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
The CMBR is old data?? Who said that?
It is irrational, in the objective sense, to put more faith than is warranted in anything, religion and science included.
JimV,
I wasn’t paying attention to how much this is just a pesky semantics issue like you mentioned. Point well taken.
@Josh:
My feeling is that we understand each other’s position very well, but both of us are not buying other side’s argument! I thought I made it clear that for religious experiences, there is no Geiger counter or any other physical detector. So the kind of evidence which is available to physics (science in general) will never be available in the religious context. If you say any non-sensory evidence is fooling yourself then we are faced with no choice. In that case we have to agree to disagree. To demand knowledge of extra sensory perceptions from experiments with sensory organs would be an oxymoron!
Even for sensory experience, there is always lot of ambiguity. If some thing happens in front of 10 people and you ask them about what happened, you will have 10 different opinions!
It is possible that we might have a *real* interpretation of QM some day to the satisfaction of everyone. But in view of 90 years of debate, I would not count on it. What is most likely is that we will drag on with the current picture for foreseeable future. Bohr and Heisenberg were right in suggesting that this stuff is unknowable with certainty even in principle and every time we do measurement we increase our knowledge of the system in the Bayesian sense.
Incidentally, even when you hear a click in a counter or see a track in a chamber, there is a big extrapolation to relate it to a particle whose “real” properties you are trying to determine. Ask Sean or any other physicist working in this area. So physicists have defined a reality in a certain sense which does not match with our concept of chairs and tables as real. This is the main reason why I brought up quantum mechanics in the discussion. One has to be insane to condemn the whole physics as irrational! Lot of classical physics is correct for sure. We have enough faith in it to risk our life by flying in an airplane and NASA has enough faith in classical physics to spend billions of dollars in sending space crafts to planets,which do end up in the right place. But we are talking about something which is completely out of our everyday life experiences .So I keep on insisting that,before we condemn religious experiences as irrational, we better think twice whether everything we know in modern physics matches with our common sense and intuition or not.This is the main point of the debate. We have learnt in modern physics not to turn down counterintuitive models. Again to repeat, we cannot demand more objective picture in our mind from religion than the one from modern physics.
I think Kashyap makes a reasonable point in what he says June 6, 2015 at 8:35 pm.
If this would help discussion (not debating for debate sake) rather than trying to defend a position (true or false in the logical sense), let’s lay aside our personal beliefs about God and just think of what Kashyap is saying:
“Even for sensory experience, there is always lot of ambiguity. If something happens in front of 10 people and you ask them about what happened, you will have 10 different opinions!
“It is possible that we might have a *real* interpretation of QM some day to the satisfaction of everyone. But in view of 90 years of debate, I would not count on it. What is most likely is that we will drag on with the current picture for foreseeable future. Bohr and Heisenberg were right in suggesting that this stuff is unknowable with certainty even in principle and every time we do measurement we increase our knowledge of the system in the Bayesian sense.”
I think most physicists would share this view on this physicist:
“People who agree on the Laws of Physics (to the extent that we are able to discover them at present) can still have radical disagreements about Metaphysics. Of these metaphysical views, some seem irrational and silly, like the Monadic view that all distinctions are illusory and that only one thing exists. But it seems to me that there are several possible reasonable (i.e. non-crazy) views. So given one and the same view of Physics, multiple Metaphysical views can be reasonable. The variety of interpretations of Quantum Mechanics is one prominent example. Choosing between these interpretations requires philosophical arguments; doing an experiment is not enough.” See Models and Metaphysics, by Aron Wall Posted on November 16, 2014.
So there!
Being a supernaturalist at heart, I’m hurrying off to church now. You all are in my prayers.
kashyap,
I agree with almost everything you’re saying in regards to QM in your newest comment. Here’s why I feel I’ve been contending with you though, in light of that agreement. At the end, you say:
“So I keep on insisting that,before we condemn religious experiences as irrational, we better think twice whether everything we know in modern physics matches with our common sense and intuition or not.This is the main point of the debate.”
