Don Page is one of the world’s leading experts on theoretical gravitational physics and cosmology, as well as a previous guest-blogger around these parts. (There are more world experts in theoretical physics than there are people who have guest-blogged for me, so the latter category is arguably a greater honor.) He is also, somewhat unusually among cosmologists, an Evangelical Christian, and interested in the relationship between cosmology and religious belief.
Longtime readers may have noticed that I’m not very religious myself. But I’m always willing to engage with people with whom I disagree, if the conversation is substantive and proceeds in good faith. I may disagree with Don, but I’m always interested in what he has to say.
Recently Don watched the debate I had with William Lane Craig on “God and Cosmology.” I think these remarks from a devoted Christian who understands the cosmology very well will be of interest to people on either side of the debate.
Open letter to Sean Carroll and William Lane Craig:
I just ran across your debate at the 2014 Greer-Heard Forum, and greatly enjoyed listening to it. Since my own views are often a combination of one or the others of yours (though they also often differ from both of yours), I thought I would give some comments.
I tend to be skeptical of philosophical arguments for the existence of God, since I do not believe there are any that start with assumptions universally accepted. My own attempt at what I call the Optimal Argument for God (one, two, three, four), certainly makes assumptions that only a small fraction of people, and perhaps even only a small fraction of theists, believe in, such as my assumption that the world is the best possible. You know that well, Sean, from my provocative seminar at Caltech in November on “Cosmological Ontology and Epistemology” that included this argument at the end.
I mainly think philosophical arguments might be useful for motivating someone to think about theism in a new way and perhaps raise the prior probability someone might assign to theism. I do think that if one assigns theism not too low a prior probability, the historical evidence for the life, teachings, death, and resurrection of Jesus can lead to a posterior probability for theism (and for Jesus being the Son of God) being quite high. But if one thinks a priori that theism is extremely improbable, then the historical evidence for the Resurrection would be discounted and not lead to a high posterior probability for theism.
I tend to favor a Bayesian approach in which one assigns prior probabilities based on simplicity and then weights these by the likelihoods (the probabilities that different theories assign to our observations) to get, when the product is normalized by dividing by the sum of the products for all theories, the posterior probabilities for the theories. Of course, this is an idealized approach, since we don’t yet have _any_ plausible complete theory for the universe to calculate the conditional probability, given the theory, of any realistic observation.
For me, when I consider evidence from cosmology and physics, I find it remarkable that it seems consistent with all we know that the ultimate theory might be extremely simple and yet lead to sentient experiences such as ours. A Bayesian analysis with Occam’s razor to assign simpler theories higher prior probabilities would favor simpler theories, but the observations we do make preclude the simplest possible theories (such as the theory that nothing concrete exists, or the theory that all logically possible sentient experiences occur with equal probability, which would presumably make ours have zero probability in this theory if there are indeed an infinite number of logically possible sentient experiences). So it seems mysterious why the best theory of the universe (which we don’t have yet) may be extremely simple but yet not maximally simple. I don’t see that naturalism would explain this, though it could well accept it as a brute fact.
One might think that adding the hypothesis that the world (all that exists) includes God would make the theory for the entire world more complex, but it is not obvious that is the case, since it might be that God is even simpler than the universe, so that one would get a simpler explanation starting with God than starting with just the universe. But I agree with your point, Sean, that theism is not very well defined, since for a complete theory of a world that includes God, one would need to specify the nature of God.
For example, I have postulated that God loves mathematical elegance, as well as loving to create sentient beings, so something like this might explain both why the laws of physics, and the quantum state of the universe, and the rules for getting from those to the probabilities of observations, seem much simpler than they might have been, and why there are sentient experiences with a rather high degree of order. However, I admit there is a lot of logically possible variation on what God’s nature could be, so that it seems to me that at least we humans have to take that nature as a brute fact, analogous to the way naturalists would have to take the laws of physics and other aspects of the natural universe as brute facts. I don’t think either theism or naturalism solves this problem, so it seems to me rather a matter of faith which makes more progress toward solving it. That is, theism per se cannot deduce from purely a priori reasoning the full nature of God (e.g., when would He prefer to maintain elegant laws of physics, and when would He prefer to cure someone from cancer in a truly miraculous way that changes the laws of physics), and naturalism per se cannot deduce from purely a priori reasoning the full nature of the universe (e.g., what are the dynamical laws of physics, what are the boundary conditions, what are the rules for getting probabilities, etc.).
In view of these beliefs of mine, I am not convinced that most philosophical arguments for the existence of God are very persuasive. In particular, I am highly skeptical of the Kalam Cosmological Argument, which I shall quote here from one of your slides, Bill:
- If the universe began to exist, then there is a transcendent cause
which brought the universe into existence. - The universe began to exist.
- Therefore, there is a transcendent cause which brought the
universe into existence.
I do not believe that the first premise is metaphysically necessary, and I am also not at all sure that our universe had a beginning. (I do believe that the first premise is true in the actual world, since I do believe that God exists as a transcendent cause which brought the universe into existence, but I do not see that this premise is true in all logically possible worlds.)
