D.H. Mellor – The Growing Block from Broad to Tooley

The Growing Block from Broad to Tooley – D.H. Mellor (Cambridge)


C. D. Broad offered his growing block theory as an alternative to McTaggart’s A-theory of the
direction of time. He and his successors, who do so too, must therefore link the direction in which
their blocks grow to those of time’s other ‘arrows’, and in particular, I argue, to that of causation.
One theory of causation that at first sight helps them to do this is that of J. L. Mackie’s 1974 The
Cement of the Universe, which takes events to become ‘fixed’ when they or their sufficient causes
become present. However, because Mackie’s theory makes some events fixed while they are still
future, it contradicts the basic premise of all growing block theories, namely that the present
precedes nothing. I turn therefore to an exposition of the most comprehensive and best-argued
causally-based growing block theory of recent years, that of Michael Tooley’s 1997 Time, Tense,
and Causation. After making the best case for his theory that I can, I conclude by sketching the
three main challenges I think his and other modern growing block theories still face: those posed by
modern physics, the indexicality of the present, and an analogue of McTaggart’s disproof of the
reality of his A series.

Full paper here.

Because the papers are works in progress, they have been password protected. To register for the conference, and get the password, please contact Graeme A Forbes at G.A.Forbes@kent.ac.uk


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  1. Peter Forrest

    Comments on Hugh Mellor’s Paper

    Of the objections Hugh makes to the Growing Block, the coherence with physics pushes me towards a position in which there is no growing chunk of space-time but a real ‘hyperpast’ that grows as states of affairs accumulate (compare Jeffreys as cited by Hugh, and Szabo, Zoltan Gendler ‘Counting Across Times’, Philosophical Perspectives, 20 (2006): 399 – 426.) Do we want to discuss coherence with physics?

    As for the other problems, I have acknowledged the importance of the now now (aka Napoleon) problem. So that leaves the problem of the changing truth-value. Suppose an eternalist in 2011 asserts that there is (tenselessly) an Olympic Games in 2012. The growing block theorist says that this token assertion is now true but used not to be. Hugh finds that puzzling, but if truth is a relation between an unchanging proposition and changing reality, where is the problem?

    1. Hugh Mellor

      ‘Suppose an eternalist in 2011 asserts that there is (tenselessly) an Olympic Games in 2012. The growing block theorist says that this token assertion is now true but used not to be. Hugh finds that puzzling, but if truth is a relation between an unchanging proposition and changing reality, where is the problem?’

      The problem isn’t with the *proposition* but with a TOKEN of it, whose truth value needs to be fixed by when IT is, not by when WE are.

  2. Peter Forrest

    Sorry, Hugh, I still don’t get it. The truth of a truth-bearer, whatever it is, is relative to Reality and so can change as Reality changes

    1. Graeme A Forbes

      If I say ‘Queen Victoria is (tenselessly) the longest reigning British Monarch ever’ this token is true.

      Hugh says we can give this token tenseless truth conditions, because it was tokened on the 24th August 2015. Said on the 10th of September 2015 a different token of the same type will (let’s hope) be false.
      Peter (and I) are going to say that the token said today will change in truth-value. What I token now will (let’s hope) turn out to be falsified.

      That doesn’t commit us to thinking anything silly like the following:
      1) The token was true when I said it
      2) The token both is (tenselessly) and is not (tenselessly) true.
      1, qua tensed claim, isn’t true, because we sould interpret the ‘was’ as directing us to consider the token as it was when succeeded by nothing (I defend this view in a forthcoming phil studies paper).
      2 gets things wrong. The token changes it’s truth-value. It is question begging to think this commits us to 2: that would only follow if we debied that the relevant kind of change in what is the case simplicter can take place.

      1. Nathan Wildman

        Sorry, I don’t understand your point here. Are you saying that (1), (2), or both are silly?

        1. Graeme A Forbes

          I was thinking that both were individually bad things to say. I’ll try and explain why.
          1: ‘Queen Victoria is (tenselessly) the longest reigning British Monarch ever’ is true. I can forsee a time when it will not be true, but it would be very bad if that prevented me from making sense of the fact that the token I have just tokened is true in this context (said at this time, when this time is objectively present)
          2: This is what we need to get McTaggart’s Paradox going. If I’m committed to saying 2, I have exactly the sort of contradiction McTaggart was worried about. That, I take it, is bad.

      2. Hugh Mellor

        ‘Peter (and I) are going to say that the token said today will change in truth-value. What I token now will (let’s hope) turn out to be falsified.’

        *What* you token now – i.e. the proposition that is its content – can change it’s truth value. this doesn’t mean the token can. And even on your own account it’s surely not silly but true to say ‘The token was true when I said it’. (Why did you say it if it wasn’t true then?)

    2. Hugh Mellor

      Changing is being different at different times. A token of a proposition, unlike the proposition itself, is only at one time, and that’s the time that fixes the token’s truth value. To say it has a different truth value later is either to confuse it with a later token or to credit it with two contradictory truth values, an instance of McTaggart’s contradiction.