Of course! I never disagreed with what you’re asking us to do here! However, the problem is that you have been seemingly quite implying that we really are demanding more at large! Now if you think this is not a holistic problem, and is instead an issues where some people do/some don’t (or even a lot do, a lot don’t) and those people shouldn’t, please acknowledge this so I can shut my yap as we would actually agree hah.
Now regarding possible evidence though, you definitely have not “made things clear.” You’ve only simply asserted that “extra sensory evidence” exists. You have not defined it. You have not given examples. You have not explained how we can “sense” it without our senses. You have not explained how we know when things are “extra-sensory” perceptions, or when they are really just perceptions of the mind. You have not discussed how it it accessible to all. You have not discussed how we can tell whether or not our extra-sensory perceptions are fooling us. You have not shown how we can arbitrate conflicting extra-sensory perception evidence. What you have done is simply claimed that a certain type of evidence exists and demanded that we accept it without providing any of the above supports!
Hopefully my comment is not too abrasive there, but when you’re making pretty lofty and terse statements like “I thought I made it clear…”, it’s worth taking a step back to look at that claim. And you seem to be implying that I’m just utterly against extra-sensory perception (whatever that means)–I’m not! Remember, earlier I said:
“The only evidence I, or anyone else, should require is evidence that is accessible to all and able to scrutinized. If you’d like to explain how some kind of extra-sensory evidence fits this bill, I’d be fine with it.”
So I left the door open there but kind of feel like it was shut in my face.
You have a claim–as I see it, “Extra-sensory perceptions exist and should be considered as evidence” (if not, then my apologies and please correct me!). If you want me or others to buy into that claim though, you need to be willing to patiently explain how this is so rather than just demanding it of us.
@Josh
Well! I am glad we agree on my statements on QM.
Now, admittedly, extra sensory experience through meditation is strictly one on one. Either you go through rigorous practice yourself and verify or believe someone who has gone through it or disbelieve without trying it. I do not think there is any alternative. Frankly I do not have any personal experience, nor have I made ESP as my area of expertise. Of course, this is a very difficult area with lots of false leads. There are frauds also. But I am willing to give meditation benefit of doubt in view of statements of some people whom I respect. Belief in religion may have other benefits also such as good behavior, happiness, morality, ethics etc. But there are many contrary cases also, so one cannot rigorously prove it for sure. Experiences in relation to belief in Christianity have been discussed extensively on this blog.
In a way, this is not completely different from people’s belief in scientific results. Understanding of most scientific results, be it discovery of Higgs boson or Genome sequencing, requires years and years of rigorous training and practice which most people do not have. The reason they believe without verifying the truths themselves is that they use the results of many scientific discoveries in their everyday life such as gadgets, medical procedures and variety of technological applications. So their main argument is that the scientific results must be right because of their successful applications. Many people themselves do not have any personal understanding of the validity of the models. Thus, even there, faith plays a big role.
kashyap,
Good, now that we’ve moved on from QM stuff.
I do think you brought up a fairly challenging point. Initially you said:
” But I am willing to give meditation benefit of doubt in view of statements of some people whom I respect.”
And my knee-jerk reaction was to pick on this. But when you put it in the context of:
“The reason they believe [in science issues] without verifying the truths themselves is that they use the results of many scientific discoveries in their everyday life such as gadgets, medical procedures and variety of technological applications…Many people themselves do not have any personal understanding of the validity of the models. Thus, even there, faith plays a big role.”
Which I actually agree with and find it probably the most challenging argument any one has presented thus far. I’ve thought about this before and, indeed, realized that pragmatically there’s some sense of faith in trusting the experts. There are a few differences I would argue that help distinguish between blind faith and esp stuff:
1) We do, as you say, see the results physically and directly (technology).
2) Even if we generally don’t verify particular science results directly, we at least have the ability to. (I’m unaware how this would work with personal perceptions)
3) The way science runs is based on stringent cross-critique by other experts and those who do attempt to validate/disprove results directly.
I would suspect that the ESP (though I’m still not sure what you mean by it) you are talking about is not capable of such things and thereby still leaves you just kind of hanging and trusting others’ perceptions. I would challenge you further that I don’t yet see how, specifically, you could:
A) Differentiate between ESP perceptions and mental perceptions.
