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
On Bill Jefferys: “Think “Messiah.” As a Jew, that was what Paul was expecting, and his brain fart pushed him over the edge to regard Jesus as Messiah, not only for Jews but also for gentiles.”
The historical puzzle here is that Jesus did not at all fit the picture of the expected Messiah. A “Messiah” who would be executed by the pagans was a ludicrous notion. If a “messiah” is killed by the pagans, and has not liberated Israel or rebuilt the Temple, that’s a sure sign that he’s another in a long line of *false* so-called messiahs. And one certainly shouldn’t be worshipping this recently-executed person as divine. That’s why Paul was going around persecuting Christianity as a heresy. There were absolutely no predisposing reasons for Paul to suddenly view this shamefully executed Jesus, of all people, as Messiah or as divine. Note that I’m not saying that’s there’s not a possible natural explanation for whatever happened with Paul. I’m just saying it seems one has to find a different direction than “predisposed to believe in Jesus”, or analogies to Hindus having visions of their deities.
That’s the nature of brain farts, Rick. They are unpredictable.
But my point is simple. Paul didn’t have a vision of Lord Krishna, nor of Lord Buddha, nor of Gitchee Manitou. The vision he had came straight from Judaism, even if it was in an unexpected way, and even if it modified the traditional Jewish view of Messiah.
Bill Jefferys and others question my assumption that God + Universe can be simpler than Universe alone. Let me explain by a rough analogy why I think God + Universe can be simpler. Conceptually dividing Universe (capitalized to mean the proper noun for our universe) into Nature (what we physicists normally study, our physical world) and Sentience (our first-person subjective conscious awareness, the sentient experiences or conscious perceptions that sentient beings have within our universe), I would say that in a certain sense that I shall explain, there is the very crude analogy,
God is to Universe as Nature is to Sentience.
God:Universe::Nature:Sentience
In particular, I propose that just as it seems simpler to explain Sentience by postulating Nature, it seems possible that it is simpler to explain Universe by postulating God.
My present sentient experience (which I synonymously also call my present conscious perception, all that I am consciously aware of at once) is all that I directly know right now. I would like the simplest hypothesis to explain it. My experience is complicated, including visual, auditory, tactile, and other sensations, awareness of beliefs of what some of these mean, memories I am presently conscious of, emotions, qualia, etc. However, there seems to be enormous correlations between many of the parts, such as the perceived frequency at which letters and spaces appear to me on my laptop screen and the perceived frequency of auditory clicks that in my experience are believed to be tappings of my fingers on the keys. These correlations lead me to believe (I think quite naturally, even before any reading in philosophy, just as many people believe quite naturally in God, even before any reading in theology) that Nature exists, a physical world external to my sentient experience that seems to have even higher correlations and regularities than my present sentient experience. Scientists have codified and compressed these correlations into laws of nature, which I believe have been remarkably successful in explaining much (though certainly not all) of our sentient experiences.
In the idealized case in which we could know the measures for all sentient experiences in all complete theories for which we would assign positive prior probabilities, I could use the normalized measure of my present sentient experience in a theory as the likelihood of that theory, multiply by the prior, and divide by the sum of these products for all theories to get the posterior probability of the theory. Of course, we are a long way from being able to do this or even to have any plausible theory for which we can calculate this likelihood, but I can imagine that if we were able to do this, we could find a theory that maximized the posterior probability. There would be no guarantee that this theory is right, but for the sake of argument let us assume that it is (or else just imagine the correct complete theory that gives the normalized measures of all sentient experiences).
The evidence from the perceived regularities of nature, including the discoveries of science, strongly suggest that the correct complete theory is much simpler than it logically might have been. It seems to be possible to do an enormous compression of the data that we have into much simpler laws of nature. On the other hand, it also seems to be the case that logically the laws of nature could have been even much simpler yet, such as a complete theory saying there is nothing concrete at all, no physical world, no sentient experiences, no God, nothing but abstractions such as mathematical theorems that one might believe `exist’ in some sense in some `Platonic world’ of logical necessities that logically cannot not exist, even though there would be no concrete beings, even God, to be aware of any of them. Of course, there are also many other theories that do include the existence of concrete entities that certainly seem simpler than what could fully describe our universe, such as a theory that only empty classical Minkowski spacetime exists, with no quantum state or quantum fields, and no sentient experiences.