I agree with you, Sean, that we learn our ideas of causation from the lawfulness of nature and from the directionality of the second law of thermodynamics that lead to the commonsense view that causes precede their effects (or occur at the same time, if Bill insists). But then we have learned that the laws of physics are CPT invariant (essentially the same in each direction of time), so in a fundamental sense the future determines the past just as much as the past determines the future. I agree that just from our experience of the one-way causation we observe within the universe, which is just a merely effective description and not fundamental, we cannot logically derive the conclusion that the entire universe has a cause, since the effective unidirectional causation we commonly experience is something just within the universe and need not be extrapolated to a putative cause for the universe as a whole.
However, since to me the totality of data, including the historical evidence for the Resurrection of Jesus, is most simply explained by postulating that there is a God who is the Creator of the universe, I do believe by faith that God is indeed the cause of the universe (and indeed the ultimate Cause and Determiner of everything concrete, that is, everything not logically necessary, other than Himself—and I do believe, like Richard Swinburne, that God is concrete and not logically necessary, the ultimate brute fact). I have a hunch that God created a universe with apparent unidirectional causation in order to give His creatures some dim picture of the true causation that He has in relation to the universe He has created. But I do not see any metaphysical necessity in this.
(I have a similar hunch that God created us with the illusion of libertarian free will as a picture of the true freedom that He has, though it might be that if God does only what is best and if there is a unique best, one could object that even God does not have libertarian free will, but in any case I would believe that it would be better for God to do what is best than to have any putative libertarian free will, for which I see little value. Yet another hunch I have is that it is actually sentient experiences rather than created individual `persons’ that are fundamental, but God created our experiences to include beliefs that we are individual persons to give us a dim image of Him as the one true Person, or Persons in the Trinitarian perspective. However, this would take us too far afield from my points here.)
On the issue of whether our universe had a beginning, besides not believing that this is at all relevant to the issue of whether or not God exists, I agreed almost entirely with Sean’s points rather than yours, Bill, on this issue. We simply do not know whether or not our universe had a beginning, but there are certainly models, such as Sean’s with Jennifer Chen (hep-th/0410270 and gr-qc/0505037), that do not have a beginning. I myself have also favored a bounce model in which there is something like a quantum superposition of semiclassical spacetimes (though I don’t really think quantum theory gives probabilities for histories, just for sentient experiences), in most of which the universe contracts from past infinite time and then has a bounce to expand forever. In as much as these spacetimes are approximately classical throughout, there is a time in each that goes from minus infinity to plus infinity.
In this model, as in Sean’s, the coarse-grained entropy has a minimum at or near the time when the spatial volume is minimized (at the bounce), so that entropy increases in both directions away from the bounce. At times well away from the bounce, there is a strong arrow of time, so that in those regions if one defines the direction of time as the direction in which entropy increases, it is rather as if there are two expanding universes both coming out from the bounce. But it is erroneous to say that the bounce is a true beginning of time, since the structure of spacetime there (at least if there is an approximately classical spacetime there) has timelike curves going from a proper time of minus infinity through the bounce (say at proper time zero) and then to proper time of plus infinity. That is, there are worldlines that go through the bounce and have no beginning there, so it seems rather artificial to say the universe began at the bounce that is in the middle just because it happens to be when the entropy is minimized. I think Sean made this point very well in the debate.
In other words, in this model there is a time coordinate t on the spacetime (say the proper time t of a suitable collection of worldlines, such as timelike geodesics that are orthogonal to the extremal hypersurface of minimal spatial volume at the bounce, where one sets 
) that goes from minus infinity to plus infinity with no beginning (and no end). Well away from the bounce, there is a different thermodynamic time 
(increasing with increasing entropy) that for 
increases with 
but for 
decreases with (so there becomes more positive as becomes more negative). For example, if one said that is only defined for 
, say, one might have something like
the positive square root of one less than the square of . This thermodynamic time only has real values when the absolute value of the coordinate time , that is, 
, is no smaller than 1, and then increases with .
One might say that begins (at 
) at 
(for one universe that has growing as decreases from -1 to minus infinity) and at 
(for another universe that has growing as increases from +1 to plus infinity). But since the spacetime exists for all real , with respect to that time arising from general relativity there is no beginning and no end of this universe.
Bill, I think you also objected to a model like this by saying that it violates the second law (presumably in the sense that the coarse-grained entropy does not increase monotonically with for all real ). But if we exist for 
(or for 
; there would be no change to the overall behavior if were replaced with 
, since the laws are CPT invariant), then we would be in a region where the second law is observed to hold, with coarse-grained entropy increasing with 
(or with 
if ). A viable bounce model would have it so that it would be very difficult or impossible for us directly to observe the bounce region where the second law does not apply, so our observations would be in accord with the second law even though it does not apply for the entire universe. I think I objected to both of your probability estimates for various things regarding fine tuning. Probabilities depend on the theory or model, so without a definite model, one cannot claim that the probability for some feature like fine tuning is small. It was correct to list me among the people believing in fine tuning in the sense that I do believe that there are parameters that naively are far different from what one might expect (such as the cosmological constant), but I agreed with the sentiment of the woman questioner that there are not really probabilities in the absence of a model. Bill, you referred to using some “non-standard” probabilities, as if there is just one standard. But there isn’t. As Sean noted, there are models giving high probabilities for Boltzmann brain observations (which I think count strongly against such models) and other models giving low probabilities for them (which on this regard fits our ordered observations statistically). We don’t yet know the best model for avoiding Boltzmann brain domination (and, Sean, you know that I am skeptical of your recent ingenious model), though just because I am skeptical of this particular model does not imply that I believe that the problem is insoluble or gives evidence against a multiverse; in any case it seems also to be a problem that needs to be dealt with even in just single-universe models.
