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
Bill Jefferys, I don’t advocate that one “stack the deck by using priors to favor the hypothesis that he or she wants to come out on top.” But I would suggest that people try equal priors for both naturalism and theism. Then one needs to look at the evidence to narrow down the hypotheses within naturalism (e.g., what the laws of nature are) and within theism (e.g., what the nature of God is). Finally, one needs to examine evidence that would test between the surviving naturalistic and theistic hypotheses, such as the evidence for the Resurrection.
I do not claim that everyone who does this will end up with Christian theology, but I do not think the result would end up so biased against Christianity as it would be if one just assigns naturalism nearly all the prior probability.
I see that other somewhat-related comments have come in after I wrote this before I could get internet access to post it, but I’ll post this now and then go back to other comments, though I probably will not have time to deal with all of them adequately.
St. Simon, thanks for the comment on free will and if you need a good and vigorous disvcussion, see the following blog post:
http://www.wall.org/~aron/blog/fundamental-reality-viii-the-hard-problem-of-consciousness/
There are scriptural passges of determinism so I’m with Professor/ St. Don in some sense.
Right now, I don’t want to abuse my prevelge of Prof. Carroll’s blog and to distract the class (so to speak) from Cosmology to the metaphysics of Concioisuness. One day when I see you in Capetown, we will have long chat covering cosmology and hypothesis testing with Bayesian Analysis.
Josh (April 6, 2015 at 8:35 am), on your point 1), the hypothesis of the Resurrection seems to me to be the simplest explanation for the historical reports if one also makes the wider hypothesis that a God exists who might want to resurrect someone He considers very special. So if the prior assigned to this wider hypothesis is not too low, then under its high likelihood given the evidence for the Resurrection would imply that the posterior probability for the Resurrection is not too low.
What I am much less versed on is the conditional probability for the historical reports purporting to be about the Resurrection given the hypothesis of naturalism, which I am agreeing would make it extremely improbable that the Resurrection actually happened. That is, I do not have a good idea what the likelihood is for naturalism given the historical reports of the Resurrection. Therefore, I do not know how much higher the prior for a suitable naturalism would have to be than the prior for a suitable theism in order that the posterior probability for this naturalism to be higher than the posterior probability for this theism.
I believe that no hypothesis can maintain itself without support of the prior, in the sense that if the prior is zero, no evidence will transform that to a positive posterior probability.
On point 2), I agree that “What we can talk about meaningfully is standards of evidence and whether that evidence exists.” However, we cannot divorce this from the priors, since if one starts with a zero prior for theism, then for almost any reasonable evidence, the posterior probability for the Resurrection will be extremely low.
On point 3), you assume that naturalism is simpler than theism, but I just don’t see this. I see laws of nature that we know (applying most of the time, and not themselves maximally simple, though they certainly do seem enormously simpler than the might have been) as being explained by the simpler hypothesis of a God who loves order (but who may choose to do what is best to satisfy His creature’s desires as well as His own).
On point 4), one should not compare a detailed form of naturalism (with all the known laws of physics assumed) with an unspecified form of theism, but rather with a more specific theism, such as the one that God does what is best and has a nature loving both orderly laws and creaturely happiness. I’m not saying that we know in detail how to predict most of the observed features of our universe from this specific form of theism, but then we do not yet know in detail how to predict most of the observed features of our universe from the best current candidate for a detailed form of naturalism, that superstring/M theory always applies.
Also, it is not quite correct that “Unless you can somehow show that this universe is of maximal well-being, then it most certainly doesn’t predict our world.” My own postulate is that this universe is not by itself of maximal well-being, but it is part of a bigger world that includes God and which is the best.
Furthermore, if both this form of theism and some specific form of naturalism predict that orderly laws of nature apply at least most of the time, whatever predictions are confirmed for these laws of nature are evidence for both this form of theism and for this form of naturalism. Only for certain miracles such as the Resurrection do the predictions differ.
Don wrote:
“Josh (April 6, 2015 at 8:35 am), on your point 1), the hypothesis of the Resurrection seems to me to be the simplest explanation for the historical reports if one also makes the wider hypothesis that a God exists who might want to resurrect someone He considers very special.”
I find this puzzling. I thought you were using the resurrection as evidence for the existence of a god; but above you seem to be saying that the existence of a god is evidence for the resurrection. This seems circular.
