Against the B-Theory of Time

April 4, 2010

There are two competing theories of time: they are named creatively the “A-Theory” and “B-Theory”.  For an introduction, see this article at Wikipedia.  Very briefly, the A-Theory of time affirms that the past and future are not as real as the present, that is, time passes.  The B-Theory of time affirms that past, present, and future are all equally real.

If the B-Theory of time is true, then this is a good rebuttal to the Kalam Cosmological Argument (KCA).  The KCA takes as one of its premises that the universe began to exist.  But this statement doesn’t make much sense on the B-Theory of time.  That is because on the B-Theory, nothing really “begins to exist”, because “begins” is a meaningless concept.  For how could something come into being if past, present, and future are all equally real?

But surely this is a strange concept, right?  It’s strongly counterintuitive, so much so that I’m persuaded it’s false.  Here’s an argument (not exactly original) to that effect:

The “Suicidal” Son
1. If B-theory is true and special and general relativity are true, then time travel is possible.
2. If time travel is possible, then it is possible for you to kill your father before you were born.
3. It is not possible for you to kill your father before you were born.
4. Therefore, time travel is not possible.
5. Therefore, either B-theory is false or special and general relativity are false (or, of course, they are both false).

1, 2, and 3 are the premises to the argument, 4 and 5 are the conclusions.  5 is a disjunction that asks the reader to give up either the B-Theory of time or scientific theories that are very well-tested.

In premise #1, time travel is supported by general relativity if we live in a universe with closed time-like curves.  Also in premise #1, we can assume certain space-time topologies within the special relativity framework to allow for time travel.  Also of course, in premise #1 we are granting for the sake of argument that the past is equally real as the present.

Luke Muehlhauser is blogging a series summarizing the KCA, wherein he articulates the premises to the KCA and arguments supporting them.  Within the series he is withholding judgment on the argument, although at several points on his blog he has hinted at the fact that he doesn’t think the conclusion of the KCA is true at least partly because he doesn’t think the A-Theory is true.  I imagine many others who aren’t persuaded by the KCA use the B-Theory as a sort of escape hatch too.  So for all you B-Theorists out there, what do you think of this argument?



  1. There is no support (either way) for premises 2 and 3 — just speculation.DJW

  2. Hi David,Re: 2, it seems to me that if certain closed time-like curves are assumed, then you could go to this previous state, yes? You're saying it's not possible? Why? Do you at least think it's possible to go to a prior state where you are in the spatial vicinity of one's father (given premise 1)?Re: 3, I state the premise like this since it seems obviously incoherent, so it must be false. You couldn't exist if your father was dead before you were born (well, conceived to be precise), so how could you kill him? This just seems obvious to me, why do you think it is speculation?

  3. Hi Thomas. I'm not familiar with the philosophy of time, but here are my thoughts, such as they are.Suppose that, instead of travelling back in time to kill your father, you travelled back in time to kill some random person without any causal connection to you. So perhaps you travel from 2010 in the USA, to 1980 in China, and find a unlucky villager. This has consequences for history, but none which would prevent you from travelling back in time and taking the action. Usually, we'd have a timeline somewhat like this..1980 -> 1990 -> 2000 -> 2010 ->…. where the events of 1980 cause the events of 1990, and so on. But in the above scenario, we get..1980 -> 1990 -> 2000 -> 2010 ->.. ↑_____________________|.. where the events of 2010 causally influence those of 1980. But of course, 1980 events causally influence 1990, 2000, and finally 2010 events in their turn, even if they don't effect yourself. So it turns out that the events which comprise 2010 include whatever the consequences of time travel there are. History has been set on a slightly different path, and the original 2010 from which you travelled back in time is no longer in the future of the 1980 you arrive at. So a better representation would be..1980 -> 1990 -> 2000 -> 2010 ->.. _______________________| ↓1980 -> 1990 -> 2000 -> 2010 ->..Ok, now take the the suicidal son case. The son also travels back from 2010 to 1980, and kills his father. This action follows the causal pattern immediately above: events in 2010 of the top row effect events of 1980 in the bottom row, causing the events of 1990, 2000 and 2010. And in these later times, no son is born to go back in time to kill his father. But, notice, there's nothing inconsistent about the bottom row. What it describes is a series of events, including the acausal appearence of yourself in 1980, killing a man who bears no causal-historical relation to you, and your persistence into the future from 1980 on. For symmetry, there's nothing inconsistent about the top row either: that describes your father living an unbothered life, conceiving yourself, and you stepping into a time machine, never to be heard from again. To be clear, I'm not advocating the existence of multiple timelines in parallel. What I have in mind is of a single timeline which changes irrevocably due to time travel, and constantly overwrites itself, as each instance of time travel 'destroys' the future from which it comes and 'creates' new history in its place. So, in my diagram, the top row (at least from 1980 on) would become non-existent with your time travel, and the bottom row would then be real series of events.Anyway, the upshot of this view would be that your 2 is false. If time travel is possible, then does indeed allow you to travel back in time to kill a man, but this man would not, in that case, be your father, and nor would the event take place prior to your birth, since your birth would not happen. Nevertheless, the impossibility of killing your father before you are born is not really a physical impossibility, but perhaps a kind semantic impossibility, in that there's no event which it could be appropriate to describe in that way.That seems correct to me, in sketch. What do you think?

