Why Carrier is Right on Fine-Tuning

EDIT: This post has been edited to better reflect Luke Barnes’ position.

Recently, Richard Carrier has re-opened his public discussion with Luke Barnes on the fine-tuning argument, in a blog post (for Barnes’ reply, see his own blog post). Their discussion is quite tedious and personal, but at the heart of things I think Carrier is right: fine-tuning is evidence against God, for the reasons Carrier champions. I’ll explain.

I think Luke Barnes, who supports the fine-tuning argument, uses a somewhat misleading terminology. What I take “fine tuning” to be, and what I think most physicists do, is the empirical finding that we live in a universe with laws of nature such that if the constants in these laws were to be altered slightly, then the laws would describe a (different) universe where life cannot evolve or survive. The constants in this sense seem to be “fine tuned” to produce life. Let us call this fact about the laws of nature of the universe we actually live in “FT”.

The fine-tuning argument is then the argument that this fact indicates that God exists. Now in judging whether God exists or not, we are contrasting two hypotheses. It does the atheists injustice to say that they simply don’t believe God exists; rather, they believe the world is natural. Barnes usefully provides a way to characterize this view: the atheists believe that all that exists is Lagrangian, meaning that it is described by one particular uniform, local, set of laws of nature. Let us call this hypothesis “N”, for “Natural”. The question is then whether the data that fine-tuning holds (FN), supports the God hypothesis (G) or naturalism (N). The real question here is whether the data is more likely under G or N.

I think Barnes confuses fine-tuning with a slightly but importantly different mathematical fact. This fact is that in the space of all possible natural (Lagrangian) universes, the ones bearing life are exceedingly rare. This is because life, as we know it, is a very complex phenomena, and its evolution even more so. In order to “build” such a thing from the very simple, local, uniform building blocks that a Lagrangian provides, you need to get things just right. Thus, the Lagrangians that support life are very sparsely distributed among all possible Lagrangians, and even small deviations from them (changing one constant by a bit) will mean a universe that isn’t life-bearing. (At least, that seems to be plausible; there is no way to actually calculate any of that.) Notice that this is a logical fact about the nature of Lagrangians (i.e. of natural hypothetical universes). It makes no sense asking what is the likelihood that we will observe it or what is the likelihood of something given it, just like it makes no sense to ask what is the likelihood that we will observe “1+1=2” or to ask what is the likelihood of something “given” that “1+1=2” (since “1+1=2” is true regardless of what else we consider “given”).

Now, what Carrier essentially argues is that we should be very careful to distinguish the finding that there is Life (let’s call it “L”) from the finding that there is fine-tuning (FT). He rightly claims, and Barnes agrees, that given that there is life in the universe, and given that naturalism holds, the probability that we will find fine-tuning is 1; P(FT|L,N)=1. This is because the few hypothetical Lagrangians that do support life are fine-tuned. In contrast, given that there is life and that the God hypothesis is true, the probability of fine-tuning is lower than 1, since God could have created life without fine-tuning; P(FT|L,G)<1. It follows from this that the evidence of fine-tuning supports atheism – the fact that we find ourselves in a fine-tuned universe lowers the probability of God. I think in this Carrier is right.

Theists in contrast often argue that if we just consider fine-tuning on its own, then it is more likely under theism than under atheism. This is because the probability of fine-tuning given atheism is very low, since the probability of life under atheism is very low, since most Lagrangians don’t support life; P(FT|N) is low. In contrast, the probability of fine-tuning under God is supposedly fairly high, since God wants to create life and he might as well do it with uniform laws; so P(FT|G) is high since P(L|G)=1.

This argument is problematic in that fine-tuning is a separate fact from life, and is only relevant in those universes that have life. So we can’t just write P(FT|N). We have to take each piece of data on its own to maintain clarity. We have to write P(FT|L,N) – and similarly P(FT|L,G). And Carrier is still right – the new data FN is certain under naturalism, so that P(FT|L,N)=P(L|N), whereas it is less than certain under the God hypothesis so that P(FT|L,G)<P(L|G), so that the new information FT actually lowers the probability of the God hypothesis.

Now, this isn’t quite Barnes’ argument. Barnes instead essentially argues that since life is rare within the space of all natural (Lagrangian), the fact that we find it in our universe indicates that the process that chose which Lagrangian to instantiate was highly-biased towards choosing life-bearing Lagrangians. Implicitly, of course, this implies God chose which Lagrangian to instantiate.