B) Differentiate between competing ESP perceptions.
C) Scrutinize one’s own ESP perceptions.
I’m aware that you mention “rigorous practice,” but as that is quite broad, I’m not sure how it fixes the above concerns.
This still leaves me wondering why we would want to bring ESP to the table as evidence. It seems, at best, to only be anecdotal. That’s not to deny the personal experience, of course, but whether it has the capacity to convince others is a different story.
@Josh
I would like discussion of “extra sensory” ideas and things! But I hesitate to engage in that discussion. First of all this guest blog came up because Sean invited his friend, Don Page who is a Christian physicist to explain his views on divinity. I would not want to fill his blog with comments in which he or Sean may not be interested. Secondly, this is not my area of expertise anyway. As for myself, I am not particularly interested in claims about reading someone’s mind or bending spoons from a distance!! I cannot bend spoons even with my hands!! I am very much interested in what ancient Hindu scriptures say about consciousness and divinity and on understanding what scientists have been able to say about consciousness. I have talked to some neuroscientists and psychologists. Unfortunately, they do not know much about the hard question “what is consciousness“from a scientific point of view. There is lot of on line material on such subjects. In particular I would recommend a blog ”dondeg.wordpress.com” run by an American neuroscientist ( Wayne state Univ. professor) who has been meditating, studying and practicing Yoga for years, if anyone is interested. As I mentioned previously, this “extra sensory” stuff is very difficult to study. My aim in these comments was to make readers aware that one should not dismiss religious ideas as “irrational and illogical” when modern physics which strictly deals with sensory data is running into such problems of interpretations. I was just making a general statement, not that some specific individuals like you made such statements.
kashyap,
That’s fine then, as long as we allow that someone can eventually come to the conclusion that a specific religion is irrational after scrutiny. Really I would allow this for all concerns though. I think a good few atheists would disagree with me, but I’m very against dismissing any claim as absurd (as opposed to dismissing claims as personally uninteresting, which I think is fine) out-of-hand.
After a busy two-week workshop in Kyoto, and two days back in my office to finish preparing a paper and talk for an upcoming conference in Peyresq, France, I am now on holiday with my wife in France before the Peyresq conference starting next Sunday. So I apologize for getting quite far behind on this discussion.
In response to a comment by Josh, I agree that I have not given an objective argument that should convince any rational person of Christianity or even just of theism, in the way that a proof in mathematics can be objectively convincing. I do believe that Christianity is objectively true, but our knowledge and interpretation of the evidence seems to be unavoidably subjective. Unfortunately, I am also not nearly the best expert to present the historical evidence for the Resurrection, which I regard as the most important evidence for Christianity.
In response to another comment, just from thinking of what seems to me to be the simplest hypothesis explaining our everyday observations (leaving aside evidence for miracles), I would conclude that theism is more probable than atheism. So that for me does not require miracles. However, for the particular form of theism in which Jesus is the Son of God, I personally need the evidence for the Resurrection of Jesus.
A Bayesian Interpretation of Skepticism
Although I admit that there are severe unknowns when one tries to do a Bayesian analysis, such as the prior probabilities and the likelihoods, it does seem to me a useful framework for discussing how one can come to different conclusions. In this regard, the following occurred to me of how I might express general skepticism within a Bayesian framework:
A skeptic effectively spreads his or her prior probabilities more widely and thinly than a non-skeptic.
That is, while a non-skeptic might assign most of the total prior probability to just a few hypotheses, so that the one with the highest likelihood could come out with a large share of the posterior probability, a skeptic might assign the priors so widely that after weighting by the likelihoods, no single one of the hypotheses comes out with a large share of the posterior probability.
I think this fits with Josh’s view that he is not being specifically skeptical about theistic claims but is just being skeptical in general. So I might regard skepticism as not a `bias’ against a particular hypothesis but rather as a `bias’ against all particular hypotheses. (Of course, one could alternatively say that non-skepticism is a `bias’ toward assigning most of the prior probability to only a small number of hypotheses, presumably the simplest if both skeptics and non-skeptics use Occam’s razor in the form of assigning higher priors to simpler hypotheses.)