Perhaps, Don, you’ve just mis-stated what you meant. If that’s the case, can you clarify your comment to make it clear what’s hypothesis and what’s evidence?
Bill Jefferys (April 6, 2015 at 9:26 am), although simplicity is often in the eye of the beholder, so that I cannot claim that you are wrong, I disagree with your criterion that “we regard a hypothesis as simpler if it allows for fewer observational outcomes than another (more complex) hypothesis.” I would instead regard a hypothesis as simpler if its basic form is simpler. For example, I regard quantum theory as being as simple as classical theory (or at least not significantly more complex), though quantum theory generally allows for many more observational outcomes. Your criterion seems better for increasing the likelihoods (by not diluting the normalized probabilities over many more possible observations) than for increasing the simplicity, so I think you are confusing criteria for high likelihoods with criteria for high prior probabilities.
As I just expressed to Josh, I also differ from your opinion (though again I cannot prove yours is wrong) of “`physics is all there is’ as simpler than a hypothesis that includes a god in addition.”
I disagree even more strongly that “in the limit of a large amount of data, the combined likelihood for “physics is all there is” against a hypothesis that includes a god approaches infinity, so that regardless of the priors, the posterior probability of “physics is all there is” approaches 1.” Unless one assumes no significant prior probability to the hypothesis that the laws of physics do not always apply (but perhaps are violated only under very special occasions), then no matter how many times one finds that the laws of physics are obeyed outside of these very special occasions, one does not get unit or even large posterior probability for “physics is all there is.” That claim is just patently false.
Bill Jefferys (April 6, 2015 at 11:14 am), I first meant that the likelihood of the Resurrection given the historical reports (the conditional probability of the reports given the hypothesis of the Resurrection) is high. Then I meant that if one makes the wider hypothesis that a God exists who might want to resurrect someone He considers very special, the conditional probability for the reports of the Resurrection would also be high, so the likelihood of such a theistic hypothesis given the historical reports of the Resurrection is high. That’s not saying that the posterior probability for theism is high, because that also depends in the priors, but my claim is that unless one assigns a low prior for a theism that would resurrect Jesus, one would not get a low posterior probability for such a Christian theism.
Don, what I wrote was: “The criterion I use for simplicity is identical to the one that Jim Berger and I used in our paper on the Bayesian Ockham’s razor. In particular, we regard a hypothesis as simpler if it allows for fewer observational outcomes than another (more complex) hypothesis.”
This is what “we” (Jim and I) assumed. It’s simple, it’s direct, it’s intuitive. An experiment in which you toss a coin is simpler than one in which you roll a die, which is simpler than one in which select a card at random, which is simpler than the stock market.
I do not agree with your definition of simplicity. It does not make sense to me in the context.
I have explained in detail why my assertion that observing that physical law is respected over and over without exception under every circumstance means that the likelihood ratio of “physics is all there is” against the hypothesis including a god who can trump physical law approaches infinity in the limit. Here, I’ll explain it again:
Let H=”physics is all there is” and G=”a theory that includes a god”.
Suppose we observe a datum D (a number in an instrument, whatever). Then
P(“D is consistent with physical law”|H)=1
and
P(“D is not consistent with physical law”|H)=0
since the sum of the two is equal to 1 by the laws of probability.
But if G is true, it is possible that any particular datum D may be inconsistent with physical law, because a god can overrule the laws of physics at any time that it wants to do so and make an observation happen that violates physical law. Therefore
P(“D is inconsistent with physical law”|G)>0
and therefore
P(“D is consistent with physical law”|G)<1 for any observation D that we make. So long as we only observe (independent) data all of which are consistent with physical law, this inequality must hold.
Therefore, observed over and over again, the combined likelihood (the product of the individual likelihoods of the individual data) approaches infinity. And, so long as you do not assume a prior that rules out either G or H a priori, the posterior probability of G approaches 1 in the limit.
I will point out that your comment about violating the laws of physics “only under very special occasions” begs the question, since you and I have no way of predicting when or under what conditions those “special conditions” could arise. Many people believe in the power of prayer to cure disease, to get their favorite team to win a match, etc. Unless you specify exactly when we can expect a god (whose mind we cannot read) to overrule physics, your “escape clause” via this assertion of yours cannot be taken seriously.
So I believe that it is your claim to the contrary that is patently false.