  3. Emily Thomas

    Thanks for sending me this last week, I thought it was great. The following comments are suggestions to make a few parts of it clearer:

    – By way of explaining the temporal reach of your paper – from Broad to Tooley – it might be worth explaining that despite the early interest in the GBT in the 1920s and 1930s, the theory lay fallow until it was rejuvenated by Mackie in the 1970s
    – On page 2, you write, ‘McTaggart admittedly shares the eternalist view that what is past and what is future are as real as what is present, just as what is elsewhere is as real’. To avoid confusing those who are unfamiliar with McTaggart, you could qualify this by adding that strictly McTaggart doesn’t think anything is past or future.
    – On page 4, you use Hume and Lewis to explain why it’s difficult to explain the time-causation link; this could perhaps be unpacked a bit further
    – I’m curious to hear more on how you understand the relationship between the growing block view, and the thinning tree model, but perhaps that question is too far away from the topic of this paper
    – As you discuss Broad in this paper, it could be useful to flag that Davidson’s characterisation of an event is different to Broad’s
    – You write at the bottom of page 4 that on the growing block theory the ‘essence’ of a present event is that there is quite literally nothing to which it has the relation of precedence. Whilst of course this is Broad’s view, and I’m assuming you share it (given that you take it to be a virtue of Tooley’s theory that it can be compatible with it) *perhaps* it could be questioned, given some sufficiently robust real/actual distinction.
    – On page 9, you discuss Tooley’s argument for substantivalism that there are locations which could hold objects but don’t. Arguably, Leibniz uses modal relationism to reply to this particular problem Leibniz-Clarke correspondence, so (given that you mention the correspondence) it might be worth noting that there are ready relationist replies to Tooley’s argument
    – It might be worth adding a short introduction, explaining the ‘direction’ (pun intended) that the paper will take?
    – I think the challenges you discuss for GBT at the end will link the paper neatly to the following ones; the later authors can make those links explicit

    1. Hugh Mellor

      Thanks Emily: brief responses to your helpful comments:
      I’ll certainly log the absence of development between Broad and Mackie.
      p.2. I know McT doesn’t believe in past and future, but I can’t think of a simpler way of saying how his ontology differs differs from presentism and growing block theories..
      p.4. It’s hard to make the case for the time-causation-link much clearer without taking too long, especially when I’m taking Tooley’s acceptance of it for granted.
      I thought I’d made the growing-block’s relationship to Storr’s thinning-tree model as clear as it needs to be in a paper on the history of growing block theories.
      It would have taken too long, and been too much of a diversion, to try and clarify and relate different authors’ different (and often ambiguous) concepts of ‘event’. I thought (and still think) it better to stick to one ‘clear and distinct’ idea, viz Davidson’s, once I found I could use it to say everything I wanted to say, especially about Tooley’s theory,
      p.4. I didn’t (and don’t) want to muddle Broad’s admirably clear concept of a growing block by weakening its commitment to the present being followed by nothing. I do offer Mackie the weaker reading of a growing block of actuality, which is clear enough on any well-known modal-realist distinction between the real and the actual.
      p.9 I can’t go into all the possible Leibnizian responses to substantivalism, and don’t need to in order to expound Tooley’s view.
      I didn’t think i needed an introduction, since i assumed (and assume) that will be in Graeme’s introduction to the whole volume: it will, won’t it, Graeme?!

      1. Graeme A Forbes

        I think what Emily meant by an introduction, was just an outline of what your paper covers. I will certainly be talking about how the papers fit together in the introduction to the volume, but I anticipate some readers might ignore my introduction and go straight to your paper, and it would make it a bit clearer to read if there was an outline at the top.

      2. Emily Thomas

        Great, I’m glad some of the suggestions were useful!

  4. Graeme A Forbes

    I’m wondering, given your discussion of Mackie on pages 4 to 5, whether Mackie would be happy with thinking that a deterministic cause being fixed is sufficient for an effect being fixed. You quote hime as saying “an effect cannot be fixed at a time when its cause is not fixed”, but that only shows a necessary condition, and you seem to be after a sufficient condition. (You give an argument that Mackie should accept this, which I’ll discuss below).
    On p.179 of The Cement of the Universe, Mackie says, “the full freedom of choice seems to require a metaphysical non-fixity in its object that goes beyond the mere absence of causal determination”. I had always taken this to be the claim that causal determination was not sufficient for fixity, merely necessary. Do you agree with this assessment of Mackie’s view? If so, that would mean that Mackie avoids the situation McCall finds himself lumbered with, where time cannot pass if the universe is deterministic.

    Your argument is that causation requires real relata. One might think that, qua cement of the universe, causation is very special, in that it is not an old way of relating some relata, but, given certain relata, brings other relata into existence. Causation, on such a view, is something that happens in the present. Causation, given causes, brings effects to existence. This involves attributing to causation some fundamental modality; causation necessitates that only one of the feasible futures comes into existence, but it seems a risky move to think that modal relations must relate real relata: that sounds like it commits one to Genuine Modal Realism.