  4. TaiChi,I'm not sure if you haven't confirmed #3 to be true rather than shown #2 to be false.From the top row, the son did go back to kill his father. But, you say, the man killed in the bottom row bears no causal-historical relationship to the son. Well, why not? If the killer is indeed his son (which it looks like you affirm), then clearly there is a relationship here. The killer couldn't be the victim's son if there wasn't such a relationship. Maybe you are assuming that causal relationships can be just uni-directional in time? It doesn't seem to me that this would have to be the case, especially if the B-theory is true. For example, do children adjust their behavior if they know how the parents would react if they were to act certain ways?So if the relationship does hold between the top and bottom row, then it really is the son killing the father at a time before the son was conceived. But of course, the idea of you killing your father before you were conceived just seems plainly outrageous. You couldn't do such a thing, because if you did, you couldn't exist. This is absurd.I'll noodle your comments some more, they are very much appreciated.

  5. Reid,Yes, I think I've confirmed #3. But I've also allowed that time travel is possible. The combination of these two commitments means I endorse the antecedent of 2, but deny the consequent, which means that 2 is false.Another example: "If travel at light speed is possible, building spaceships which travel at light speed is possible". The antecedent is true, since light travels at light speed, but the consequent is false, since a spaceship would be too massive to be accelerated to the speed of light. By truth table, the conditional is false.On the causal-historical relationship: the son certainly has a relationship with the Father along the top row. But he doesn't kill anyone on the top row – he kills someone on the bottom row. And the events on the bottom row are consistent with that killing. So the events on the bottom row do not include the son's birth. But the birth, child-rearing, etc. are what would count for a causal-historical relation between the son and the father. So the son doesn't actually kill his father, and we really should be talking of a 'son' and a 'father'.On reverse causality: no, I don't think this makes causality uni-directional, for not every instance of time-travel will erase its future causes, and time-travel is itself an instance of reverse causality.Having said all that, I don't think I've been true to B-theory. These ideas of one timeline changing to another, and of time 'overwriting itself', are themselves temporal. Perhaps they could work for A-theory, but since time is supposed to be given 'all at once' in B-theory, I can make no sense of the changing I've suggested.But there's another option for B-theory which is worth mulling over: David Lewis suggests that there is an equivocation concerning 'can', or in your argument it would be the word 'possible'. The paper is here, if your interested: http://www.csus.edu/indiv/m/merlinos/Paradoxes%20of%20Time%20Travel.pdf

  6. Hey TaiChi,You wrote:Yes, I think I've confirmed #3. But I've also allowed that time travel is possible. The combination of these two commitments means I endorse the antecedent of 2, but deny the consequent, which means that 2 is false. ~TaiChiRight, but it seems like one either has to endorse the consequent in #2 or give up the idea that it really was his son that travelled back in time. I think you're denying the consequent of #2 by asserting that there's no causal-historical relationship between the killer and victim in your "bottom timeline". In my previous comment I questioned how we could think that if we also affirm that there is indeed a father-son relationship that remains intact.Thanks for the paper recommendation, I'll check it out.

  7. Reid,That's right. I am giving up that the son would kill his father, and denying the consequent of 2.

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