Models: design, formulation, and testing. That’s my background.
On the question of model simplicity and elegance: Given competing models for some phenomenon in question (black holes, demand for oranges, global warming, etc), for the same explanatory and predictive power, the simplicity prize goes to the one with the least number of assumptions (and if you think about it, it’s not hard to see why).
Simplicity has nothing to do with predictive outcomes. So I’m with the profdessor on that.
Don, posterior probabilities can only be evaluated relative to the competing hypotheses, such as (in this case) that “physics is all there is”, and the (in my view, meager) evidence for the resurrection can be explained by purely mundane means, e.g., lying of witnesses, “whisper down the lane” in which successive telling of a story exaggerates it till it finally gets written down, creation of myths, making previous myth fit the current story (e.g., the birth narratives of both Luke and Matthew fall into this category), the general credulousness of people in the ancient world, etc.
After all, in the ancient world, dying and resurrecting gods were a dime a dozen. Why credit just this one story as fact while dismissing the rest?
To me, the simplest explanation, the one most in accord with my experience in life, is that this is all myth. We humans like to tell stories, fantastic stories, but that doesn’t make them true.
Bill Jefferys,
I’ve been suspicious that this is a large circular argument for some time now. Neither the prior of theism (matter of the specific theism of ‘maximized good’) has been shown to stand supported alone, nor the resurrection. As I understand it, he has already acknowledged that his belief keys on that theism supports the resurrection which supports theism. This is obviously circular, but I think he believes this is ok because there is some reasoning to support either one independently (not enough though) or that the Bayesian thinking is glueing that idea, and so in some sense looking at them together pushes them over the hill of doubt.
——————–
Don,
On Point 1/2)
Yes, if you begin with a prior that is consistent with the resurrection, you will of course find the resurrection more likely. That’s precisely why my whole contention in my first point is that you divorce yourself, at least momentarily, from that prior to see whether the evidence for the resurrection is actually well-grounded on its own.
Now you say:
“I believe that no hypothesis can maintain itself without support of the prior, in the sense that if the prior is zero, no evidence will transform that to a positive posterior probability.”
I have no idea what this means. We can certainly attempt to dissociate ourselves from our relevant biases and look at issues independently. We should do this for the resurrection, indeed as a means to check if the world we see is continually consistent with any preceding biases.
I think you clarified when you said:
“However, we cannot divorce this from the priors, since if one starts with a zero prior for theism, then for almost any reasonable evidence, the posterior probability for the Resurrection will be extremely low.”
Yes we can. We do not have to approach the resurrection from a strict Bayesian thinking, and as I argued, we can not meaningfully do so any ways. We could instead approach it from the same evidential stand point of the historians. And we can do so without expecting to either verify strong naturalism or theism. Certainly there is some creeping prior involved in making any decision, but we can at least allow the ones that would be effected by our decision to momentarily step aside.
Semantically, much of your statements I’m quoting can be paraphrased as an unwillingness to look at the matter without your prescribed biases. This sounds much like presuppositional apologetics and a large barrier to getting at truth.
On Point 3) I feel like you’re missing much of my main point here . Although I acknowledge that I think refraining from positing anything more than the natural world is simpler, this is not my take-home. I was largely saying that so little is known about the mechanics of god that a meaningful comparison can not even be made. Because of this, god shouldn’t be established as a prior on the grounds of simplicity, not because there’s zero chance he could be simpler (he may be), but because we should be biased against establishing biases. We should have a very strong reason to claim god as a prior, and simplicity is not a robust one. You could entertain it all you want, but you would never want to make a truth argument just from this.
On Point 4) I’m not sure what you meant by that first part since I was mentioned both general theism and specific (Christianity) to be thorough. Nonetheless, what does theism predict that we would not already have? Miracles/resurrection, I presume. Then what causes you to root for theism or remain silent must be whether those miracles/resurrection did in fact occur, and you must divorce yourself from that prior to impartially determine whether they occurred or not.
Remember, this is not necessarily a matter of naturalism vs theism. Your choice is not a dichotomy here and could well be to remain agnostic or posit some other choice (maybe a teleology of some sorts for instance). We are not forced to assume a prior of either theism or naturalism, and so we shouldn’t do so without an extremely persuasive reason. If we are going to argue for such a prior, our premise can’t be within our conclusion.