If one does not want to see a rather technical mathematical description of this, one can skip the following, but let me give it for those who would like the math:
Suppose both the skeptic and the non-skeptic consider the same countable set of hypotheses H_n, with n being a natural number (positive integer). Suppose each assigns a prior probability P_n to the nth hypothesis. One way to write this is to choose a function f(n), with f(0) = 1, that monotonically decreases (or stays the same) as n increases and that approaches 0 as n it taken to infinity. Then one can say that the prior probability of the nth hypothesis is
P_n = f(n-1)-f(n),
which are nonnegative real numbers that sum to unity when one does the sum over all n.
Let us further assume that both the skeptic and the non-skeptic agree that H_n is simpler than H_(n+1) (so that the hypotheses are given in the order of increasing complexity) and that P_n > P_(n+1) (e.g., by assigning higher priors to simpler hypotheses). This requires that f(n-1)-f(n) > f(n)-f(n+1), so that f(n) is concave upward.
Now my point is that skepticism could be interpreted in a Bayesian framework as choosing prior probabilities P_n that decrease more slowly with n.
For example, one simple (though ad hoc) one-parameter algorithm for choosing the priors after fixing the ordering would be to let the parameter x be a real number between 0 and 1 and let f(n) = x^n, so that the prior probabilities are
P_n = x^(n-1) – x^n = (1-x)x^(n-1).
In terms of this algorithm, skepticism might be expressed by choosing x near unity, so that 1-x is small, and hence the prior probability for each hypothesis (which is bounded above by 1-x) is small. On the other hand, I am less skeptical and might choose x = 1/2, so that P_n = (1-1/2)(1/2)^(n-1) = 1/2^n.
For a skeptic that chooses x very near unity, even a large amount of evidence for, say, the Resurrection, might not suffice to make its posterior probability high. There would be so many different hypotheses of nearly equal prior probability that even if the likelihood of each one is small, after the priors are weighted by the likelihoods and normalized to give the posterior probabilities, they would be so widely spread over the hypotheses that I can see that the Christian hypotheses (assuming that they make up only a small fraction of all hypotheses, as I would believe) would end up sharing only a small fraction of the total unit posterior probability. On the other hand, for a non-skeptic, I would think that the posterior probability of Christian theism would be much higher.
Even if one accepts a formula such as P_n = (1-x)x^(n-1) for the prior probabilities, I see no way to give an objectively convincing argument for choosing x not very close to 1. However, it does seem simpler to me to choose 1-x to be, say, 1/2, than to choose 1-x to be much smaller than unity.
That is, it seems simpler to me not to be an extreme skeptic, but I admit that I don’t have any really convincing arguments that a high degree of skepticism is objectively wrong.
Don, that’s a nifty way of modeling ones degree of skepticism. In theory there could be an infinite number of monotonically decreasing curves f(n) ALL starting from 1. But there could also be a family of such curves starting from 1 but dropping to zero and coinciding with the horizontal axis, which means there is no hypothesis that can convince such a person that God exists . That would be # 7 on the Dawkins scale.
What supports such skepticism in the extreme, I wonder.
Richard Dawkins scale of skepticism:
1. Strong Theist: I do not question the existence of God, I KNOW he exists.
2. De-facto Theist: I cannot know for certain but I strongly believe in God and I live my life on the assumption that he is there.
3. Weak Theist: I am very uncertain, but I am inclined to believe in God.
4. Pure Agnostic: God’s existence and non-existence are exactly equiprobable.
5. Weak Atheist: I do not know whether God exists but I’m inclined to be skeptical.
6. De-facto Atheist: I cannot know for certain but I think God is very improbable and I live my life under the assumption that he is not there.