    1. Hugh Mellor

      I agree Mackie doesn’t think causal determination is necessary for fixity, since an uncaused event can become fixed by becoming present. What causal determination does is transmit the fixity of a present cause to its future effects.

      I agree causation isn’t ‘any old relation’, because it’s not a relation at all. I think that way of putting it is less confusing than saying it’s a real relation that doesn’t need real relata, or saying that causation ‘happens in the present’ when effects are later than their causes so that both can’t be present at the same time.

      Since we all agree (I hope) that at no time is there more than one real present or real past, it doesn’t take causation to ‘necessitate that only one of the feasible futures comes into existence’. All sufficient causes do is determine which of several incompatible but equally feasible future events will become part of the one and only present and past

  5. Peter Forrest

    I take it , Hugh, that you are not happy with saying that a change in truth-value is a Cambridge change?


  6. Natalja

    Thanks Hugh, I really enjoyed this.

    I take it all sides were agreeing that tokens are tokened at, and then exist only at those, times. So the k token (of ‘d exists’) exists before t (d’s location) whereas the k* token exists after t.

    Hugh was saying, k must be false and k* true, since d comes into existence at t. Peter and Graeme are saying tokens change truth-value, so we can’t ask whether k and k* are true or false, only whether they are true or false at times – hyper-times actually, since presumably it makes no sense to ask whether a token that exists at one time is true at another time (of the same temporal dimension). (This, Hugh, is what I take you to be pointing out, and what I think you’re illustrating with the spatial and personal analogues.) I suspect, given Graeme’s remarks, that these hyper-times are A-times (so this is what I’ve called the hybrid growing block).

    So we’re disagreeing over whether the kind of hyper-change that is passage, in which hyper-time is objectively present, can affect the truth-value of tokens in the block(s). I’m not sure. But since I think the hybrid view and its use of the notion of hyper-time is problematic in many ways, I’m inclined to side with Hugh.

    I’d like to ask a clarificatory question, on p. 5, first paragraph: I think I didn’t follow the move from ‘we still need real relata’ to ‘all presently possible future events are real’. Would you point me towards the relevant idea?

    1. Graeme A Forbes

      I want to eschew any commitments to hyper-times. I think, if one is committed to hypertimes, one is vulnerable to all sorts of arguments (including your own, Natalja).

      1. Natalja

        Agreed (:)). So can I ask Graeme, do you disagree that ‘it makes no sense to ask whether a token that exists at one time is true at another time (of the same temporal dimension)’? I guess it comes down to what it is for the whole of reality to change (and thereby effect a change in truth-value in tokens, if it does). I shall study your paper closely to try to understand better how you’re thinking of this.

        1. Graeme A Forbes

          So, there are a whole range of times that exist, the latest ones are in August 2015, and there are lots and lots earlier than that.
          If we are saying that there exists a token, at some time, then I’m not sure what it means for us to say that the token is at some other time with a different truth-value (it sounds like we aretalking about a different token). There is just the token, and it has what truth-value it has.
          However, the Universe changes as time passes (indeed this change is constitutive of time passing).
          So the token (the very same one) can change truth-value, (without any intrinsic change to the token). This is because the truth-value of the token might depend on things that are not part of the time the token is tokened. (Recall my example above: ‘Queen Victoria is (tenselessly) the longest reigning British Monarch ever’ depends on whether there exists one who has reigned for longer).

          I’m happy talking about how things will go in the future – the laws of nature allow me to know what events will happen, and, indeed, that more events will happen. The laws of nature are likewise useful in explaining that in the past fewer things had happened. But a commitment to hyper-times would involve me thinking there exists some (hyper)time at which a different Growing-Block stage exists. But in my ontology I just have this Growing-Block stage.

          I see the worry — It is David’s worry that I am committed to ‘reality pointing beyond itself’. But I think temporal reality can point beyond itself without my being ontologically committed to different growing block stages, just as I think I can be committed to reality modally pointing beyond itself without thinking that I’m ontologically committed to merely possible worlds.

          1. Natalja

            Ok thanks. To me that seems like standard realism, which I think has to leave an explanatory demand hanging (namely in this context an explanatory demand that concerns the question how the token changes its truth-value, i.e. what it is that isn’t part of the token’s time that is such that the token’s truth-value depends on it – that thing, whatever it is, doesn’t seem like it’s part of reality (the one block), as you say).

  7. Peter Forrest

    Thanks Natalja

    I do not hold a tense theory for hyper-time (That would I say be hyper-presentism, which is my fall-back if the now now problem is insouble) So Hugh’s problem is just as easy to state for my so-called hypertime, which I take to be genuine time. I submit that truth is a relation between a token proposition and the whole of the half block in which it is located.


    1. Natalja

      I see I need to study your view in more detail too. By ‘token proposition’ you mean token of the proposition, right? So if that’s what truth is, the relation must change on your view (the relation between tokens and the blocks in which they’re located). I guess I thought that’s what we were agreeing doesn’t happen, when we were agreeing (if we were!) that tokens exist only at the times they are tokened. Clearly you either disagree with the latter point or think of the existence of tokens at times differently somehow. Thanks Peter.

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