Don wrote:
“Simplicity has nothing to do with predictive outcomes.”
We’ll have to disagree on this. The Bayesian Ockham’s razor, well-known in the Bayesian literature, would also disagree. Jim and I were not the only ones, nor even the first, to point this out.
Don,
You mentioned something in response to Bill that I thought was crucial:
“…but my claim is that unless one assigns a low prior for a theism that would resurrect Jesus, one would not get a low posterior probability for such a Christian theism.”
In such a case your posterior probability for a Christian theism would, so far, be undefined except for the prior. The prior, unfortunately, we have little reason to establish as a bias beyond preference. Therefore the probability contributed by the prior tells us little about truth. What then would still give a high probability for a Christian theism?
On the subject of evaluating posterior probabilities for these hypotheses I stand by what I said before. I agree with Bill Jefferys’ recent points about simplicity given a model of naturalism informs our choice of formal language. An omnipotent god is capable of allowing every sentence to be true, while naturalism would restrict the set of true sentences in the language according to the logical syntax that represents the physical laws of the universe. The information content in specifying naturalism is thus smaller unless the “god axiom” can algorithmically generate every sentence that would be true if a god did exist.
As for the discussion regarding Don’s point about evaluating the likelihood that the resurrection occurred, I don’t think widening the hypothesis to naturalism/theism is enough. I believe every such claim for resurrection needs to be included, each assigned a prior weighted by the degree of belief in them or some other historically supported metric. Jesus being the son of God should also be evaluated alongside every other claimed messiah: http://en.wikipedia.org/wiki/List_of_messiah_claimants
…adding to what Daniel just posted, here is a discussion of dying-and-rising gods:
https://en.wikipedia.org/wiki/Dying-and-rising_god
Also here:
http://www.patheos.com/blogs/crossexamined/2012/04/jesus-just-one-more-dying-and-rising-savior/
The premise that worldview is evaluated in an iterative way seems sound, because data hits our timeline in a consecutive manner.
This started as a discussion as to how one might use a numerical Bayesian methodology to do the evaluation. We have discussed veracity of evidence, and more fundamentally, what constitutes admissible evidence. The values are always likely to be subjective, and the admitted evidence selective as well. Hence detailed discussions on religious faith. A worldview with a naturalistic bias will not only affect the prior, but the credibility assigned to other types of evidence.
Personally I agree with Prof. Page that the fact that the cosmos has thus far yielded to deterministic/statistical mathematical models, and that God left some big clues in history, should be enough to set people on track with worldview.
“For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.
(Rom 1:19-20)”
Projected possibility: The Cosmos turns out to reduce completely to simple deterministic/statistical rules/boundary conditions beyond GUT/GR. Why? (Why ask why? Because we always did up to this point. That’s science).
Hypotheses:
1) Someone really big and clever thought it all up
2)???
Simon noted:
“Hypotheses:
1) Someone really big and clever thought it all up
2)???”
2) Shit happens. We wouldn’t be discussing this otherwise (the actual meaning of the anthropic principle).
Bill,
Careful that “dying and rising gods” is a sort of misnomer category. Most gods in the list don’t fit the category exactly (Jesus is some sense as well).
Nonetheless, all of those gods or god-likes on the list should have their claims evaluated under the same conditions as Jesus and provide real contenders. A prior of a god “who maximizes good” might be able to eliminate some of them, but I have no idea how algorithmically that prior would assign any higher likelihoods to Jesus than some others.
Bill Jefferys, it’s 10:33 p.m. here, so I am heading to bed and will have to see whether I have time to respond more tomorrow, but before I do, I would like to understand what you mean by “Therefore, observed over and over again, the combined likelihood (the product of the individual likelihoods of the individual data) approaches infinity.”
I thought likelihoods were all between 0 and 1 inclusive, so how can their product approach infinity?
Sorry, Don, I meant “likelihood ratio”. The likelihood ratio can be anything between 0 and infinity (including 0). It’s this ratio (from my earlier posting):
Oops, I see that the equation disappeared, probably do to the bug I had earlier. Here, let me correct it all:
—-[start correction]
P(“D is consistent with physical law”|G)<1
Therefore, the likelihood ratio in favor of H and against G of such an observation D is:
P(“D is consistent with physical law”|H)/P(“D is consistent with physical law”|G)>1
Therefore, observed over and over again, the combined likelihood ratio (the product of the individual likelihood ratios of the individual data) approaches infinity. And, so long as you do not assume a prior that rules out either G or H a priori, the posterior probability of G approaches 1 in the limit.