Don,
That was an interesting take on skepticism and Bayesian. I’m not sure the way we’re thinking about it are compatible in the ways we’re wanting here. Perhaps they are just mutually exclusive epistimeologies. Anyways, I had a few direct concerns on the skepticism/bayesian take and then a couple on the larger argument going on:
——-
Your skeptcisim/bayesian model:
1) On simplicity, you say: “However, it does seem simpler to me to choose 1-x to be, say, 1/2, than to choose 1-x to be much smaller than unity.” Why would this matter? It would be much simpler just to set our entire prior as “1” after all, but that doesn’t make it the best prior. This goes back to where we mentioned appropriate use of Occam’s. Priors would need to show equal utility in establishing truth before it’s worth picking and choosing which is simpler.
2) Also regarding simplicity you mention: “Let us further assume that both the skeptic and the non-skeptic agree that H_n is simpler than H_(n+1) (so that the hypotheses are given in the order of increasing complexity)” But I don’t think this is necessary. Various H_n’s may have similar complexity’s, or even more likely, we may not be able to speak about their complexity in any meaningful way to differentiate them.
3) Regarding the general setup, you say: ” One way to write this is to choose a function f(n), with f(0) = 1, that monotonically decreases (or stays the same) as n increases and that approaches 0 as n it taken to infinity.” And I feel a bit hesitant in the results of n towards infinity. Conceivably, with an infinite number of hypothesis, I would imagine any individual prior would need go to 0, as so I don’t know how a skeptic would commit to any idea in this model. Like I said earlier, things like this make me wonder if it’s really possible to write that epistemology in this context.
I wouldn’t be surprised though if some philosopher or another has already attempted such. I’m not sure if you’ve browsed around for it yet or not, but it might be interesting.
—–
Now regarding a couple of major concerns regarding the discussion at large:
1) Concerning being conniving you agreed: “I agree that I have not given an objective argument that should convince any rational person of Christianity or even just of theism…”. My question then is why would you, yourself, believe? It seems to me that the natural corollary of this is that your own belief must not find theism or Christianity to be conclusively true, and so the push-over-the-edge into actually believing must rest on a preference of some sort. If this is so, why not instead simply acknowledge the possibility but remain agnostic (in the “lack of knowledge” sense) in claims?
2) You don’t seem to feel very confident in argumentation about the resurrection, so wouldn’t you feel equally uncomfortable in trying to convince yourself of it?
3) As there’s nothing on the table that really should convince all rational others, what are we heathens to do hah?
Sorry, my comment near the bottom in 1) should say “concerning being convincing“, as I certainly don’t think anyone is attempting to be conniving hah.
Don,
Something got me thinking about skepticism via the lens of Bayesian though on the drive home, and I realized you could think about it much more simply if desired:
A) A skeptic is one who rarely (if ever) gives the benefit of the doubt in the process. In other words, one would not accept a Bayesian argument as meaningful or valid until one has directly shown how to calculate likelihoods and the justification of the priors.
or
B) A skeptic might just run through the process as normal but then, personally, would require a higher posterior probability than others to make a commitment to that idea in practice.
Or both.
Anyways, this fits me at least and doesn’t require jumping through as many hoops (though the topic is somewhat tangential).
Don
Welcome back, I’m still reading and hope you don’t mind me asking…
I’m not sure what you are saying with your ad hoc model of skepticism. You seem to me to be saying that the skeptic is disinclined to greatly prefer any hypothesis over any another, and that the non-skeptic is inclined to be discriminating (though not necessarily accurately) and assign high relative credibility to a small number of possible evidence scenarios.
I think the non-skeptic in your model, if I’m understanding it right, would be a natural decision-maker. However, which sets of facts (hypotheses) that decision-making tendency locks onto as being of high weighting is still up for grabs. They may not be the Christian Theism ones.
Did I understand you right?
Last night I got thinking about the apologetic explanation for the sacrifice of Jesus to redeem sinners in terms of paying the fine for another person’s criminal act. I parsed it as follows.
There are several parties to the “paying the fine” scenario:
1) A law-maker, e.g., Town Council, state legislature, national parliament, etc., which formed the law or regulation which has been broken.
2) The legal system, minimally consisting of a prosecution, a defense, and a judge.
3) The guilty party who has broken the law.
