The Atlas of Reality
Page 77
The strongest argument against Tooley's version of special relativity is the conspiracy-of-silence objection raised by Elie Zahar in an exchange with J.L. Mackie (Zahar 1983). Zahar argues that the non-standard interpretation requires an unlikely coincidence, namely, that the laws of nature are fine-tuned to ensure that the actually privileged frame of reference is empirically undetectable. This sort of claim introduces some thorny issues, in particular, the question of whether it makes sense to assign some sort of prior probability measure to alternative laws of nature, a measure that can be used to assign a very low-probability to conspiracy-of-silence coincidences. On some views, the laws of nature are metaphysically necessary, in which case it can be difficult to assign the actual laws a probability other than 1. However, the appeal to coincidence is a compelling one, as it is in the case of anthropic coincidences, so this is merely a challenge to the probability theorist to come up with a model of the cogency of the reasoning.
A better response is the one offered by Tooley, who argues that it is special relativity itself, and not the non-standard interpretation, that is the true source of the conspiracy-of-silence coincidences. On the standard interpretation of special relativity, there is no way to measure the one-way velocity of light. It is merely a stipulation, and not an observable result, that the speed of light in one direction is the same as its speed in the opposite direction. Thus, the Lorentz transformations themselves seem to support a kind of conspiracy, even without the assumption of a privileged frame.
Our knowledge of physics isn't sufficient to adjudicate this dispute. We're inclined to guess that the undetectability of any privileged frame does count against the existence of such a privileged frame, even without relying on any dubious kind of verificationism.
In addition, there is another problem with the view that there is an empirically undetectable privileged frame, one pointed out (in conversation) by Brian Cutter. If there is a metaphysically privileged frame of reference, we are probably moving relative to it. A body's true shape would be its shape and size relative to the privileged frame. A high velocity relative to that frame would cause a contraction of length along the axis of absolute motion, according to the Lorentzian transformations. So, if there is a hidden frame and we are moving at a significant velocity in relation to that frame, then we are systematically misperceiving the true shapes of things. This argument assumes, plausibly, that shape is something intrinsic to bodies, and not a relation to frames of reference, together with the Reliable Perception Presumption (PEpist 4).
There is another tack Tensers can take: a minimalist accommodation of special relativity to the demands of Tensism. Tensers might simply stipulate that, in addition to the frame-relative relations of physical simultaneity, there is a frame-independent relation of metaphysical simultaneity representing those events that belong or have belonged to a common present. The metaphysical relation partitions spacetime into a set of three-dimensional hypersurfaces; each represents a single moment of real, metaphysical time. Physical simultaneity relations do impose a constraint on this partition: each hypersurface must consist of events that are pairwise space-like separated. That is, for each pair, there must be some frame relative to which they are physically simultaneous. However, we need not assume that this gives a privileged frame of reference. It may be that none of the hypersurfaces consists of events that are all physically simultaneous relative to a single, privileged frame of reference. (Note the shift in quantifier scope: for every pair, there is a frame relative to which they are physically simultaneous, but there may be no frame relative to which all such pairs are physically simultaneous.)
The minimalist view avoids the conspiracy-of-silence objection, since it does not privilege any particular frame. It is ontologically more economical, since it posits only a new binary relation and not the existence of a substantival space. It remains true that the relation of metaphysical simultaneity is empirically transcendent. There is no way to verify empirically that two space-like separated events are or are not metaphysically simultaneous. But this isn't surprising, since unless we're verificationists, there is no reason to suppose a priori that every fact must be empirically discoverable. In fact, there's every reason to suppose that a great many facts are empirically inaccessible to us.
Before leaving the topic, let's consider briefly the possibility of embracing both Tensism and the standard interpretation of relativity (without any kind of absolute simultaneity). Storrs McCall (1976) recommends doing so. On McCall's view, there is a unique, metaphysically privileged present moment, but which facts belong to that unique moment is a matter relative to one's frame of reference at that time. Let's suppose that our current frame of reference makes a particular event E on Alpha Centauri present. Event E1 occurs on the worldline of a particle p that is moving rapidly relative to our frame of reference. Let's call our frame F1 and the frame of p F2. Relative to F2, some event on E2 Earth in 2009 is part of the present moment. So, whether reality includes E2 is relative to one's frame of reference: it is real relative to F2 and unreal relative to F1. This position seems dialectically unstable. If we are willing to embrace such radical perspectivalism, why not embrace a view according to which which moment is present is also a matter of one's perspective? That is, why not simply embrace the Anti-Tensism?