Sean, at one point your referred to some naive estimate of the very low probability of the flatness of the universe, but then you said that we now know the probability of flatness is very near unity. This is indeed true, as Stephen Hawking and I showed long ago (“How Probable Is Inflation?” Nuclear Physics B298, 789-809, 1988) when we used the canonical measure for classical universes, but one could get other probabilities by using other measures from other models.
In summary, I think the evidence from fine tuning is ambiguous, since the probabilities depend on the models. Whether or not the universe had a beginning also is ambiguous, and furthermore I don’t see that it has any relevance to the question of whether or not God exists, since the first premise of the Kalam cosmological argument is highly dubious metaphysically, depending on contingent intuitions we have developed from living in a universe with relatively simple laws of physics and with a strong thermodynamic arrow of time.
Nevertheless, in view of all the evidence, including both the elegance of the laws of physics, the existence of orderly sentient experiences, and the historical evidence, I do believe that God exists and think the world is actually simpler if it contains God than it would have been without God. So I do not agree with you, Sean, that naturalism is simpler than theism, though I can appreciate how you might view it that way.
Best wishes,
Don
#include the following comments by ‘andrew’.
Bill Jeffreys & Don Page – it is an honour to discuss such a lofty topic with two famous thinkers! I will think about your words.
Sean – you have cultivated a stimulating and friendly blog and comments section. It is rare for a discussion on the internet – especially one about god! – to be so reasonable.
Best wishes to all.
Please treat the same sentiments as coming from me as well.
Signed,
James Bonilla, who believes in software component reuse.
James, I’m glad you liked my paper with Jim Berger. It has been a pleasure discussing this with everyone. I think I’ve said just about all I want to say on the topic so unless something really new comes up, I’ll just shut up.
Bill Jefferys, if it is valid for most evidence E to assign positive prior probabilities to theories T_i that give P(E|T_i) < P(E|E) = 1, I don’t understand your claim that is effectively the claim that it is invalid to assign positive prior probabilities to theories T_i that give P(L|T_i) < P(L|L) = 1, where L is the evidence that life (or observership, which is perhaps more basie in the anthropic principle and fine-tuning arguments, but let me follow your use and continue to call it life). I see nothing wrong in assigning prior probabilities to theories (both naturalistic and theistic) that give P(L|T_i) < 1, so your argument with Ikeda certainly does not seem to me to be a sound argument against a form of fine-tuning argument that makes that assumption.
However, if you think that we have reached the point of diminishing returns in discussing this particular issue via comments on this blog, I would be willing to continue to discuss it privately by email (though probably at a slower pace). So far you have not convinced me, and I have not convinced you, though the discussion has brought out that you seem to think that L is sufficiently special evidence that one should not consider theories giving P(L|T_i) < 1. However, I have yet to see why anyone should be convinced that any evidence E, such as L, is sufficiently special in this way. You might assume it and think it is obvious to you, but it certainly is not obvious to me and in fact seems to be wrong.
Don, do you worry about this when you do any physics experiment at CERN or SLAC or wherever? Do you calculate a prior for your existence as an observer under the theory you are trying to test (e.g., that that “bump” is the Higgs) before doing the calculation? If that prior is very low, do you just throw up your hands and say “God did it?” No?
Then why does it matter when you do this particular experiment (determining if “the constants are right”)?
What’s the difference?
Really, what’s the difference?
I really think we need to take this to email. We aren’t making any progress.
Josh, I’m sorry that with being at a physics workshop I have not had time to respond more to your comments as I would like to have done. I did agree with most of your comments of April 8, 2015 at 9:55 am down to the point where your wrote,
“Don attempts to provide justification for his faith by suggesting that the resurrection would be likely in light of the prior of his theism, and also that theism would seem likely given the resurrection. Noting, as above, that he has provided neither the evidence that his theism must be simpler nor the exact Bayesian analysis linking it to Christianity (as well as evidence of the resurrection), we must acknowledge this argument as clearly circular and his noting of priors realistically only tantamount to biases.”
There are indeed many gaps in my argument, just as there are many gaps in the argument that the laws of physics explain our observations (or at least most of them in my view). However, I do not see that they are circular.
One confusion may arise from the highly counter-intuitive meaning of likelihood in probability theory, which is the technical term for the probability of an observation, say O_i, given a particular hypothesis or theory, say T_j. That is, the likelihood of the theory T_j is P(O_i|T_j), the probability of the observation (not of the theory) conditionalized upon the theory (not upon the observation), which is not the same as the posterior probability of the theory given the observation, which is P(T_j|O_i).