4) A separate 4th party who pays the fine for breaking the law – perhaps a relative who feels a kinship obligation, someone who already is in debt to the guilty party, a loan-shark who expects to be paid back, etc..
Now apply this analogy to the (assumed) Christian events. The law-maker is “god”; there is no need for a legal system (we can shoot all the lawyers) since the law-maker is omniscient and knows who has and who will break the law (everybody); the guilty party is any individual human; and the fine-payer is also “god”.
So the analogous situation is that a legislature makes a law (knowing that everyone will break it), requires a fine of $1 trillion be paid by the guilty, but being omniscient also knows that some individuals are sorry for breaking the law and are determined not to break the law in the future, so it gives them the $1 trillion to pay the fine, which they then must hand right back to pay the fine, leaving them ethically in debt to the law-maker for the $1 trillion, which debt however will be forgiven.
If I were this god, able to make and change laws (miracles being the temporary changing of a law of nature) and omniscient, I would have simplified matters by adding this codicil to the original law: anyone whom I in my omniscience determine to be truly repentant for breaking the law need not pay the fine; thus eliminating the need to hand out fine-money (torture and crucifixion of Jesus) to be exchanged for an eternity in a paradise rather than an eternity being tortured in a hell. This handout, after all, causes any ethical person to incur a debt for said handout – an infinite debt which cannot be repaid. Since it can’t be repaid, it is implicitly forgiven by the law-maker, who then might just as well and more simply have forgiven the original crime instead of forgiving the debt for the handout.
Anticipating a semantic argument over “gift” vs. “forgiving debt” (although the original concept and use of “gift” implied a return obligation), if one wants to call the debt-forgiveness a gift, one could also call the fine-waiver (without any handout exchange) a gift.
(Side note: under Dr. Page’s theological assumption, as I understand it, time in hell is temporary, and even Hitler winds up in paradise for eternity – so under that assumption there was no need at all for Jesus’s fine-paying sacrifice, and an ethical person might chose to do his or her own temporary suffering in hell rather than sharing responsibility for the JF-PS by accepting it.)
Someone might try to rescue the fine-paying scenario by saying that although it makes things more complicated than necessary, and in way which increases the amount of suffering (by adding Jesus’s), it was good advertising – a great PR stunt. To which I say, a better stunt, as long as we’re using miracles, would be to make Jesus unbreakable, such that whips would not touch him, and nails would not pierce his skin. Then he could still be preaching today, reaching not just a small minority at the time in his home town, and a small minority overall of all the people who have ever lived, but everyone, with his authentic message not distorted by word-of-mouth and inconsistent histories in the gospels. Even supposing there is some law of conservation of miracles to a minimum amount, I can think of other ways to use the miracle-equivalent of showing a resurrected human to a few people before making it disappear (plus Jesus’s other supposed miracles) which would provide better evidence to more people.
Similarly, in the Moses story, a god who can move the water of the Red Sea and bring mana down from the sky could have simply teleported all the Israelis across the Red Sea without a lot of plagues and killing of innocent first-born children. It seems to a skeptic that the Christian god prefers the use of a lot of suffering as part of its mysterious ways. (This makes sense historically since Yahweh was the warrior-god of the El pantheon according to scholars of the region.)
In Bayesian terms, the conditional probability of the Jesus and Moses stories being the result of a super-rational, beneficent, omniscient being with great technological power seems small to me, and have over-ridden the prior which was indoctrinated into me in my youth. (I also think my grandmother was wrong about the moon being made of green cheese, although she made a great elder-berry pie.)
Don, T.Y. and others as interested
Following our discussions on the relationship between mathematics and God, my cousin Prof. Charles Read responded briefly by saying essentially that God is clearly a God of reason, and has set in motion a creation with reason working at various levels, such as cause and effect, both relationally and physically. Math(s) is part of that picture.
I got a response from Simon Wenham, the research assistant for John Lennox of Oxford University. John is a Christian, a philosopher and a mathematician. He was mentioned by someone who set up a talk for me to do on the convergence of science and faith a week or two ago.