So although I believe the correct complete theory of our world is enormously simpler than it might have been, it looks to me almost certain that there are still very many other logically possible complete theories that are even simpler. To put it another way, I have the hope that the world can be completely described by a theory with a finite amount of information, say a finite number N of binary bits, but it seem almost certain that N is considerably larger than 1. (E.g., I might take the one bit 0 to denote the world with nothing concrete existing, and the one bit 1 to denote the world with all of the infinitely many logically possible sentient experiences occurring with equal measure, which then if normalized would give zero probability for any particular sentient experience and hence zero likelihood for that simple theory.)
So in my mind, Sentience (all sentient experiences) may be completely explained by Nature, which may be completely explained by a complete theory that has only a finite number of bits N of information in it, but this measure of information N is not maximally simple, even though it is simpler than an infinite number of other logically possible complete theories. I strongly believe that the correct complete theory of Nature would have much less information than that in a typical individual sentient experience, such as my own present one, which might require P bits with P much greater than N. Therefore, I believe that one can get a much simpler theory of Sentience by postulating the existence of Nature, so that Universe = Nature + Sentience is much simpler than Sentience alone.
Thus adding an entity to Sentience does not make the total more complex. Often the whole can be simpler than the parts, as I believe the full set of natural numbers is simpler than almost all individual members of this set (their complexity lying in the complexity of their selection out from the simple set).
The analogous question is whether or not one can similarly get a simpler theory of our Universe by postulating the existence of God, so that God + Universe is simpler than our Universe alone. Because of the analogy above, I certainly believe this is logically possible. Whether it is true is another matter.
Becoming much more speculative now, I do wonder whether postulating a God who loves simplicity in any universe He creates (low N for our Universe) and who maximizes the total value (His appreciation of simplicity and the value, say something like the pleasantness, of the sentient experiences in the universe or universes He creates) might require even less information, or a smaller number M of bits to specify, than the N needed to describe our Universe. Of course, I cannot be sure of this, but it does seem to be at least plausible that M might be less than N, in which case God + Universe would be simpler than Universe alone.
Now I will admit that this reasoning alone (e.g., leaving aside evidence for the miracle of the Resurrection) would leave me highly agnostic about the existence of God. I am mainly presenting it here as an argument that just from the evidence of our sentient experiences that lead to the postulate of fairly simple laws of nature for our Universe, one should be at least open to the possibility of the existence of God. Then one can approach historical evidence for the Resurrection without having a huge bias against the hypothesis of theism.
In February 2007 I emailed Richard Dawkins the following syllogism I wrote, with help tidying it up from philosopher friends such as William Lane Craig, to summarize Chapter 4 of Dawkins’ book, The God Delusion:
1. A more complex world is less probable than a simpler world.
2. A world with God is more complex than a world without God.
3. Therefore a world with God is less probable than a world
without God.
I then wrote in my email the following:
Do you think that this accurately gives a succinct formulation of your argument? Can you suggest any improvements?
Personally as an evangelical Christian, I would primarily object to Premise 2, as noted in my previous email at the bottom. However, your Oxford colleague David Deutsch has also objected to Premise 1 in his interesting email below. So I shall have to rethink my fundamentalist scientific faith in simplicity. However, I have little idea what to replace it with. Do you or anyone else have any suggestions?
Dawkins that same day sent back the following obviously hurried response:
Date: Thu, 1 Feb 2007 20:06:27 +0000
From: Richard Dawkins richard.dawkins@zoo.ox.ac.uk
To: Don N Page don@phys.ualberta.ca
Subject: Re: Revised syllogism to summarize Richard Dawkins’ main argument
for atheism in The God Delusion, Chapter 4
Your three steps seem to me to be valid.
Richard Dawlkins
Don
I think , in terms of naturalism, it is a category error to argue in terms of causation when by definition what is being considered is the everything that is. Causation only applies to processes that are a part of the universe. This actually may not be a good argument against theism since what theists and naturalists disagree about , is whether or not the natural universe is all that exists. But at least naturalists have a coherent explanation absent a god hypotheses in my opinion.
But we need to get beyond these more or less respectable philosophic arguments to get at what is really being claimed. I don’t see how any of this connects to the Bible or any other alleged holy book. Here , it seems to me, simple historical scholarship ,and simple common sense, is devastating for the veracity of these books. I find it amazing that anyone could view these books at anything other than myth based understandings from a pre scientific community. Here I think the will to believe is neutering the mind’s ability to engage in rational analysis.
