- 11.
Cf. Bergson’s criticism of associationism, which “requires that each psychical state should be a kind of atom, a simple element.” (Bergson 1913, 172): “The capital error of associationism is that it substitutes for this continuity of becoming, which is the living reality, a discontinuous multiplicity of elements, inert and juxtaposed.” (171).
- 12.
“Motion is the occupation, by one entity, of a continuous series of places at a continuous series of times” (Russell 1903, §442, 469) .
- 13.
To be pedantic, the infinity of frames between any two must be a non-denumerable one, on Cantor’s account, otherwise this will only yield the property of denseness , and not full mathematical continuity.
- 14.
Despite his agreement with much of what Bergson says about time as rooted in lived experience, Whitehead agrees with Russell in this criticism: “in so far as Bergson ascribes the ‘spatialization’ of the worlds to a distortion introduced by the intellect, he is in error. This spatialization is a real factor in the physical constitution of every actual occasion belonging to the life history of an enduring physical object .” (Whitehead 1930, 489).
- 15.
Cf. Bergson: “But suppose now that this homogeneous space is not logically anterior, but posterior, to material things and to the pure knowledge which we can have of them; … suppose that homogeneous space concerns our action and only our action, being like an infinitely fine network which we stretch beneath material continuity in order to render ourselves masters of it, to decompose it according to the plan of our activities and our needs.” (1913, 307–8). I am much indebted to my colleague Barry Allen both for this reference and for correcting some misconceptions I had of Bergson’s views.
- 16.
Steven Savitt has made the same objection. Anyone asking where change is represented on a spacetime diagram “is confusing a static representation with a representation of stasis.” (Savitt 2002, 162–3). Cf. Lee Smolin : “the fallacy of the spatialization of time … is a consequence of forgetting the distinction between recording motion in time and time itself.” (Smolin 2013, 35).
- 17.
Here again I am indebted to Barry Allen for his sage advice on Bergson.
- 18.
Although Dunne is explicit in acknowledging his sources, he does not mention the idealist philosopher Bradley. But according to McTaggart (he does not give references), “The second objection is based on the possibility, discussed by Mr. Bradley, that there might be several independent time series in reality. For Mr. Bradley, indeed, time is only appearance. There is no real time at all, and therefore there are not several real series of time. But the hypothesis here is that there should be within reality several real and independent time-series .” (McTaggart 1908, 466).
- 19.
There’s a potential for some confusion here. By “serial time” Dunne means his infinitely regressing series of time dimensions. This should not be confused with the “serial order” of events in time (referred to, for example, by Russell) . This is what is now usually called a “strict total ordering”, denoting a relation that is asymmetric, transitive, and simply connexive; that is, for any three events x, y and z, if x is before y then y is not before x; if x is before y and y before z, then x is before z; and if x and y are different events, one is before the other. As we shall see in Chap. 6, this last property does not hold for point-events “being in the absolute past of” one another in special relativity, which is instead a strict partial ordering.
- 20.
Notably, however, even (bosonic) String Theory, with its posited 25 dimensions of space, still has only one of time.
- 21.
The notion of indexicality was introduced by Charles Sanders Peirce (see the term ‘Index’ in the Digital Companion to C. S. Peirce at http://www.commens.org/dictionary/term/index); the notion of token-reflexiveness is due to Reichenbach (see the Oxford Reference under ‘token-reflexive’: http://www.oxfordreference.com/view/10.1093/oi/authority.20110803104818996).
- 22.
“For in order to get change,” McTaggart argues, “and change in a given direction, it is sufficient that one position in the C series should be Present, to the exclusion of all others, and that this characteristic of presentness should pass along the series in such a way that all positions on the one side of the Present have been present, and all positions on the other side of it will be present ” (McTaggart 1927, 463).
- 23.
McTaggart’s contention that events in his ‘C’ series are “permanent” is also objectionable, since again this would require a time in which they would remain the same, contrary to the alleged timelessness of the series. If these events are not ordered in temporal succession, moreover, it is impossible to see what their order is supposed to consist in.