Simon said that John did not really specialize in this, and referred me first to William Craig Lane, and then to Vern S Poythress. I must say I have found Vern’s stuff to be really good, if quite hard going. There is an article at
http://www.frame-poythress.org/a-biblical-view-of-mathematics/
I cannot possibly do justice to this. He says that God has “an eternal numerical nature” as manifest in Trinity. In essence, he says that mathematics is inherent in God, and that our math(s) is likely a granted subset of that available to God. Also that our math(s), i.e. that accessible in principle to us, is that decreed for us and our creation. Math(s) models for us the internal consistency of God.
Some highlights:
“(God is) wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties.
It is God who sustains mathematics, not vice versa.
…..the most basic question to ask about mathematical structure and laws is this: are they aspects of creation or of God? Are they, as it were, created things or God, or are they perhaps in some third category? This question is still ambiguous, because its answer depends on what we mean by “mathematics.” “Mathematics” may refer to (a) the historically growing science manifested in textbooks, articles, conferences, lectures,etc.; (b) the thoughts of the mathematicians; or (c) mathematical “structure” for the world, somehow existing independently of our thoughts (two apples and two apples making four apples; two distinct points determining a unique line between them; etc.). Mathematics (a) clearly consists in[created things and activities of created men; mathematics (b) consists in human thoughts which, as such, never have divine status (Isa. 55:8-9; Ps. 147:5).
The Bible never represents the world as being governed by laws as such, independent of the Creator, but rather by the decrees of the King, by God Himself speaking (cf. Gen. 8:22-9:7; Jer. 33:25; Ps. 33:6-11, 18-22; 147:15-20). Because His decrees are in accordance with who He is (Ps. 19:7-9), we expect them to be wise and orderly (Ps. 104:24; Prov.8:22-31; Rom. 11:33-36).
God Himself has a numerical nature. He is three in one. It is interesting that Jesus uses the plural pronoun ”we” (John 17:21; cf. John 14:23) and plural “are” (esmen, John 10:30) in speaking of the Father and the Son. Mathematics (c) is eternal because the Father, Son, and Holy Spirit (3!) are eternal (John 1:1; 17:5; Heb. 9:14). And God’s eternal numerical nature is manifested in creation much as His love, wisdom, and justice are manifested.
Because there is one Lord, there is an inner consistency in everything that He does. Wisdom expresses itself in orderly rule, in justice, in proportioned love and hate (Prov. 8:13-17).
In saying “1 + 1 = 2″ we are thus stating a truth about the Trinity: a truth about the Wisdom of God, and then, secondarily, a truth about the world that He governs. (Note, however, that since the Trinity and the Wisdom of God are incomprehensible, God’s own “mathematics, as it were, is not accessible to us in all its fullness. We cannot assume that our mathematics (b) is necessarily all true or exactly equivalent to God’s “mathematics.”)”
JimV,
Just an aside to you– I’ve never personally found focusing on very specific parts of religious Dogma (such as the rationality of the resurrection atonement) a very productive conversation route personally. It always seems to be like trying to grab a fish. For instance, even if the there was acknowledgement that the face-value scenario was unethical or irrational, there’s always a backdoor for the theist that god worked in such a way due to some other ethical concern or instructive point. These points are further justified by god being the sole provider of ethics, and therefore everything remains conceivably justifiable if god willed it within such a system. To argue against this would be to work from the ground up how and where we should derive our ethics (which is a whole other rabbit hole and distraction). That’s one reason why I try not to focus on actively attacking any particular point of any religion, but an even stronger reason not to is that, even if you forced the theist to divorce his/herself from that particular piece of dogma, their belief system can normally be sustained by claiming they don’t rely on that particular piece. So like I said, even if you can catch the fish (a particular point), it’s not something easy to hold on to.
Anyways, I just wanted to mention that in case the thought meant anything to you. To me, it always seems to be much more effective to keep the conversation along the lines of simply “Why should we actively believe?” and addressing the responses generated. Herein you generally find (it seems to me) that it all boils down to faith or preference anyways, so it’s a bit quicker cut to the core.