To make your sentence “Don attempts to provide justification for his faith by suggesting that the resurrection would be likely in light of the prior of his theism, and also that theism would seem likely given the resurrection” to be correct. one would have to interpret the first “likely” to be in the intuitive but technically incorrect sense of saying that P(R|T_1) is high, where R is the observation of the Resurrection and T_1 in my theory of theism, but then the second “likely” in the counter-intuitive but technical sense in which I tried to use the word, which also means that P(R|T_1) is high. So your sentence only correctly captures what I meant if you interpret both clauses as meaning the same, which is what I do believe.
However, I have at least tried to avoid claiming that I know for certain that the posterior probability P(T_1|R) is high, since this depends on the prior probabilities for my theistic theory T_1 and also for other competing theories. I would say that I would personally assign the priors so that indeed P(T_1|R) is high, but I can easily understand how others might assign lower priors for T_1 so that P(T_1|R) is low.
Therefore, I certainly do not have a complete argument for why one should come to the conclusion that the posterior probability of Christian theism is true. I have only sketched the form of what I regard as a plausibility argument. I do not see that the argument is circular, but it does have many gaps, just as all other arguments for other broad metaphysical conclusions have many gaps.
P.S. As you hoped, I forgive you “for listing this bluntly and impersonally, which was done only for the sake of clarity in discussion,” as I appreciate the honesty that you and others have exhibited even while disagreeing with me.
Bill Jefferys, since you did respond by a comment, I’ll reply by a comment. I think the difference for why we don’t usually worry about our existence in ordinary physics experiments is that we are trying to determine features of the laws of physics that do not depend much on great metaphysical questions such as whether theism or naturalism are true. On these more mundane questions, theists and naturalists think the experiments will reveal essentially the same information about the laws of physics.
However, when one is considering the deep metaphysical questions, what different hypotheses or theories predict about such things as the existence of life do make a big difference. Therefore, in this case one should be able to consider theories in which P(L|T_i) < 1. I don’t see any justification for your claim that one should not be allowed to do this, even if for more mundane questions we do not need to do this. What possible reason could you give for forbidding someone to consider (say assign a positive prior probability to) a theory T_i giving less than unit probability for life, L?
It is now just after midnight here in England, so I shall have to say goodnight.
James Bonilla said:
?”Buddhists and bhikkhus, this is why it is important not to let anyone categorize you. It is not that atheists don’t like to hear this said. It is that they don’t know what to make of such claims. Because if you can invoke magic to explain away things, why can’t I? This is one of the reasons Nagarjuna warned us about categories – they prevent us from perceiving reality. In this case, the category of atheists is a very broad one – there are “atheists” who are more accurately described as agnostics, and then there are “atheists” who simply have been categorized as such by someone else. One should not let oneself be categorized in any way, because to be categorized can mean to have one’s views be decided upon by someone else.”
A very good point…actually one of the more liberating in this thread (which I’ve enjoyed reading). I’ve thought for a while now that it is more possible for an atheist to move onward spiritually than a theist, since an atheist can eventually reject the labels theist/atheist/agnostic as being too limiting. The mind has a need to categorize everything it perceives, which is evolutionally useful and mostly beneficial, but once that process is understood those labels can be legitimately disregarded as mere reflections of that very process. At that point one becomes “unstuck” as theist/atheist/agnostic and is free to move on. Conversely, a theist will always self-reference as a theist and by doing so remains bound to theism.
Don wrote: “What possible reason could you give for forbidding someone to consider (say assign a positive prior probability to) a theory T_i giving less than unit probability for life, L?”
None whatsoever. You can consider counterfactuals all you want, Don. You can consider counterfactuals such as “a different spermatozoan from my father might have made it first to that ovum, so that a female would have been born instead of me.” Totally OK, and totally irrelevant to your life, since it is counterfactual. It was you that was born, not someone else, you know that, everyone knows that, and you can and do use that fact in your daily life. You do not worry that you might become pregnant as a result of sexual intercourse, since that’s not what happens to men. If you got a traffic ticket, you would not go before the court and argue that perhaps someone else might have been born instead of you so that you should get off scot-free.
Similarly, it’s perfectly fine (for example) to think about multiverse scenarios in which some universes have observers and others do not. It’s an interesting physics question of course. The only problem is that it is entirely irrelevant to the question of whether our observing that “the constants are right” for our universe has anything at all to do with whether that should make us more or less confident that “physics is all there is”.
The fact that counterfactually our universe might not have contained observers is irrelevant. It does contain observers, you and I amongst them, that’s a fact, and you can always condition on facts. That’s basic Bayesian inference, and if you do not understand this you do not understand Bayesian inference.
Furthermore, you must condition on relevant facts, facts that affect the actual observations we are interested in (like whether “the constants are right”).
Really, Don, I don’t think you are thinking this through very clearly. Please think on it for a few days and get back to me by email.