For example, in Christianity;
God needs a gruesome blood sacrifice to keep himself from damning billions of humans to infinite torture, but this is conditioned on belief without evidence, so billions are condemned anyway , yet he loves us.
If the message that Jesus brought to humankind is so important , why didn’t he come at a time when he could be on CNN , isn’t the point of a message to have people believe it , not punish those with infinite torture who don’t?
And why is the Bible true and other “holy” books lies? Don if you were born in Saudi Arabia, wouldn’t you be making the very same arguments for the Quran? If god really gave us a holy book, shouldn’t there only be one , and there would be no doubt about it.
It seems to me that by applying rational analysis and some simple common sense, it’s obvious that ALL these holy books are relating man made myths that no reasonable person can take seriously. I think the problem here is the will to believe.
I still don’t get how we’re measuring simplicity with “bits” of information when the informational content of a bit is determined by a choice of formal language. Not every language has the same “bit” and consequently statements do not have the same informational complexity represented in different languages. For example while the set of all natural numbers is “simpler” than the set of all real numbers in a von Neumann universe, the Löwenheim-Skolem theorem requires there exist models of ZFC where the real numbers are equally complex as the naturals (there exists a bijection between the two). In this example we’re syntactically restricted to ZFC set theory which is not analogous to Don’s argument. If we relax that the syntax is ZFC, we can get even more variance.
For the cosmological simplicity argument, the choice of language is completely up in the air. To use informational complexity as the metric is to assume the universe operates in some “absolute” formal language. Usually the assumption is a formal language that could be computed with a Turing machine, though there’s no reason to assume the universe is limited to such choice of languages. Further we can’t assume that the universe is a Turing machine or abstract machine of any particular kind.
Without the assumption the universe is a Turing machine (or some particular abstract machine), I don’t see how it’s possible to come up with an absolute definition of complexity classes. If the models of the universe don’t have a common formal language between them or even a common method of evaluating sentences in their respective formal languages, then there’s no common metric of complexity that can be compared between the different models. Doing so will yield different results depending on which model you’re using to calculate the simplicity. I just don’t see then how simplicity can be a cosmological metric for all possible models of the universe. I would need a model-independent formulation of simplicity to buy this claim. Casting the definition in information theory is not model-independent.
Re:
“1. A more complex world is less probable than a simpler world.
2. A world with God is more complex than a world without God.
3. Therefore a world with God is less probable than a world
without God.”
I see some possibility of semantic confusion between what Dr.s Page, Dawkins, and Deutsch mean. Are we more apt to be mistaken when assuming an unnecessarily complex cause than a simpler cause? I would say yes, as I think would Dr. Dawkins. On an absolute scale does a complex cause turn out to be the case much less often than a simple cause? I don’t know that probability and wouldn’t feel confident assuming a value for it in a syllogism.
Of course as Mr. Zannelli says above, to even consider probabilities as a useful way of thinking about something, we must assume multiple cases (to give a denominator for the probability ratio), which might be problematical with respect to “the Universe”. However, as long as we are using what I consider the Dawkins viewpoint where the probability refers to our chances of making mistaken conclusions based on incomplete evidence, then there is plenty of denominator, and numerator, in my case.
Don, the reason why I think that physical theory + god is more complex than (the same) physical theory alone is simple, and goes right to my paper on the Bayesian Ockham’s razor with Jim Berger. The former has more degrees of freedom since more things can happen if you have a god that can override the predictions of physical theory alone.
But my argument against your assertion that repeatedly observing that physics is respected is a likelihood argument and has nothing to do with the priors.
Don,
I think that one point of confusion may be a logical one.
Earlier, when I gave names to hypotheses, e.g.,
T=”physics is all there is”
and
D=”Don’s theory” (i.e., that god is somehow involved and can do things contrary to physical theory)
I wrote T’={T,D} to indicate the combined theory.
But the addition of D did not mean that T was restricted further by the addition of D, but rather (as I noted) that D could override what T predicts (as for example resurrecting someone from the dead).
The reason why I used a comma ‘,’ instead of an ampersand ‘&’ is because I use ‘&’ on informal web communications to mean logical conjunction, that is, only things that are compatible with both hypotheses can happen.