—-[end correction]
(Actually, in a technical sense the likelihood is an equivalence class of functions which differ from the probability only due to a common factor, and technically the common factor can be anything. The reason for this definition is that if you have different criteria for a random experiment, such as “counting heads and stopping the sampling when you’ve sampled twelve times” vs. “stopping the sampling when you observe 9 heads” in a coin tossing experiment, the probabilities if you get 9 heads and 3 tails in 12 tosses are different in the two experiments because the binomial coefficients are different, but they are proportional since the binomial coefficient is, as far as the experiment is concerned, irrelevant to the quantity of interest which might be the probability of getting heads in the long run. This is important in certain Bayesian vs. frequentist discussions and is related to the Likelihood Principle.)
Correction in the last sentence of my correction. Should be:
—-[start correction]
P(“D is consistent with physical law”|G)<1
Therefore, the likelihood ratio in favor of H and against G of such an observation D is:
P(“D is consistent with physical law”|H)/P(“D is consistent with physical law”|G)>1
Therefore, observed over and over again, the combined likelihood ratio (the product of the individual likelihood ratios of the individual independent data) approaches infinity. And, so long as you do not assume a prior that rules out either G or H a priori, the posterior probability of H approaches 1 in the limit.
—-[end correction]
Cautionary note for people using HTML codes for special characters.
Thanks to those that told me how to do this.
But if you decide to edit an already-posted note (before the edit time expires) there’s another danger.
The edit window that comes up converts your carefully coded bit of HTML into the actual character, and unless you recode it as HTML, disaster can strike.
This is what happened with my recent note that puzzled Don.
I had a “<” sign followed by a “>” sign in a later paragraph. The “<” was carefully coded in HTML.
But when I called up the edit window, I did not notice that the edit window had removed the HTML coding and left just “<“. I therefore didn’t fix that, and on completing the edit, the all the text between the “<” and the “>” in the later paragraph just disappeared.
Which made my message at least incoherent.
Apologies to Don, and a suggestion to the person who wrote the edit window software (maybe Sean can contact him): Fix this by having the edit window display HTML for these special characters. Also, the edit window doesn’t have a display of how it will be displayed as does the window for the comment when you first compose it, so that you can scan for such elementary errors. That should also be fixed.
Until then, friends, be aware of this and take mental precautions to prevent it from happening to you!
Bill (Jefferys), I admire your tenacity and conviction, seriously. Full marks go to you and I’d love to have you as a student and may I say, friend. I ‘m reading though my e-mails, and I have a cup of coffee to keep me awake after a tough day. Can I humbly propose something? This argument about the historicity of Jesus and hence whether Christianity is true or a hoax was covered pretty well more the 2 years ago in Professor Aron Wall’s blog posts (pardon me if I sound like a boring promo exec.).
My two cents won’t add much to what the professor/ St Aron is saying, and I don’t believe in reinventing the wheel, so with this I let him do the talking about applying Bayesian analysis in his post “Let us calculate”.
http://www.wall.org/~aron/blog/let-us-calculate/
And this post as well in “Christianity is True”: http://www.wall.org/~aron/blog/christianity-is-true/
Professor Wall is not pulling a wool over readers’ eyes in these two posts. In the second one mentioned, he considers the main factors weighing for and against Christianity and then he methodically looks at each factor. He’s not trying to stack the priors, as a few writers in this blob mentioned.
Main factors weighing against Christianity:
(A1) prior probability due to specificity of Christian doctrine,
(A2) prior probability due to the weirdness of Christian doctrine,
(A3) prior probability due to Jesus being only one of billions of people.
(B) the Argument from Evil
Some of the factors weighing in favor are:
(C) the Fine-Tuning version of the Argument for Design.
(D) circumstantial facts of Jesus’ life prior to his death, making him more likely to be the Messiah
(E) multiple testimonies to the Resurrection,
(F) modern-day miracles.
Friends: please read the [posts and the readers’ responses with an open mind and if you still have questions (no need mentioning this) Professor Wall would happily reply to your e-mails, if understanding is what you desire rather than just writing or winging stuff in a blog.