Thanks TY for your repeated citations to my blog (and to Sean for providing a forum for the discussion). However I feel obligated to point out that I am currently a postdoc, not yet a professor.
Also, I think Don is clearly correct in his debate with Bill Jeffreys about the need to take your own existence into account when doing Bayesian reasoning (on an equal basis with everything else you know). Most mundane physics experiments don’t involve discriminating between hypotheses which predict different probabilities for our existence, but if any of them do, we would need to include that in the analysis.
For example, suppose the LHC were trying to distinguish between two naturalistic theories X and Y with the property that if X is true, I definitely do not exist (or perhaps, only with 1 in a gazillion chance), but if Y is true, I exist with reasonable probability. The mere fact that I exist is then obviously good reason to prefer theory Y, and it makes no difference when I learned the fact that I exist. Just as if, had theory X predicted that most likely everyone has blue skin, that could also be good reason to prefer theory Y.
As another example, if I were raised by wolves on a desert island and then found by explorers, it would be a fallacy to say that, since I know for sure I exist either way, there is no reason to prefer the theory where I was born of human parents to the theory where I was spontaneously assembled from sea foam.
The correct prescription is something like, consider the space of all possible hypotheses (including those where you don’t exist), assign them each probabilities based on how plausible they are (not taking into account your existence), then remove the ones which don’t contain you and all your experiences, and renormalize the probabilities so they all add up to one again.
Now there’s some reasonable controversy (Boltzmann brains, sleeping beauty paradox, etc.) about how to apply this procedure if there might be a multiverse… But Bill’s procedure is equivalent to segregating the theistic hypotheses and the naturalistic hypotheses into two separate categories T and N, and then conditionalizing on your existence in T and N separately, with a different rescaling factor for T than for N. That is completely wrong and different from the way we do Bayesian reasoning in any other context.
Aaron, you wrote:
“But Bill’s procedure is equivalent to segregating the theistic hypotheses and the naturalistic hypotheses into two separate categories T and N, and then conditionalizing on your existence in T and N separately, with a different rescaling factor for T than for N. That is completely wrong and different from the way we do Bayesian reasoning in any other context.”
No, it ain’t. It’s conditioning on previously known facts, and Bayesian inference always allows you to do this, and mandates that you do it when those facts are relevant to the data you intend to look at.
I make no distinction between T and N. You can always condition on known facts and should do so if the facts are relevant to the data. I really don’t care about whether the hypotheses are naturalistic or not. That is irrelevant to the ability and obligation to condition on facts that are relevant.
If you think that what you wrote is true, you do not understand Bayesian inference. Please read Ed Jaynes’ book. You will learn a lot.
@Don,
I agree with you in that it could very well be that M < N. But ‘M’ (God and the laws He chooses) does not seem to me to be the simplest theory that would predict our experience. In particular, may I ask what do you think of Max Tegmark’s mathematical universe hypothesis, which essentially requires zero bits to specify ‘actual’ physical laws of our universe, since all possible worlds are equally real? Would you consider that to be a simpler theory (and hence worth a higher prior probability)?
If a theistic god created this universe for the purpose of having it inhabitable on this one small planet by humans, it was willing to wait over 13 billion years, and half the useful life of our sun, for it to happen. Another possibility which occurs to me is that any universe which includes any form of quantum mechanics would have the (very remote) possibility of randomly forming one or more vacuum-resistance creatures just by spontaneous assembly of virtual particles (half of which might have to go down a black hole to balance the other half, depending on the physics involved in that universe). It might take several septillion years to happen, but it seems this hypothesized god is very patient. So the range of physical constants which could (given enough time) produce observers might be even larger than Dr. Stenger calculated (which I think was just those in which solar systems could form). (To add a minor footnote to Richard’s excellent summary.)
That’s if you accept physics as all there is, once a universe is established. If you’re willing to let miracles intervene and accelerate things, then I don’t see how any universe could be ruled out (of observer potential).
I hope theists aren’t being like the proverbial “Texas Sharpshooter” who claims that whatever part of large barn-side which has a bullet hole is exactly where he aimed his gun. To be credible, you’re supposed to call your shot in advance, not after the shot was fired (by some 13 billion years).
Of course, maybe this happens to be the best possible universe that a god could have created, and humans the best possible observers; and therefore it’s possible that the TS was aiming at that exact spot on the barn. “All things are possible, to him who believes.” But not to those who use Mario’s Sharp Rock.
It seems that last word on Bayesian inference is not spoken,(if ever).
If it is important, as it seems to be, we lesser informed beings would like to be enlightened. Private communications might serve some purpose, but eventualy some public forum will serve us better.
Thank you Don and others reacting at such a pace and at such a high level of sofistication. And also thanks to Sean for opening up your blog. It can easily develope in a risky, messy affair but you risked it (in faith).
Bill Jefferys said
“Furthermore, you must condition on relevant facts, facts that affect the actual observations we are interested in (like whether “the constants are right”).”
Are we not, as fine tuning proponents here, just pulling out one variable; our existence; from the initial scenario of the anthropic argument, and using Bayes theorem in a way we know full well to be abstract? Provided we do the math right, our stats are accurate for our starting assumptions. The math is not bothered by our metaphysics.