I used a comma ‘,’ as an indication that this was a logical disjunction, that is, things that are compatible with either hypothesis could happen.
This is the underlying reason why I think that T’ is more complex than T. It allows more things to happen than T by itself.
It may be that using ‘+’ is misleading because it is read “and”, since we shouldn’t be talking about ‘and’ but ‘or’ when we talk about things like “physical theory + god”. (That is a logical ‘or’, not an exclusive ‘or’, of course. Logical ‘or’ is true if either hypothesis is true.)
So, does this help you to understand why I think that T’ is more complex than T?
Your first paragraph mentions evidence, but provides none. Then you try the bait-and-switch, talking about plausibility, not evidence.
The record is much weaker than you make out, unless one substitutes “church tradition” for “historical evidence.” You could start with Wikipedia, which notes:
Using that as a starting point, you could investigate these traditional accounts more deeply. You will find that they do not go back to the first century.
Let’s see what the Catholic Encylcopedia has to say on the topic of St. Thomas the Apostle:
Two things I will point out here:
1) The claim that mentions in the Gospels, pious accounts written decades after the alleged described events, constitute “certain knowledge.”
2) It goes downhill from there, and even the Catholic Encyclopedia acknowledges the questionability of other accounts.
This is really weak sauce.
Bill
‘But the addition of D did not mean that T was restricted further by the addition of D, but rather (as I noted) that D could override what T predicts (as for example resurrecting someone from the dead).’
-What physics is over-ridden?
-Is the cosmos permeable to the interventions of God, perhaps by some hidden asymmetry?
Bill, I don’t think Don is saying “Universe+God” is strictly a disjunction or conjunction of every sentence in T with every sentence in D. I think he’s claiming T and D have generating axiom schemata that when combined result in a set of sentences that are just as complete as sentences in T but have less complexity. I don’t think this is hard to imagine. There are plenty of statements within ZFC and ZF (ZFC without axiom of choice) set theories that are shared. However, the proofs for them in ZF are much more complex without the axiom of choice even though ZFC has more axiom schemata. I think Don is using this as an analogy. You wouldn’t encode ZFC as the disjunction of every sentence generated by the axiom of choice and every sentence in ZF, that isn’t right.
Don, this analogy is at the heart of why I find your case for God unconvincing.
Yes. It works formally in the sense that, if you assume a God (who would want to create a universe like ours) is simpler than the universe alone, in the same way that Nature is simpler than sentience alone, then you get the conclusion you want. But there’s absolutely no reason to think the assumption holds. On the contrary, the way we talk about these things indicates that God and Sentience are the same sort of thing (having feelings, desires, beliefs etc.), and should therefore be assumed to be similarly complex, while Nature and the Universe are also the same sort of thing, if not outright identical. The fact that making your analysis work requires analogizing completely unlike things is a bad sign. There are also good reasons for thinking God, as traditionally conceived, is not a very good explanation for physics. The closest thing I know of to an attempt to derive laws of physics from theology resulted in Aristotelian physics — which is decidedly incorrect (and even there, the reasoning looks a lot more like rationalization than true deduction from first principles.)
I noticed similar issues with your “optimal argument for God” by the way. I must say when I got around to reading it, it was a theodicy I had never seen before — God as a utility monster. It is very clever, but it is 100% backwards from how Christianity typically conceives of things. In your scenario, humans suffer so that God can experience Plato’s heaven made real in our mathematically elegant universe. However in traditional Christianity, it is God who suffers so that humans may experience heaven. It might be a better fit for Islam actually… but even there, very human politics looks like a much more realistic explanation for the origin of the ideology.
Daniel Kerr, you made an excellent point in writing, “I just don’t see then how simplicity can be a cosmological metric for all possible models of the universe. I would need a model-independent formulation of simplicity to buy this claim. Casting the definition in information theory is not model-independent.”
I alluded to this problem in my email to Dawkins when I wrote, “David Deutsch has also objected to Premise 1. … So I shall have to rethink my fundamentalist scientific faith in simplicity” (a faith that I seem to share with Dawkins and most other scientists, and indeed with most other humans). This seems to imply that Occam’s razor is unavoidably subjective, and I would like to understand better how we can be justified in using it.