Note that this amounts to what I will call the “argument from life”, namely that life is much more likely under God than under naturalism; P(L|G)=1 whereas P(L|N) is very small. And this is exactly the same place where the more usual theist argument leaves us – having established that Carrier is right that the finding that our universe is fine-tuned (FT|L) supports N, we are still left with the question of whether L does. So – how can the atheist reply to the argument from life? Well, he has two replies to this.

First, one can note that the specific God hypothesis the theist is working with is already carefully selected to fit the data that there is life. There are lots of other gods we can think of, that won’t create life. So the fact that P(L|G)=1 isn’t really saying much. To be fair, we should really consider all possible gods, and there is really no way to calculate the likelihood of life under that theory but it stands to reason it would be very low too. Or, if we decide to limit ourselves to just the life-permitting gods, then we might as well limit ourselves just to the life-permitting natural universes, and then P(L|N)=1 too.

In Barnes’ variant of the argument, this amounts to saying that even though a natural Lagrangian-selecting process that chooses a life-bearing Lagrangian seems unlikely, a divine ones that does so is also unlikely. (Technically, the atheist here doesn’t accept that there is a process that chooses the Lagrangian; rather, there simply is a particular Lagrangian. So what Barnes’ really shows is that if you believe in Naturalism is that life is surprising (assuming that Lagrangian space is indeed sparse as is assumed); and the atheist replies that it’s surprising if you believe in God, too.)

This objection is closely related to the fact that one can’t really do rational probabilistic analysis unless one knows beforehand how to divide the landscape of possibilities. The answers you get from a probabilistic analysis, especially one involving infinities such as the values of the constants in the Lagrangians or the possible types of deities, will depend on how you divide the infinite range of possibilities up. This is part of the reason why I said above that we can’t really calculate how common are life-bearing naturalistic universes among all naturalistic universes.

Secondly, one can object to Barnes’ (or the more usual) argument by declining Barnes’ characterization of naturalism. I said above he effectively defines it as maintaining that there is one Lagrangian – implying that there is one uniform, local, simple set of laws of nature. But quantum physics seems to suggest otherwise. A big part of our understanding of the laws of nature that we have involves the idea that some of the “constants” in our laws didn’t start that way, but rather had a range of possible values and “froze” at the values we see (this is called “spontaneous symmetry breaking”). This occurs in a quantum theory, and one of the leading interpretations of quantum theory – the leading one in quantum cosmology, I think; this is the Many World Interpretation – is that whenever there are multiple possibilities, all of them are realized, each in a separate parallel universe. Thus, instead of reality consisting of the laws of nature we have in our universe, with their current values of the constants, contemporary physics suggests that reality actually consists of a multiverse with numerous parallel universes, each with their own “constants” of nature.

This is hardly well-established science; it’s just an interpretation of current science (although one I tend to believe in, for reasons unrelated to the fine-tuning argument). If one adopts something like this view, then, one is led to define naturalism not as there existing one Lagrangian but rather a plethora of Lagrangians describing parallel universes, perhaps even an infinite variety of all possible Lagrangians. In such a multiverse, the probability of there being a Lagrangian universe with life in it is 1; P(L|N)=1.

We have therefore reached the stage where both under naturalism (in the multiverse sense) and under theism the probability of life is 1; so the argument from life fails.

Now the question becomes – which is more likely, the multiverse or God? That’s yet another argument to be had, but I’ll simply note that I think the multiverse is strongly suggested by well-established physics, whereas God is a childish, anthropomorphic (in the “mind of a human”, not “body of a human”, sense), metaphysically incoherent (when the so-called “theologian’s God” is meant), and is in short a highly unlikely hypothesis. At any rate, this question bears little relation to the question of whether fine-tuning implies that God exists – which, as I argued above, it does not.

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13 thoughts on “Why Carrier is Right on Fine-Tuning

  1. Hi,

    First of all, I agree that fine-tuning does not allow us to distinguish between a multiverse and a God as plausible hypothesis (btw. my own uninformed view is that the multiverse is the likely explanation). However in TEC Carrier considers fine tuning WITHOUT the multiverse and argues that in this case fine tuning is evidence AGAINST god. This is the argument I think Luke is addressing.