There may be commonly adopted philosophies for mandatory evidence admission into Bayes, but they are not truly mandated in this particular scenario because we have defined exactly what we are calculating for. We are not claiming that it correlates with our only known present reality.
The observer/calculator does not need to be a being that emerged (or not) from the calculations; any being/machine with the same reality paradigm and analytic powers as us would do. For the purposes of Bayesian evaluation by such an entity, we are merely a possible outcome of the experiment.
The following may well be obvious to the experts.
Don wrote;
“Bill Jefferys (April 8, 2015 at 12:11 pm) wrote, “H–>D; if “physics is all there is”, then it is a necessary consequence that we will observe that our universe’s physical constants lie in the anthropic zone.”
I disagree. If “physics is all there is”, then it is a possible consequence that we not exist at all and hence not observe that our universe’s physical constants lie in the anthropic zone.”
This seems to me to cover the fine-tuning ones that would not have succeeded in making us. If we pull our presence out of the evaluation, this statement seems to me to allow us to subsume the anthropic principle into the fine tuning argument.
I shouldn’t have used ‘us’ in the last sentence! Pulling us out allows an hypothesised observer to subsume the anthropic principle into the fine tuning arguement. But we can agree with that hypothesised observer, can’t we?
Concerning the larger discussion, I personally own up to looking for theistic openings anywhere I can perhaps see them. So I have postulated both theistic starting conditions for a deterministic universe and also theistic intervention. Both need investigating on their merits. Miracles would not look like miracles unless they were rare. A small degree of departure from determinism with fixed processes and parameters implies a small degree of intervention in the known universe that made us. That small degree of departure does not do much to change the stats for the fine tuning argument.
I also want to thank all respondents for civility and patience. I also sometimes suspect I am out of my depth but one can only really change ones own understanding when one in convinced on ones own terms. Unless one trusts another implicitly.
Bill Jefferys, Aron Wall and Luke Barnes (I think) and I are disagreeing with part of what you wrote (April 9, 2015 at 6:09 pm):
“No, it ain’t. It’s conditioning on previously known facts, and Bayesian inference always allows you to do this, and mandates that you do it when those facts are relevant to the data you intend to look at.
“I make no distinction between T and N. You can always condition on known facts and should do so if the facts are relevant to the data.”
I agree that Bayesian inference always allows one to condition on previously known facts, but I disagree that it mandates this when the facts are “relevant.”
First, even if one somehow thought (why?) that Bayesian inference mandates conditionalizing on known facts that are relevant, it seems to me entirely ambiguous which known facts are “relevant.” All known facts could be construed as “relevant” in at least some way, so if one conditioned on all known relevant facts, one would have nothing left that one knows for which to calculate the conditional probability. E.g., if the hypothesis or theory is T and the facts are, say, E and E’, both of which are seen to be relevant and hence conditioned upon (and are mutually consistent with T), then the only conditional probabilities one can calculate are trivial ones such as
P(E|T&E&E’) = P(E’|T&E&E’) = P(E&E’|T&E&E’) = 1.
But the Bayesian inference works even if one conditions on no known facts (in principle, though of course the prior probabilities are subjective and it is often very hard to calculate the conditional probabilities, say for the Resurrection given some naturalistic or theistic hypothesis and the facts we know that include the historical records of reports claiming observations of the resurrected Jesus). Then the prior probabilities are absolute priors, logically entirely before all observational evidence, including “life” (which I shall here use as the word Bill used but think it really means observership, the existence of observations, which I personally take to mean sentient experiences, or, synonymously in my use of the phrase, conscious perceptions, though for my argument here one need not agree with me on precisely what an observation is).
I have a paper on Cosmological Ontology and Epistemology and a presentation at a Philosophy of Cosmology conference (at which Luke Barnes gave an excellent lecture) explaining some of this.
For example, I personally might assign a prior probability of 1/2^n for the nth simplest theory T_n. The simplest theory I can think of, T_1 (which should not be confused with my theistic theory that in a previous comment I called T_1, there not implying that it is the simplest theory), is the theory that nothing concrete exists (but only logical truths such as mathematical theorems that I personally believe logically could not fail to exist, at least in some abstract Platonic realm that is not concrete). However, since for any concrete entity C, say God G, or life (or observership) L, or any particular observation O_j, P(C|T_1) = P(G|T_1) = P(L|T_1) = PO_j|T_1) = 0, this theory with the maximum prior has zero likelihood, it has zero posterior probability, P(T_1|C) = P(T_1|L) = P(T_1|O_j) = 0.
The next simplest theory I can think of, T_2, is the theory that all logically possible observations O_j occur with equal probability, e.g., by a slightly more detailed version of Max Tegmark’s mathematical multiverse model that Ruidong Chen mentioned (April 9, 2015 at 7:51 pm). Since presumably there are an infinite number of logically possible observations, the probability of each one is one divided by infinity, which gives P(O_j|T_2) = 0 for any observation one might use to test this theory, so it has a posterior probability of P(T_2|O_j) = 0.