However, the fact that nearly all of us continue to use it (even if unknowingly) shows that this is a problem for both naturalists and theists (and indeed nearly all humans), so I do not see that it tips the balance in either direction, though it might be cause for being less dogmatic about any of our conclusions.
Don there’s no doubt it’s a problem with cosmological arguments in general, not just your argument. I think when dealing with an assumed theoretical framework for the universe (not a cosmological argument) it’s okay to use a model-dependent concept of simplicity. As you pointed out before it may not be the “truth,” but it will yield the most likely, practical model. So for a naturalist’s approach, I think it’s fine for applications not referring to the origins of the universe.
However, it is your claim that cosmologically, simplicity is the metric for assigning likelihoods to possible models. I can buy given this model-dependent formulation of simplicity it’s possible that Physics + God, though requiring more information to define the axiom schemata, overall lead to models which are of lower complexity class than Physics on its own. Again, this is making a certain assumption about the architecture of the Universe implied by your choice of simplicity metric.
The definition of simplicity is not as important to other cosmological arguments, but it is integral to yours. I agree with you that the balance won’t be tipped between your argument and those using the same metric of simplicity, but your argument will certainly be tipped depending on the definition used when compared with cosmological arguments that don’t utilize simplicity.
I found Daniel Kerr’s example of ZFC vs. ZF very helpful in trying to understand Dr. Page’s viewpoint. My issue with that viewpoint, however, is still what I tried to state in my first comment: I know of no, and can conceive of no (which of course may be my fault) natural principle which is understandable more simply with the addition of the God Axiom. That is, barring miracles (supernatural rather than statistical), which have never been observed with sufficient reliability for admission to a peer-reviewed scientific journal, nor to a court (except for ecclesiastical courts, which permit hearsay evidence). To my mind, adding this axiom only generates further questions: where did God come from? How does it manipulate the laws of physics? What are its motives? These issues have led to disagreements which, under Christianity, have generated many separate sects – Google says 41,000, to which I think we must add one for Dr. Page’s idiosyncratic views on hell. This does not seem to be the result one would hope for from a simplifying axiom.
“Why does fire burn? The fire god makes it burn.” sounds simpler than the principles of combustion, but to me this is only because it avoids the questions of how and why the fire god does this, and what produced the fire god. “I don’t know, let’s do some experiments and see how much we can figure out” seems like a simpler and better answer to me.
Bill Jefferys, thanks for your comments, which help me see what I think is the difference between our assumptions. I think you are assuming that naturalism is a single set of laws of physics, and that theism is this set plus the possibility that God could perform miracles in arbitrary ways to violate these laws.
On the other hand, I am pointing out that naturalism per se allows many different sets of laws of physics, and I supposed the actual set required N bits of information to specify. (This would have to be relative to some background information or “a choice of formal language” as Daniel Kerr nicely explained; here I shall have to leave aside this difficult issue.) Then there would be about 2^N logically possible sets of laws of physics simpler than the actual one.
Also, the theism that I am assuming includes the hypothesis that God does what is best, so although I agree that it is logically possible that a god could arbitrarily do anything not incoherent, I am assuming that God’s nature constrains Him to maximize the good. Now I do think that what is the best not only includes the good within all universes God creates but also what is good for God Himself, and this latter depends on further aspects of the nature of God, besides His nature to do what is best. I postulated that it might require M bits of information (again, in some unknown formal language) to specify the full nature of God. But then this nature would determine what set of the laws of physics God chooses to create, and what miracles He chooses to perform for actions that He does differently from those laws.
Finally, I was arguing that it certainly seems possible that M is less than N, in which case theism would be a simpler explanation than naturalism. I personally believe that this is actually the case, but I admit that this belief is much more speculative, so that others might well disagree.
“-What physics is over-ridden?”
That miracles do not happen if physics is all there is. No resurrections. No water-into-wine. Etc.
“Bill Jefferys, thanks for your comments, which help me see what I think is the difference between our assumptions. I think you are assuming that naturalism is a single set of laws of physics, and that theism is this set plus the possibility that God could perform miracles in arbitrary ways to violate these laws.
“On the other hand, I am pointing out that naturalism per se allows many different sets of laws of physics, and I supposed the actual set required N bits of information to specify…”
Not quite, Don. By naturalism I mean that amongst those possible different sets of laws of physics we choose the one that agrees with experiment. But as Brent and I pointed out, once you allow miracles (resurrections, water-into-wine, etc.) you leave the realm where any naturalistic physical law can explain. That is, after all, what you mean by ‘miracle’.