    Now, I agree with what you (and Ikeda and Jeffreys) write, but I disagree with the interpretation. What we are interested in when we consider if fine-tuning is evidence for or against God is the relative probability of Gods existence (or non-existence) in light of *all* evidence:

    (1) P(G|L FT)/ P(N |L FT)

    The problem is I do not see how the inequality:

    (2) P(FT|L,G)<P(L|G)

    in itself says anything about this quantity and so I disagree with the assessment:
    "so that the new information FT actually lowers the probability of the God hypothesis."
    I provide a counter-example here if you are interested (Carrie the Lawyer):

    If you understand how Carrier connects the inequality (2) to (1) I would be very interested in hearing it — as far as I see it is based on a simple misunderstanding.

    Cheers
    T

    • I think the system just needed me to approve it, for some reason. I believe it appears now. I hope that your future comments will appear automatically, or I’ll have to delve into WordPress’s definitions…

  2. Hi Tim,

    My understanding (I could be wrong…) is that Carrier is arguing as follows:

    Let us treat the denominator and numerator in (1) P(G|L FT)/ P(N |L FT) separately, for ease of notation. Then for the numerator,
    P(G|L,FT)~P(G)P(L|G)P(FT|L,G)<P(G)P(L|G)=P(G|L)
    where I used P(FT|L,G)<1 (not quite your (2), but close) to get the inequality. Whereas for the denominator,
    P(N|L,FT)~P(N)P(L|N)P(FT|L,N)=P(N)P(L|N)=P(N|L)
    Thus,

    Odds(G to N|L,FT) < Odds(G to N|L)

    or in other words, the fact that there is fine-tuning (FT) has lowered the probability of the god-hypothesis,
    P(FT|L,G)=P(L|G)P(FT|L,G)<P(L|G)
    but hasn't affected the probability of naturalism,
    P(FT|L,N)=P(L|N)P(FT|L,N)=P(L|N)

    Now I haven't read your reference, so I might very well be making the same mistake Carrier is and not realizing it. But the argument does seem valid to me.

  3. Thank you for this well-written summary! Assuming you have represented their positions accurately (and I’m sure if they read your post there will be several multi-thousand-word dissections forthcoming) it does seem that Carrier just about has the upper hand. Either way, though, I think you hit the nail on the head with your last paragraph. EVEN IF all arguments for a supernatural creator are true, the connection between such a being and the Christian God (or any god you care to name) is SO much more difficult to justify it becomes a painful exercise in question-begging. What exactly is p(Brahma|G)?

  4. panpsychist:

    Thanks for your response. So of course I agree with the conclusion that

    (1) p(G|L,FT)/p(N|L,FT) < p(G|L)/p(N|L)

    The issue (as I see it) is that we should compare this our prior odds rate i.e.

    (2) p(G)/p(N)

    and in general this can be very different.
    So ofcourse a person can say that by the fine-tuning argument he mean (1), however I think this is a bit misleading since I think the existence of life is relevant evidence for the fine-tuning argument and should be treated–that is we are interested in comparing against the probabilities (2). I realize that Ikeda and Jeffrey are talking about (1) and that's why i agree with them on a formal point — i just think it is a bit confusing. That's what the Lawyer example is supposed to address.

    Now this is only an argument about what we *call* things so if this was all there was to it I wouldn't say i disagreed with Carrier, however if you look at what Carrier is doing he is arguing for the probability

    p(G) = 1/4

    (You can find his argument quoted in my document above; notice he is certainly *not* discussing life in the argument)
    and then equating this with p(G|L)

    p(G|L) = p(G) = 1/4

    It is *this* move i disagree with.

    • “I think this is a bit misleading since I think the existence of life is relevant evidence for the fine-tuning argument and should be treated”

      Well, I think that things are clearer if you call the fine-tuning argument (1). This way allows us to note that FT actually reduces the chances the God hypothesis is correct; regardless of whether in the final account L increases this probability so much that it won’t matter. We can then move on to discuss L, regardless of FT, to see if this is indeed so. I think that’s clearer.

      In your Carrie the Lawyer example, it’s like noting that having not found fingerprints increases the chances that the accursed isn’t guilty; and only then moving on to discuss what the effect of finding the corpse does. Of course it may very well turn out that overall, finding the corpse increases the chances of guilt so much that we should find the accused guilty even though there are no fingerprints. But that doesn’t change the fact that not finding fingerprints lowers the chances of guilt.