At the other extreme would be, for a particular observation O_j, the maximum likelihood theory T_i_j that gives unit probability for the observation O_j, P(O_j|T_i_j) = 1, and zero probability for all other possible observations. However, if I use my present observation (or all the facts that I know) as O_j, it seems sufficiently complex that I would guess that T_i_j has its index i_j being such a large integer n that the prior probability 1/2^n I would assign to it would make the posterior probability P(T_i_j|O_j) = 1/2^n extremely small.
Therefore, Bill is not using the standard Bayesian assumption that one can condition (or not) on whatever one chooses, and if one conditions just on a hypothesis or theory T_i, one can certainly have P(L|T_i) < 1, contrary to Bill’s arbitrary more restricted assumption.
Simon:
” If “physics is all there is”, then it is a possible consequence that we not exist at all and hence not observe that our universe’s physical constants lie in the anthropic zone.”
Counterfactual. We do exist and we do observe that our universe’s physical constants lie in the anthropic zone.
You can spin counterfactuals all you want, but that has nothing to do with reality.
Here’s another counterfactual: “If the victorious allies after World War I had concluded a peace that was fairer to Germany, World War II might and the holocaust might never have happened.”
They didn’t, and it did. Deal with it.
Don, I am taking this to email. You are not correct. Bill
Don,
Since you took the time to give a pretty thorough reply, let me yield one last critique, then a compliment, then I’m gone for good hah.
Regarding the probability argument, you say:
“That is, the likelihood of the theory T_j is P(O_i|T_j), the probability of the observation (not of the theory) conditionalized upon the theory (not upon the observation), which is not the same as the posterior probability of the theory given.”
I understand that this would make a difference. My argument is that, until you actually provide such an analysis wherein meaningful values can be calculated, I have to take it on faith that your theism is actually a viable theory upon which observations can be really conditionalized. It may be, but I don’t think in practice it can, and I don’t see why I should take it on faith to entertain the idea seriously. That’s why I said “link to the resurrection”–not necessarily in the sense of “it follows,” but in the sense of providing a mathematical means by which you really can conditionalize and have it effect your posterior probability (noting that I don’t take for granted that the resurrection follows from your version of theism). This is why I’m also claiming circularity–I know the means in which you would intend to employ the analysis is not circular (but rather, iterative in a sense); however, I argue that in practice, having not done so, a circular argument is all that we are left with.
Also, certainly we know so few (if no) things for certain. But we do know some things ‘extremely confidently.’ I am willing to build worldviews and lifestyles on these things I know confidently. I should then be able to make objective arguments (objective only in the loose sense that considerable external entities agree) that these things I build upon provide more empirical power than other ideas. Framed this way, we can see that whether you take faith in theism or not is not a case where you must choose X or Y or Z (theism or naturalism or etc.). It is a case of whether, employing skepticism (my bias, and generally the bias of scientists), you are willing to accept the positive claim that is theism or simply acknowledge a lack of knowledge. I accept that everyone’s internal barometer can be different depending on how ‘objective’ their evidence is, but it strong seems to me that, given what we have for the case on theism compared to the various other competing theories, we should remain ignorant, and to buy into it is indicative of wishful thinking. I believe you might find this distinction paralleled in many of our higher-order physical theories (string theory, any TOE candidates, QM interpretations, etc.). I just wanted to make this distinction as I’m not sure it has be addressed in this discussion at large yet.
All that said, I’d like to compliment you for venturing down this train of thought. Moreover, rather than seeking to “deconvince” you of sorts, I’d almost rather hope to encourage you to convince your fellow Christians of the same virtue. I think critical faith scrutiny and dialogue with oppositional parties leads to a much more open social structure, and particularly one that breeds much less of an “us vs them” mentality. In America, we’re pretty darn guilty of that I feel (especially in respect to Christians and atheists), and so I believe any such bridges are actually impressively meaningful and you deserve due credit for it.
Thanks for the discussion and the forgiveness of my bluntness! If you respond to this, know that I’ll read it and consider it fully, though I won’t respond as I need to have some cut-off line to pull myself away from the discussion hah. Regards, and I’m off for good this time!
Aron, I’m glad you are participating in what I regard as an important subject, like those of your own blog and the recent posts on “Fundamental Reality” and “Did the Universe have a Beginning?”
I had promised to bow out of the debate (sorry Simon and others for the change in heart) but as I was standing outside the debating hall, I heard JimV mention Stenger and my ears perked up. JimV said:
“So the range of physical constants which could (given enough time) produce observers might be even larger than Dr. Stenger calculated (which I think was just those in which solar systems could form). (To add a minor footnote to Richard’s excellent summary.)” April 9, 2015 at 9:03
Look gents and ladies: we are free to cite our favourite expert (and that’s admissible) but at the same time scholarship obliges us to name the dissenting voices, so that any one may look up the information and weigh the balance of arguments. It is for this reason that I named reputable theistic physicists and ones with no particular metaphysical leaning in my comments.
In this vein, here is a rough “blow-by-blow” or recap, based solely on the publicly available sources.