- 24.
Here one might argue that, once passage is denied, there is equally no basis for the asymmetric ordering McTaggart supposes for his C series. If a given event a comes after another b, then b cannot come after a. This gives an asymmetric ordering. But if events are just ‘at’ their positions in time, as Russell and McTaggart assume, then we simply have a set of events with no natural ordering, not an asymmetric ordering with two different senses. I will return to this issue in Chap. 4.
- 25.
The Hegelians had rejected the reality of number, space, time and matter on the grounds that they were internal relations, and therefore contradictory. Rejecting such relationalism at the turn of the century, Russell came to believe in a direct realism, where all relata exist along with external relations among them. “I began to believe everything the Hegelians disbelieved,” he reports. “This gave me a very full universe. I imagined all the numbers sitting in a row in a Platonic heaven. I thought that points of space and instants of time were actually existing entities …” (Russell 1959, 48) .
- 26.
Although I attribute this to Russell’s and McTaggart’s baptism in Hegelianism, there are many thinkers who are by no means Hegelians who think it natural to regard events as existing independently of their becoming. Thus A. N. Prior (1968, 1–2) refers to the “becoming ever more past” of events, and Norton (2010, 24) writes that future events “become present” and then “drift off into the past”, as Oliver Pooley notes (2013, 322). Although Pooley defends the objective passage of time, he endorses this conception of passage, claiming that it is a key challenge for the B theory to explain “why we are inclined to take the ‘becoming more past’ of events as an objective feature of reality” (Pooley 2013, 326) .
- 27.
Cf. Russell on Bergson: “His whole doctrine of time is necessary for his vindication of freedom, for his escape from what William James called a ‘block universe’, for his doctrine of a perpetual flux in which there is nothing that flows” (Russell 1912, 34) .
- 28.
An explicit version of this argument is given by Craig Callender, in the course of criticizing so called “hybrid theories”: “Because [upholders of] hybrid theories accept that a four-manifold is the arena of world history, they cannot—on pain of incoherency—analyze becoming in terms of the coming into existence of events. It simply doesn’t make sense to say an existent event comes into being ” (Callender 2000, S590). As Steven Savitt observes, however, it is perfectly coherent for an event to exist in the spacetime manifold (as “eternalists” insist) and yet “to occur at its allotted instant” or now, as the presentists insist (Savitt 2006, 126).
- 29.
I believe it can be seriously questioned whether the ‘is’ in ‘7 is prime’ is an ‘is’ of existence. It appears rather to be an ‘is’ of predication, which does not occur in a language like Kiswahili. But I am allowing it here on the principle of charity. It is usually referred to as connoting “tenseless existence”, on which more below. Savitt (2006) also explores other possible meanings of ‘is’, including the “detensed” ‘is’, where “x Is Φ” means “x either was, is or will be Φ”.
- 30.
This formulation, it seems to me, is fully in keeping with what Nerlich wants to say about the reality of spacetime and spacetime structure. See Nerlich (1994, 40ff).
- 31.
“If N is ever earlier than O and later than M, it will always be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent .” (McTaggart 1908, 96); “every term is eternal, timeless, and immutable; the relations it may have to parts of time are equally immutable” (Russell 1903, 471) .
- 32.
- 33.
I take the view that if ‘is’ or ‘exists’ is being used atemporally, then it is a confusion to add a temporal qualification such as “at time t”, a qualification which only makes sense for a temporal sense of ‘exists’. Steve Savitt (personal correspondence) reports that this was the view of A. N. Prior regarding verbs used tenselessly, such as saying an event is to take place tomorrow: “What place can a word like ‘tomorrow’ have in a strictly tenseless form?” Savitt himself allows such temporal qualification of tenseless verbs.
- 34.
Cf. Kent Gustavsson, summarizing Broad’s views in this period: “Temporal passage is the continual growth of the sum total of existence ” (Gustavsson 2014).