      “p(G|L) = p(G) = 1/4

      It is *this* move i disagree with.”

      Well, yes, this is more problematic. As an aside, I find Carrier’s reasoning on why 1/4 is reasonable …. unconvincing to say the least. More importantly, in this instance you can by no means ignore the normalization, i.e.
      P(G|L)=P(G)P(L|G)/P(L)=P(G)/(P(G)+P(N)P(L|N))
      My argument above was against the move P(L|G)=1 here (or, alternatively, in favor of P(L|N)=1 too) for a single-universe naturalism, and for P(L|N)=1 for multiverse-naturalism. Simply going P(G|L)=P(G) is clearly wrong.

      However, this is all about L. Not FT. Carrier’s main point, that FT lowers P(G|L), still stands regardless.

      • Hi again,

        Sorry my previous post was not very well written, I was cooking. It seems like we agree on the first part at least from a formal perspective. I would perhaps say that at least in the “Carrie the lawyer” example putting the conclusion as for instance: “The finding of blood in his apartment does not affect his guilt” (compare to “fine-tuning is irrelevant for determining the existence of God) is possibly *misleading* (but not wrong!) to the casual reader and that’s why I would prefer to include both pieces of evidence. At the end of the day, I do not disagree with IJ’s conclusion of course, and this come down to what theists mean by “the fine tuning argument” (conditioning on FT or FT and L) and is more of a linguistic discussion.

        I think i might disagree with you if “Carrier’s main point, that FT lowers P(G|L), still stands regardless.”. I think the main conclusion of the chapter is this:

        —-
        “This entails the Bayesian conclusion that the probability that God intelligently designed the universe
        cannot be any higher than 15 percent (and is almost certainly a great deal less than that). That means no
        rational person can believe the probability that God intelligently designed the universe is any better than 1
        in 6. This means every rational person must conclude God probably didn’t do that.” (TEC)
        —-

        this is at least the conclusion I am trying to examine. If you look at the Bayesian computation that leads to this conclusion (see the footnotes), the prior probability used is:

        p(G|L) = 1/4

        and this value is just arrived at by the above argument (footnote 8) which seems to be for p(G) = 1/4 (it’s based on “pure logic” in Carriers words)

        (fyi, iirc. the computation is:
        p(G|FTL) = p(FT|GL) p(G|L)/[ p(FT|GL) p(G|L) + p(FT|AL) p(A|L)]
        = 1/2 * 1/4 / (1/2 * 1/4 + 1 * 3/4) = 1/8 / (1/8 + 6/8)
        = 1 / 7
        )

        justifying this move — p(G|L) = p(G) — has been all the discussion have been about at least from my perspective.

        What do you for instance make of Carriers last attempt on RCB? (fourth post)
        http://freethoughtblogs.com/carrier/archives/9630#comments

        Notice what he derives is formally equivalent to: (and observers are roughly equal to L in your terminology)

        p(observations|{either observers or ~observers}) = P(observers)
        (is it clear what “observations” are here? I think the shift from just events such as G or FT to “observations” may be because he wish to claim that the event is not just FT, but that the event is: *someone* is observing FT, see section 5.4 in my document)

        Okay then notice “observers or ~observers = True” so this is formally equivalent to:

        (3) p(observations) = P(observers)

        from which it is concluded that:
        “And yet, because the ~observers option zeroed out, per Descartes, P(observations|observers) = 1.
        The lesson?
        P(observers) is always 1 when anything is observed.
        Listen to Descartes.”

        So this may either be trivially true (an observation is the event an observer observes something and an observer by definition performs observations automatically) but then I do not see how it demonstrates p(G|L) = p(G) or why P(observers) = 1.
        On the other hand, “observations” may be general observations (such as fine-tuning or what I had for dinner) the argument seems trivially false because then p(“I had fish for dinner”) = p(observations) = p(observers) = 1.

        So my head hurting and I feel just as far as ever from understanding why this proves p(G|L) = 1/4…

      • Hi Tim,

        “this is at least the conclusion I am trying to examine”

        I don’t think it’s defensible. I am sure not trying to defend his final conclusion – I’m only trying to defend what I take to be his MAIN point, namely that FT lowers the probability of God. I by no means defend all his derivations or probability estimates, nor his interpretation of probability.