This is bad enough, but things get worse. Suppose that we now accelerate from F1 to F2. Since E2 lies in our absolute future, it is impossible for it to become part of our present. Instead, what happens is that our present shifts in such a way that it no longer includes E in Alpha Centauri, instead including events there that occurred years before E1. In other words, by accelerating, we have changed the status of E1 from real to unreal. (McCall admits this on p. 352.) On McCall's model, branches that had fallen off are grafted back on again (or more precisely, the substance of the intact branches shifts in such a way that events that had fallen off are pushed back onto extant branches). This strikes us as crazy and as incompatible with the motivation behind Tensism.
21.4 Epistemological Problems for Tensism
We turn now to three epistemological problems for Tensism.
21.4.1 Does anybody really know what time it is?
The first epistemological objection is easiest to appreciate for Growing Block Tensism. Growing Block Tensers maintain that the past and present are real, while the future is not. The epistemological problem is that this view seems incompatible with knowing that one is experiencing the present moment. Past moments, and hence past experiences and thoughts, are just as real on this view as the present. How can one be sure that one is not living in the past, possibly billions of years in the past, at a great temporal distance from the real present moment? All of one's experiences are just as real and just as vivid, even if one were living entirely in the distant past. There are far more people living in the past than on the cutting edge of reality. Hence, we are all far more likely to be deluded than to be well informed about our temporal location. A similar problem faces Simple Tensism, with its moving spotlight of presentness. What does presentness look or feel like? How do I know that this moment, the moment of this very experience or thought, really has this mysterious property of presentness?
This objection doesn't work against Presentism, since there are no past people to be deluded on that view. If one knows that one exists at all, one knows that one exists in the present.
The situation is not so clear with respect to the Modal versions of Tensism, such as Falling Branches Tensism. We might suppose that we have some direct knowledge, through our awareness of our own free will, for example, that times immediately after this time are open, and that all earlier times are fixed. If so, this knowledge would provide us with the information we need to locate ourselves at the juncture of the present.
21.4.2 Everything we see is unreal
A second objection is directed specifically at Presentism. If Presentism is true, then we never perceive a real event, and many of the objects we see are non-existent, since sensory perce
ption takes time. What I perceive now is in fact the state of the world a few milliseconds in the past. The events and many of the entities (photons and so on) that existed then no longer exist now. Hence, much if not most of what we perceive is a kind of illusion. This would seem to undermine the reliability and trustworthiness of our senses, since they present their objects as really existing.
21.4.3 The problem of induction
As Alexander Pruss (2010) has pointed out, the problem of using past and present evidence to predict the future is more acute for Tensers, since the future represents a fundamentally different domain of reality. We know of many cases of sulfur samples burning with yellow flame, but all of these instances are located in either the past or the present. If the future is fundamentally different in nature, what grounds do we have for thinking that samples of sulfur will burn yellow in the future? Consider two hypotheses:
(8) Every sample of sulfur has burned yellow in the past.
(9) Every sample of sulfur has burned yellow in the past, is burning yellow now, and will be burning yellow in the future.
For Tensers, (9) is more complex than (8). Hence, we should prefer (8), but that's obviously a crazy result since we want induction to extend into the future. This problem largely disappears for Anti-Tensers, since they believe the past, present, and future are intrinsically indistinguishable, differing only in their relations to a present observer.
21.5 McTaggart's Paradox
Here is an attempt to reconstruct McTaggart's famous (or infamous) argument for the self-contradictory nature of the A series:
The A series is real. (Hypothesis for reductio ad absurdum)
If the A series is real, then there are three temporal statuses: past, present, and future.
If these three statuses exist, then it is necessarily the case that every event has* all three statuses. [What sort of ‘having’ is involved here is the crucial question.]
It is impossible to have* all three statuses, unless the compossibility of doing so can be explained by and so is dependent on the fact that it is possible to have* the three statuses at different times.
The fact that it is possible to have* the three statuses at different times is identical to the fact that it is possible to have* each of the following three meta- statuses: having* the status of being past in the present and future (and very near past), having* the status of being present in the more distant past, and having* the status of being future in the still more distant past,
having* the status of being past in the future, having* the status of being present in the present, and having* the status of being future in the past,
having* the status of being future in the past and present (and very near future), having* the status of being present in the more distant future, and having* the status of being past in the still more distant future.
The three meta-statuses are identical to the three statuses, i.e., having* (i) = having* the status of being past, having* (ii) = having* the status of being present, and having* (iii) = having* the status of being future.
Hence, if the three statuses exist, then it is necessarily the case that every event has* all three meta-statuses. (From 3, 6, and Leibniz's law)
It is impossible to have* all three meta-statuses, unless the compossibility of doing so can be explained by the fact that it is possible to have the three statuses at different times. (From 4, 6, and Leibniz's law)
Explanation is a transitive and irreflexive relation of facts.