I don’ understand the rest of your comment, it doesn’t make sense to me. Sorry.
Bill Jefferys, you wrote, “But my argument against your assertion that repeatedly observing that physics is respected is a likelihood argument and has nothing to do with the priors.” Last night I enjoyed reading your article with James Berger on “Ockham’s Razor and Bayesian Analysis” in American Scientist, Vol. 80, No. 1 (January-February 1992), pp. 64-72 (which I found on Google Scholar and then accessed through my university’s subscription to JSTOR, so I don’t know a URL to give for public access). There you noted “the need to choose prior probabilities can be avoided” by considering instead the Bayes factor that is the ratio of likelihoods. This seems to me essentially a form of maximum likelihood, though here applied to compare two discretely different models, and not just restricted to continuous parameters.
You nicely applied this to compare an Einstein model (with essentially no continuous parameter beyond the known mass of the sun and the semimajor axis and eccentricity of the orbit of Mercury) with a fudged Newtonian model that had another parameter with an assumed normal distribution with zero mean. In this case the likelihoods favored the Einstein model over the fudged Newtonian model that had the complication of an additional parameter.
However, one could consider a different fudged Newtonian model in which the parameter a in arcseconds per century has a single value, the same as The Answer to the Ultimate Question of Life, The Universe, and Everything in The Hitchhiker’s Guide to the Galaxy. Then the likelihoods of both the Einstein model and this Hitchhiker’s Newtonian model would be essentially the same with the original data, basically determined by the experimental uncertainty that was large in comparison with the difference between 42 and the modern value you gave of 42.98. Of course, I think most of us would say the Einstein model is simpler than the Hitchhiker Newtonian model, so we would assign it a higher prior probability, thus getting a higher posterior probability for the Einstein model.
Other examples can be even more extreme. The maximum likelihood model for my present sentient experience would be that only it exists, since then its probability would be unity. However, I would suspect that the complexity of my present sentient experience would make this extreme solipsistic model (not even having any of my memories corresponding to real experiences at any previous time) sufficiently complex that its prior probability would be much less than the product of the prior and the (admittedly extremely low) likelihood for a simpler theory giving my sentient experience as just one out of an enormous number of other sentient experiences.
In conclusion, I think that only in certain simple examples, such as the nice one you and Berger discussed, can one ignore the prior probabilities. I further believe that you really need to consider priors in coming to your conclusion that the Resurrection has low posterior probability, since if that hypothesis were true, it would certainly explain a lot of the written records we have (admittedly almost entirely based on those in the New Testament, which has many books about Jesus other than just the Synoptic Gospels, and even just those show strong evidence of more than one earlier source). Therefore, it seems clear to me that the likelihood of the Resurrection is high, though I admit that the posterior probability also depends on the prior probability that is assigned, which certainly could tip the balance either way.
Paul Wright
I kind of feel I may be doing you no favours by continuing to contend with you, based on my previous statements in response to Reginald about ‘hardening the heart’. I’ll just say I am pretty confident about the correlation between prayer and medical outcome being statistically significant in my life and that of others known to me. I have not tried to formalize this, but in the case of the man with the knee issue, he felt burning when I put my hand on his knee, and asked me to keep my hand there until the pain went, which took about two 10 minute sessions.
I have heard several second hand reports of people being raised from the dead, periods being in the half-hour to several hours range. One man I know who claims to have seen three people raised from the dead in Mozambique is an acquaintance, and I and others have found him to be a totally reliable and straightforward person; Surpresa Sithole. He is the son of witch doctors and now travels internationally. God once repeatedly prompted him to read Romans 13 when on a flight to the US. When he got there, the immigration official asked what his business was. He said ‘preacher’. The man asked him what Romans 13 was about. He correctly answered ‘submission to authorities’. I have no remembrance of reports of totally recreated limbs from anyone known to me.
I know the following statements are at the extreme fringes of the present discussion but they do IMO have a bearing on all this: I think Don would agree with me that God is worth knowing for the sake of knowing him. He loves you and understands you better than you understand yourself. He has also bought me into richer relationship with others. If you dislike the idea of God you have in your head, you will be disposed against any rational argument for him. I know personally two life sciences people, one BSc and one PhD, who become Christians and dropped evolution virtually on the spot. Not that evolution is the prime issue.