1. Luke Barnes’s critique on Victor Stenger’s “The Fallacy of Fine-Tuning: Why the Universe is Not Designed for Us. In his article, “The Fine-Tuning of the Universe for Intelligent Life” published in the Astronomical Society of Australia, 29, 4, pp. 529, Jan 21, 2011. Barnes debunked Stenger’s calculation of the cosmological constant of 10 to the -110 (Stenger), and reminded him that the entropy of the universe implied a fine tuning of 10 to the 10th power raised to the 123rd power of potential universes (Roger Penrose; please see my April 8, 2015 at 6.04 am comment above). http://arxiv.org/PS_cache/arxiv/pdf/1112/1112.4647v1.pdf
2. Stenger response with an article “Defending the Fallacy of Fine Tuning” Jan 28, 2012. http://arxiv.org/ftp/arxiv/papers/1202/1202.4359.pdf
3. Barnes’ response on May 2, 2012, in Letters to Nature, “In Defence of the Fine-Tuning of the Universe for Intelligent Life.”
https://letterstonature.wordpress.com/2012/05/02/in-defence-of-the-fine-tuning-of-the-universe-for-intelligent-life/
4. Robin Collins’ article “Stenger’s Fallacies” and in that critique takes Stenger to task, even on the basic physics. Collins is a well-know Christian apologetic.
http://home.messiah.edu/~rcollins/Fine-tuning/Stenger-fallacy.pdf
I have not seen any subsequent response by Victor Stenger and, since he was the outlier in that regression line (and he must have realised this), I thought he would come back with a suitable response to Barnes and Collins but I haven’t seen one. Too bad that Stenger (God rest his soul) is not alive to speak for himself, but he’s got Bill Jefferys et. al.
I don’t think Bill disagrees with Don’s point, I think Bill disagrees with the notion that such an analysis can result in refuting the claim “physics is all there is.” Bill’s whole point is that possibility cannot be used to detract from measured data. Sure, before conditioning on that data you can do all of the analysis you want, but ultimately the constants took on the values that they have now, so all counterfactual analysis has no bearing on the analysis.
If the opposite were true, then all rejected theories of physics would have to be considered in analysis moving forward. After all, it is possible that the ether could have been real before the Michelson-Morley experiment. If we choose not to condition on that data, then relativity is not enough to do cosmology, we must also evaluate all data in the context of every variant of ether theory. I think it’s safe to say you don’t do this in practice, Don, I think you accept the ether is not a validated theory.
The fact of the matter is that imaginative possibility cannot be evaluated on the same grounds as realistic possibility. Richard’s assumption 3 of his outlining of fine-tuning gets to the heart of the issue. Our description treats every combination of constants as equally likely, but there is no correspondence to what is physically likely. You can’t include this in an argument regarding claims like, “physics is all there is,” when the relevant data does not allow us to even investigate the counterfactuals. You may continue your analysis of these other possibilities if you wish, but ultimately you can’t say anything globally about them once you include the relevant data.
There’s been a lot of back and forth and excess expression of these ideas so it’s hard to say but this seems to be the crux of it to me.
Aether theory* pretty sure we all know ether is real chemical compound.
In response to Ty on Stenger:
The half-baked thoughts I have presented on this thread are my own (no doubt influenced by others of like minds but my own conclusions). I have not read Dr. Stenger’s publications although I have heard of them. I was not the first to mention him on this thread and did not link to him, nor express any opinion on his writings (which I am not qualified to give, although that doesn’t always stop me, unfortunately). My statement that the range of universes capable of hosting observers may be much larger than he calculated does not depend on the accuracy of his calculations to be true, but stands or fails based on the reasons I gave for it.
That said, it is of course fair to present rebuttals to Dr. Stenger’s arguments (but I am not sure it is fair to chide me for not doing so, if that was intended, since I didn’t use them). I checked the links to Dr. Barnes rebuttal, Dr. Stenger’s reply, and Dr. Barnes re-reply, but due to the aforesaid lack of qualifications was not able to make much of them, although a significant part seemed to involve semantic differences over what was said or meant.
Speaking of semantics, this statement by Dr. Barnes bothered me a little:
“The fine-tuning implied by entropy is 1 in 10^{10^{123}} according to Penrose.”
This was in rebuttal to Dr. Stenger’s much smaller estimate of the amount of f-t necessary to produce biological life similar to ours. However, we read from Dr. Sean Carroll elsewhere, this:
“The entropy didn’t need to be nearly that low in order for life to come into existence.”
So Dr. Barnes, who accuses Dr. Stenger of equivocation in terms, appears to be equivocating on the meaning of “fine-tuning”, changing from Dr. Stenger’s meaning (the least amount necessary to produce biological life) to some other meaning.
I note as well he does not address any of the other concerns which I and others have raised here, although perhaps he has done so elsewhere. If not, if his argument is only about the specific number of decimal places in physical constants, then it seems to me it is the Texas Sharpshooter argument. Indeed, he mentions a dart hitting a bullseye, but he never painted a bullseye around the physical constants of this universe before the Big Bang launched its dart. (The Texas Sharpshooter always paints his bullseye around his bullet hole after shooting.)