If it is possible to have* all three meta-statuses, then the fact that it is compossible to have* all three meta-statuses is explained by the fact that it is compossible to have* all three meta-statuses. (From 8, 5, and Leibniz's law)
The fact that it is compossible to have* all three meta-statuses is not explained by the fact that it is compossible to have* all three meta-statuses. (From 9)
It is not possible to have* all three meta-statuses. (From 10 and 11)
It is not possible to have* all three statuses. (From 12, 6, and Leibniz's law)
The A series is not real. (From 13, 2, and 3)
From the point of view of Tensers, the weak points in the argument are steps 3 and 4. On Tensism, there is nothing problematic about one moment of time having each of the three statuses, once we distinguish having from having had and from going to have. The use of past and future tense insulates the predication of the three statuses from contradicting one another, and no further explanation in terms of meta-statuses is needed.
McTaggart would respond by claiming that he cannot understand how tense performs this logical magic, except in terms of the three meta-statuses introduced in step 5, and that this explanation ultimately fails, as the rest of the argument demonstrates. We leave it to the reader to discern whether he or she can understand what McTaggart could not.
21.6 Brute Necessities of Time
However the truthmakers of past-tensed and future-tensed truths are supposed to be, there are certain necessary connections among times that need to be explained. For example, consider the following:
(10) If p, then it once was the case that it would be (or at least, might be) the case that p. (If p, then PFp.)
(11) If p, then it will be the case that it once was the case that p. (Symbolically: if p, then FPp.)
(12) If it will be the case that it will be the case that p, then it will be the case that p. (If FFp, then Fp.)
(13) If it was the case that it was the case that p, then it was the case that p. (If PPp, then Pp.)
Anti-Tensers have relatively little difficulty in explaining these. They have to suppose that spacetime is so structured that events can be put in linear time-like relations of before and after. If so, to say that p entails FPp simply means that there is a time index later than the one by which one's assertion is being evaluated: from the perspective of that later index, the current index is in the past. Similarly, to say that p entails PFp is simply to say that there is an index earlier than the one used to evaluate the assertion. The necessity of (12) and (13) can be explained so long as earlier-than and later-than are transitive.
Anti-Tensers will need some explanation of the direction of time. What makes some events later than others, rather than earlier? Why are causal relations lined up, at least for the most part, with time, in such a way that causes are typically earlier than. or at least no later than, their effects? We will take up some of these questions again in Chapter 27.
Explaining these necessities seems to be something of a challenge for Tensers, however. Let's take them in reverse order. Tensers might be able to argue that (12) and (13) are merely verbal necessities, and so are true by definition. Perhaps the fundamental properties of events in terms of which we define past and future are not such as to make (12) and (13) true, but we make use of defined notions of pastness and futurity such that (12) and (13) are trivially true. In other words, if we define ‘future’ in terms of being future* or future* in the future*, or future* in the future* in the future*, and so on (where ‘future*’ is the metaphysically primitive property), then (12) will come out as true by definition.
Let's turn then to (10) and (11). First of all, it is not obvious that these propositions are universally and necessarily true. Suppose, for example, that time had a beginning (something for which we found some support in Chapter 19). In the first moment of time, (10) would be false, since it would have been false then that anything had already been the case. Similarly, if there should be a last moment of time, (11) would be false. Let's take care of this possibility by introducing the sentences ‘PT’ and ‘FT’, where ‘T’ is supposed to represent some tautology (like ‘0=0’). Let's suppose that ‘PT’ is true just in case there has been some past time, and ‘FT’ is true just in case there will be future times. Consider (10*) and (11*):
(10*) If p and PT, then PFp.
(11*) If p and FT, then FPp.
(10*) and (11*) would be true, even in a first or last moment of time. Tensers must provide some account of the necessity
of the truth of (10*) and (11*), even if just the minimal account that posits a set of brute necessities corresponding to each of the two. In fact, (10*) and (11*) don't give the whole story. There are also converse implications to consider. For example, if it was the case n units of time ago that it would be the case n units of time in the future that p, then p would be the case now. Let's look, then, at the following two necessities instead:
(14) If PnT, then: p if and only if PnFnp.
(15) If FnT, then: p if and only if FnPnp.
However, there is one more complication. If the future is open, then ‘Fnp’ should be interpreted as saying something like ‘It might be the case that p, n units of time hence.’ If we do interpret ‘Fnp’ that way, then (14) will come out false, since PnT and PnFnp do not entail that p. It could be that it was n units of time ago the case that p might be the case n units hence, even though p did not in fact happen. All that's needed is for p to have been an open possibility n units ago. Thus, we will have to replace ‘F’ with something stronger, an operator that means that something must happen in the future. Let's use ‘Gnp’ to represent ‘It is definitely going to be the case that p n units of time hence.’ We can define ‘G’ in terms of ‘F’:
Definition of G. Gnp if and only if FnT and ∼Fn∼p.