Just briefly, TY, fine-tuning does not in any way support theism, as Michael Ikeda and I demonstrated in our paper on the subject (citation in previous comments). The fine-tuning argument completely misunderstands Bayesian inference.
As for the rest of your reading suggestions, at age almost 75 I’ve seen it all. I started out as a devoted Christian (dad was a clergyman) and with much study, including of scripture and lots of scholarly works on scripture and theology have come to my present position. Christian apologetics isn’t going to get anywhere with me at this point, so I think I’ll pass on your reading suggestions as I probably already know why they are flawed, and really don’t have the time in my remaining few years to waste on such ventures.
Thanks for thinking of me, though. There is still time for you!
I find this thread frustrating.
Don is correct on most of the technical points. e.g.
1) Simplicity is important in setting priors
2) The preference for constraining theories over non-constraining theories has to do with likelihoods not priors
However, he gets in trouble whenever he needs to estimate something, because doing a full calculation from first principles is impossible (e.g. Kolmogorov complexity is non-computable and encoding-dependent even for well defined theories, and Theism is not well defined. Moreover, by his own admission he doesn’t know how to calculate likelihoods for the relevant evidence given naturalism, and I think he’s over optimistic in calculating likelihoods from theism.) By the way, some attempt to make this quantitative indicates that these are not by any means small errors.
First of all the priors:
So, we’re basing this on simplicity. Well, Don isn’t particularly clear what he means by “God” but he makes it clear that it’s the sort of thing you can attribute sentience and desires to. The only thing which uncontroversially has these properties is the human mind, as embodied in the brain. So how much information is required to specify the structure of the brain — according to this link, the answer is 1.5 petabytes. (As god is not postulated to be the result of anything like human development. The much smaller 6-billion bits contained in the human genome, which creates a human brain through its interaction with the cytoplasm of a human egg cell in the environment of a healthy human womb does not seem like an option for specifying the mind of god. Likewise, the inability to postulate that God is the result of a process akin to evolution cuts out other pathways that might simplify the hypothesis.) So, my estimated prior that a sentient being (e.g. God) is the unexplained underlying reality for the whole universe would be something like 2^-(10^16). Don in contrast has it around 2^-1. This is not a trivial error.
Now the likelihoods:
I think Don is overoptimistic here. I don’t think there’s a way to get to Don’s “1 resurrection per planet and no other miracles” hypothesis simply by assuming a benevolent and mathematical-elegance-loving deity. But even if we do get there, it’s not at all clear that the amount of evidence we have for the most convincing case of purported resurrection is more probable on Don’s hypothesis than on a hypothesis of naturalism.
Assuming Jesus is the most convincing such case. On Don’s hypothesis we must find naturalistic explanations for the next-most convincing such cases including e.g.
1) Romulus
2) Apollonius of Tyana
3) Elvis Presley
4) Tsar Alexander I (complete with an empty tomb story that made it into newspapers as late as the 1930s)
I’m sure I could come up with more if I was really trying, but you get the point. Maybe these cases are less convincing, but they’re not that much less convincing. The point is that either way, we have odd events (on par with those in the Gospels and letters of Paul) that have made it into marginally credible historical sources, and that need to be given naturalistic explanations. Moreover, if I was assuming a God was trying to get his one miracle in the history of civilization noticed, I would expect much better evidence than what we have. (e.g. instead of predicting the fall of Jerusalem in 70ad, and having those predictions recorded in documents that can’t be securely dated before the 2nd century, he could have predicted in the same documents, the supernova of 1054, complete with right ascension, declination, and date of first visibility.) In any event, I don’t think you can make a credible case that the NT is 2^(10^16) times more likely on a hypothesis of theism than on one of naturalism, and I’m not convinced it’s more likely at all.
Bill, isn’t life funny! I meet you in a blog. In terms of religion and faith, we are diametrically opposed. And yet I can see you as a friend. I was brought up as a Christian (Anglican), had my spell of questioning the faith, its teachings, the Nicene Creed and so forth, and did some serious thinking — as most Christians do at some stage of their lives — and my faith has become even stronger. It’s part of who I am and, imperfect as I am, I try to live it. I am one of those types who see no conflict between science and faith. I admire an elegant equation and a beautiful verse from Psalms.
Best wishes Bill, and hope you have found contentment in your senior years.
Allow me to say: Blessings (as your dear dad would have said).