Don, if you want to compute posterior probabilities you need priors.
My point is that the likelihood tells you whether the data favor one theory or the other, independent of the priors. In the case we are discussing, if there is a possibility that the theory that includes god could (because of a “miracle”) produce an observation that violates physical law (because it is a “miracle” which by definition defies physical law), then upon observing a datum that is consistent with “physics is all there is”, the likelihood ratio between “physics is all there is” and the theory including god necessarily favors “physics is all there is” with a likelihood ratio that is greater than 1. I’ve explained this in detail in earlier comments so won’t repeat myself.
If you continue to observe a large amount of independent data, all of which is consistent with “physics is all there is” (as with the data from the physics experiments you described), that likelihood gets as large as you wish, and regardless of the priors, the posterior probability of “physics is all there is” approaches 1 in the limit. Just a single observation that is inconsistent with “physics is all there is” — a miracle if you will — refutes “physics is all there is” in favor of the theory that includes god.
Don, as Brent remarked, a remark you have not adequately dealt with:
“Suppose there’s a miracle. Everybody recognizes that a miracle is evidence for a supernatural God. Don observes that the universe is orderly and law like. That’s the same as observing there are no miracles. Miracles and no miracles can’t both be evidence for the same proposition. Since miracles are evidence for God, no miracles must be evidence against God.”
Michael Ikeda and I made a similar observation in our paper on the Anthropic principle.
This is why I say that the priors are basically irrelevant. All of the real data that I am aware of is consistent with “physics is all there is.” Claims of miracles, including the resurrection, are simply not believable because their provenance is very doubtful. You may think differently, that is your privilege, but you will have a hard time convincing me.
By the way, Don, I’m glad you enjoyed reading my paper with Jim Berger. An earlier version of this paper can be found linked on this website:
http://bayesrules.net/Papers.html
…along with some more comments about the paper.
I think a definition of what constitutes a “miracle” would be good. I understand Bill’s point, but I wonder if miracles from the perspective of the natural world would be miracles according to “Physics is all there is” + Don’s theory. If you took Newtonian mechanics with electrostatics as your “complete physics,” the appearances of magnetic fields would be pretty damn miraculous. However, with the correct adjustment with Maxwell’s Laws and/or relativity, it would not longer be miraculous.
Is Don suggesting that when God is combined with the tenets of naturalism these miracles become consistent features of the theory? So physics works for all “non-miracles” as is but has no explanatory power for miracles on their own?
I think that Don would have to explain how a physics augmented with god would predict resurrections. Not by handwaving, but using equations. That means he’d have to write down the underlying physical equations. I don’t think this is possible.
Bill Jefferys,
I might be misunderstanding you because I haven’t read the entire thread, but I find disagreement with your claim that “priors are basically irrelevant”. Priors are the only thing that penalizes us for introducing ad-hoc or unevidenced aspects to a predictive model. If priors are irrelevant we become steeped in hypotheses that predict the data at hand without good reason to prefer one over another.
If we assume the premise that a god exists, the only way theists get “God did it” off the ground as an explanation in the case of Jesus’ resurrection is to add additional assumptions to the model, e.g. This god can and was motivated to do such a thing (as we have no evidence doing such things was a regular occurrence for God). Their model must be penalized for such assumptions (via a non-information prior, something that ensures unity when we sum all our priors), our only way to penalize a theist for adding assumptions like this to their model (assumptions that increase P(Evidence|Model)) is to decrease their models prior probability, a method we equally use when one offers an explanation that aliens made the evidence appear as it is.
Cam, the point is that with enough data, and we do have enough here, priors become essentially irrelevant because the likelihood (product over all the data) approaches a limit which in this case is infinity for “physics is all there is” and against the hypothesis that includes god, so long as all the data is consistent with “physics is all there is”. In this case the posterior probability approaches 1. This is basic Bayesian inference.
Only an observation of a “miracle”, and it only takes one, can refute “physics is all there is” and make us confident of the hypothesis that includes god.
It’s generally the case in Bayesian inference that in the limit of infinite data the priors are irrelevant so long as they do not exclude any hypothesis a priori. This is well known and often discussed in the literature. There are some pathological exceptions that do not apply here.