- 35.
Ellis proposes an “Evolving Block Universe”, “a spacetime which grows and incorporates ever more events, ‘concretizing’ as time evolves along each world line” (2014, 5). He conceives the present time as “that instant along our world line where at this moment the indefiniteness of the future changes to the definiteness of the past. It continually moves to the future, incorporating ever more spacetime events as time passes” (5). Similarly, Muller claims that “the explosion of the universe continuously creates not only new space but new time. The forefront expanding edge of time is what we refer to as now, and the flow of time is the continual creation of new nows” (Muller 2016, 10). “The future does not yet exist…; it is being created. … Every moment, the universe gets a little bigger, and there is a little more time, and it is this leading edge of time that we refer to as now. … Now is at the boundary, the shock front, the new time that is coming from nothing, the leading edge of time” (2016, 293). I am indebted to David Wright for bringing Muller’s work to my attention, and for discussing it with me in correspondence.
- 36.
Barry Allen takes exception to this criticism. He contends that Bergson “does not even implicitly assume a universal now”, so that there is nothing in Bergson’s views on becoming that would commit him to the view “that becoming is not local, or that it is a single simultaneous wave front rolling across the universe” (private communication).
- 37.
“All actual events, experiences and intuitions must be there in the block representation, exactly at the spacetime position where they actually occur. … More generally, since all actual events in the history of the universe are faithfully represented, with all their characteristics and mutual relations, there cannot be anything missing in the four-dimensional picture at all.” (Dieks 2006, 169). Tim Maudlin has expressed a similar view about the compatibility of the block and real temporal passage: “Insofar as belief in the reality of the past and the future constitutes a belief in a ‘block universe’, I believe in a block universe. But I also believe that time passes, and see no contradiction or tension between these views .” (Maudlin 2002, 260).
- 38.
This is similar to Whitehead’s notion of the “passage of nature”: “The passage of the cause into the effect is the cumulative character of time. The irreversibility of time depends on this character .” (Whitehead 1920, 237). But as Hurley notes (Hurley 1986, 96), there is an idealistic underpinning in Whitehead’s thinking about time indicated by such statements as “Nature is nothing else than the deliverance of sense awareness” (1920, 185).
- 39.
Grünbaum acknowledges this debt, allowing that this distinction probably has its origin Bertrand Russell’s claim that “past, present and future arise from time-relations of subject and object, while earlier and later arise from time-relations of object and object ” (Grünbaum 1971, 215–216).
- 40.
This denial of the now in physics can be quite ironic. In his About Time (1995), Paul Davies subscribes to the block universe view (in version 1), which depicts the ‘now’ as purely subjective. Yet he provides diagrams on pp. 133, 221, and 260 on which the ‘now’ is explicitly marked! (It has to be, of course, in order to discuss whether the universe began 14 bya.).
- 41.
Cf. also “This genetic passage from phase to phase is not in physical time ” (Whitehead 1930, 434).
- 42.
Whitehead’s ideas about the relation of time to consciousness are very convoluted; relations of succession are ultimately rooted in “feelings of causal efficacy”, but the extensive aspect of such relations treated in physics requires the existence of fully conscious beings . See (Whitehead 1930, esp. 373–390); for analysis , see (Hurley 1986, 102–3).
- 43.
“Si el tiempo es un proceso mental, ¿cómo lo pueden compartir miles de hombres, o aun dos hombres distintos?” (Borges 1997, I, 418).
- 44.
Weyl makes a similar point: “The point-nature of the Now within the time continuum raises a certain difficulty within the conception of metaphysical time, for within a continuum , a point, without the neighborhood through which it is bound to the whole continuum , is not capable of existence. A point in a continuum is not an element of a set, but rather an ideal boundary of continuous partitions.” (Weyl 2009, 32–33).
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Arthur, R.T.W. (2019). Modern Objections to Time’s Passage. In: The Reality of Time Flow. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-15948-1_3
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