Josh, I admire your patience and endurance, and perhaps it is the most productive method, certainly for keeping a discussion going, but … it seems to me many of the same circular rationalizations can be applied to the “why believe” question (e.g., because the Bible tells them to). In fact, one possible answer to your question is “why not?” – at which point my arguments come into play (such as they are).
I don’t expect to change anyone’s mind, but feeling the “paying the fine” analogy is an unsatisfactory one, as I do, I feel behooved to point out its flaw, that it becomes ridiculous when the law-maker, judge, and fine-payer are all the same entity. They can ignore me or fall back on “god’s ways are incomprehensible” or come up with a better analogy, or some other counter. That’s up to them; I’ve done my part. I am sure that I am not the first person to see that flaw, probably not by hundreds or thousands of years, but having worked it out for myself, I don’t see why, if people are making a flawed argument on a science blog, that I can’t point it out. That’s what we do on science blogs. (It usually isn’t very productive in terms of changing people’s minds when it’s a science issue either, but it is the way science is supposed to work.) I didn’t go on a religion blog to do it, nor would I.
JimV,
Many of the same rationalizations can and, indeed, are often applied to the question of “Why I believe.” Something interesting I’ve noticed though is that, when such things are given as the primary reason for belief, there seems (in my anecdotal evidence) a higher willingness to recognize that the argument is not ultimately 100% convincing. This then can lead to a discussion about faith or standards of evidence, which I might argue is the final arbitrator of whether one is willing to believe such claims or not.
A quick example might be worth it here. I might ask a theist “How they know that Paul saw Jesus on the Road to Damascus?”, and of course the answer must be some semblance that “The Bible told me so.” If I called the theists on this, it would probably be a long, windy, and stubborn dance. Now if I ask the theists why they believe, they respond with the Bible, and I call them on it, the response normally seems softer and more willing to admit where they have faith (whereas I almost never see acknowledgement of faith in the former conversation).
That’s just my anecdotal sampling of course, but to me getting at that root issue of faith is prime. All the same, I do think pointing out those specific arguments as you were is important too! I think these such theistic arguments need to have their true colors revealed. And I suppose the type of argumentation we should employ depends on our intent.
JimV
You are indeed identifying a fault line of Christianity. Not that the fault can destroy believe in God
To state my position:-I am a serious believer in God, the Source, Creator an Upholder of the material world.
There is a small slow but sure growing group of believers coming to the realization that sacrifice and atonement to restore relationship is not fitting with their perception of the what God is. Jesus swept away primitive man’s perceptions in declaring that God love all his creatures and that the relationship was placed on a child-parent basis underpinned by divine love. Jesus enlarged this concept to embrace all humanity.
In a slow evolutionary way Christianity will change part of its doctrine of atonement away from Paul’s concepts.
William,
If a person no longer believes in the foundational claims of their religion, those claims most basic to their religion such that without them the religion is unrecognizable, then what good reason is there to suppose that any of the other claims that are left are accurate? If you have decided that the sources of your religion were in error about the primary “structural components” of the religion, why then continue to believe that anything from those sources is accurate?
It seems to me that if reason were the only mode of choosing what to believe, which of course is not the case with any human being, that by the time you get to the diluted Christian beliefs typically claimed by modern day “liberal” Christians, that so often scoff at atheists who criticize more traditional Christian beliefs along the lines of, “no one actually believes that anymore” (when actually plenty do, just look at the comments here, or the words of the champion apologist WLC invoked frequently here), then the only reasonable position that retains a deity would be deism.
JimV wrote (June 14, 2015 at 10:37 am)
(Side note: under Dr. Page’s theological assumption, as I understand it, time in hell is temporary, and even Hitler winds up in paradise for eternity – so under that assumption there was no need at all for Jesus’s fine-paying sacrifice, and an ethical person might chose to do his or her own temporary suffering in hell rather than sharing responsibility for the JF-PS by accepting it.)
No, I think that Jesus’ sacrifice is just as necessary if all are eventually saved by it as it would be if just those who put their faith in Jesus in this life are saved.