        “What do you for instance make of Carriers last attempt on RCB? (fourth post)?”

        I think he mostly uses ill-defined equations to argue against your general approach. He didn’t really answer your question.

        I think the key to understanding him there is “The probability that observers exist is 1; we’re here, after all”. As a frequentist, Carrier cannot really consider hypotheticals such as “p(O|b)” – as far as he is concerned, the probability that there are observers is 1. Where this gets confusing is where he tries to do so for the sake of argument despite it making no sense in his eyes….

  5. I appreciate your careful discussion, but you’ve misrepresented my argument. Try this post:
    https://letterstonature.wordpress.com/2010/10/26/terms-and-conditions-a-fine-tuned-critique-of-ikeda-and-jeffreys-part-1/

    In particular, you say:

    “Barnes in contrast essentially argues that if we just consider fine-tuning on its own, then it is more likely under theism than under atheism. This is because the probability of fine-tuning given atheism is very low, since the probability of life under atheism is very low, since most Lagrangians don’t support life; P(FT|N) is low. In contrast, the probability of fine-tuning under God is supposedly fairly high, since God wants to create life and he might as well do it with uniform laws; so P(FT|G) is high since P(L|G)=1.”

    This is not how I run the argument, though I have seen this version attempted. In particular, I would say that p(FT|G.B) = p(FT|~G.B).

    Also, note this sentence of yours:
    “What I take “fine tuning” to be, and what I think most physicists do, is the empirical finding that we live in a universe with laws of nature such that if the constants in these laws were to be altered slightly, then the laws would describe a (different) universe where life cannot evolve or survive.”

    How can there be an *empirical* finding about what would be the case if the laws of the universe were different? We can’t experiment with changing the laws of nature, or observe other parts of the universe where the laws are different. Any such conclusion must be theoretical – we change the constants in our equations.

    In which case, we’re left with this version of FT: “The Lagrangians that support life are very sparsely distributed among all possible Lagrangians”. (Actually, I’d include initial conditions in FT, which aren’t in the Lagrangian but in a solution to the equations. But that’s a minor quibble. I find thinking about FT in terms of Lagrangians to be very helpful.)

    • Thank for chiming in. I’ll respond to your points out of order,
      “I find thinking about FT in terms of Lagrangians to be very helpful.”

      Absolutely. I think your framing of the discussion in this way is great.

      “How can there be an *empirical* finding about what would be the case if the laws of the universe were different? ”

      I’m sure we’d agree that it’s a contingent empirical finding that the laws of nature are what we find them to be (the standard model and so on). It’s also a mathematical fact that if we alter the constants in THESE laws, we get a universe that can’t support life. Notice then the the sentence “if we alter the constants in the laws we observe, we find a lifeless hypothetical universe” is a contingent fact (we could have found ourselves in a universe with broadly-tuned laws so that it won’t be true), which is at least closely related to the empirical finding of what the laws of nature – of our universe! – are. In this sense, it an empirical finding.

      In contrast, the fact that life-supporting universes are sparsely distributed in the space of all Lagrangians is a purely mathematical fact. It will hold true regardless of what we find our own laws of nature to be.

      I think this is a major point as I think of “fine-tuning” as the first, empirical, meaning. And I believe that finding out that this is the case – that our own empirically-found laws of nature are fine-tuned for life – actually decreases the likelihood for God, as I explained in my main post.

      “This is not how I run the argument, though I have seen this version attempted.”

      Yes, I see. I’ll amend my main post (not immediately; I want to think on how best to do so first). It appears your argument is more along the lines of (rightly) noting that since life-bearing Lagrangians are sparse, the fact that we find ourselves with one suggests that the selection of which Lagrangian to instantiate was highly-biased towards life-bearing ones. I hope that’s a better depiction?

      I note that you avoid contrasting to the God hypothesis, at least formally; I still maintain that if one does, one is left with the conclusion that the empirical finding of FT (as opposed to the purely-mathematical sparsity) lowers the odds of the God hypothesis.

      I also note that your argument is essentially what I called an “argument from life” – the fact that life is so rare in the space of all possible Lagrangians means that the naturalist has a hard time explaining it. This is true regardless of the question of empirical fine-tuning; even if ALL life-bearing Lagrangians (including ours) were COARSELY grained, but they were still rare (i.e. most Lagrangians aren’t life-bearing), your argument would work exactly the same.

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