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
Don,
Congrats on the son’s MD!
I’m glad we clarified that then, as I was arguing against B these last few comments.
And when you say this:
“I am saying that whatever the cultural differences are, they seem to have the result of effectively making the priors different between the two sides”
I think that’s fine, if you’re coming from the perspective of thinking A is true, though I just wouldn’t sum up cultural differences that way (point “B”) unless you caveat it like you did here (otherwise it paints a different, narrow picture).
Granted I didn’t agree with A of course, hah, but that was long ago; so sorry for the bantering over thinking your point was strongly B.
Don, congrats on your son’s MD. When you write “proud father” I felt the same when we attended our daughter’s graduation. But it wasn’t snowing in June of last year, and the campus was lush green. You and Cathy have every reason to be proud parents and it is always a great feeling to see our children reach these heights (and more to come) through the grace and power of God acting on us (the parents) to show example, and on the children to do the right things. God knows how ardently my wife and I still pray for our two children (graduated and working). In my (Anglican) church we have a part of the service called Prayers of the People, (names read aloud) and I will add your son to the list this Sunday for thanks and continued guidance. I will write “Don Page’s Son who graduated with an MD.” God being omniscient, He will know who the person is.
Thanks for the response.
Congratulations to Don and his family concerning his son’s MD, and may he enjoy this profession, so gloriously free from basic uncertainties and ambiguities (well maybe).
Don, forgive me if you have already answered this, implicitly or explicitly. I did not watch your video you suggested a while back, and now could not find the link quickly.
Further to the discussion on determinism:
Tegmark’s multiverse hypothesis ‘considers equally real all universes that can be described by different mathematical structures’.
http://en.wikipedia.org/wiki/Multiverse#Max_Tegmark.27s_four_levels
Do you believe, in your tentative world(s)view, that a mathematically realizable construct leads necessarily to a substantiated reality? For us? For God? If you believe in many worlds, are they all real just because they are mathematically realizable?
As I have said before, I am seeking to form a worldview whereby my view of physics accommodates my theology. I see time-wise freewill actions of sentient beings, including God and other (created) spiritual beings, as genuine modifiers in the time evolution of the state of the one real universe. The one universe has a nature defined by God in terms of starting laws and conditions, but is also subject to on-going modification as above.
And he is before all things, and in him all things hold together.
(Col 1:17)
I see in QM a possible ‘permeability’ in known physics for these modifiers to act. Obviously, in our human case, we have no idea how such a mechanism might act.
In a nutshell, I see reality hinging less on physics as we see it and more on the relational plans and pursuits of God. In freewill, we have attributes and influences greater than a deterministic framework of our evolution alone would predict.
Is my tentative worldview ruled out, in your opinion, or is it a possibility? These points are of serious interest to me, I may write on them. Thanks.
Simon, on determinism, you write: “In a nutshell, I see reality hinging less on physics as we see it and more on the relational plans and pursuits of God. In freewill, we have attributes and influences greater than a deterministic framework of our evolution alone would predict.”
I would phrase it a bit differently like this:
“In a nutshell, I see physical reality partly described, certainly not determined, by science, which always remains subject to the relational plans and pursuits of God. In freewill, we have attributes and influences greater than a deterministic framework of our evolution alone would predict.”
Reason? I want to keep separate and immutable the ONE or Ultimate Scientist from the march of science or our discovery of knowledge in general. We do not know what science will discover or fully explain in the future. Quantum Mechanics (QM) is a nondeterministic theory in the sense that you can only predict the probabilities of the experimental outcomes. Don thinks QM is incomplete, but that “God could determine (and would, in my view) what is left undetermined by the incomplete theory. So at one level (that of the incomplete indeterministic quantum theory) there would be indeterminacy, but at a higher level (that of a complete description of world) there would be determinism.”
“Another God of the Gaps!” the atheist says, “God of the Gaps filling in the holes in the body of scientific knowledge.” Not so. God of the Gaps according to Luke Barnes goes like this:
The question is asked: What is lightening?
The response: We don’t know.
The answer given: God did it.
That is not what Don has in mind. God is integral to the Laws of Nature and the complete model, and therefore not ad hoc, which goes all the way back to St. Augustine.
I like to refer to Luke Barnes on the Fine Tuning. Total time 1.16.31 hour interview with atheist Luke Muehlhauser on May 19, 2010 in Design Argument. If you don’t want to listen to the entire podcast but just the points I make above, move the cursor to 30.50 minutes and listen for the next 6 – 7 minutes.
http://ia902708.us.archive.org/4/items/ConversationsFromThePaleBlueDot040-LukeBarnes/040-LukeBarnes.mp3
Hi TY
“I want to keep separate and immutable the ONE or Ultimate Scientist from the march of science or our discovery of knowledge in general. We do not know what science will discover or fully explain in the future. Quantum Mechanics (QM) is a nondeterministic theory in the sense that you can only predict the probabilities of the experimental outcomes.”
A good distinction to keep in mind on science and The Scientist, or rather, Author of Physical Law. However the QM indeterminacy thing has been going a while and in general I feel the ‘gaps’ argument is more valid than ever. Sean Carroll and the determinist/many-worlds camp would probably disagree. QM indeterminacy is I believe frequently voided in the literature by decoherence and/or many-worlds. Decoherence is a rather ill-defined idea in terms of implications, and many-worlds is why I asked Don about the associated realities.
Many-worlds, if descriptive of substantive worlds, is not a belief I am willing to adopt for prior theological reasons.
The case for full physical determinism allies with the theological position of ultra-Calvinism and ‘irresistible grace’. I’m inclined to think from scripture that God did not want to leave us with that impression, and therefore, it is unlikely to represent the truth. It seems to me to undermine the intensity of the gospel message, never something Jesus did in any way.
If God ordained freewill, then physics may reveal avenues for it to find expression. Even if it does not, as per your concern, then physics is no final word. Jesus is.
Paul Wright (May 7, 2015 at 9:55 am) asked about priors not just for theism but for “the sort of God who’d resurrect Jesus.” I agree that this is an important issue. Let me cast this into the Bayesian form that I find most useful, though recognizing that others such as Josh seem to prefer non-Bayesian approaches that I would have to learn much more about in order to understand.
Ideally (though I realize this is certainly impossible in practice for any of us finite beings within the universe), one would have a complete set of complete hypotheses H_i for the world (all that exists, including God in hypotheses in which He exists), each such hypothesis implying a complete description of that logically possible world that would be actual if the hypothesis were correct. Then for what I often call an observation O_j, meaning all the data one has access to for testing the hypotheses, one would like the posterior probability of each hypothesis given the data, which is denoted by P(H_i|O_j), where the vertical bar separates the condition to the right of it from what on the left of it one is calculating the probability, conditional upon what is to the right. By Bayes’ theorem, this posterior probability is given by
P(H_i|O_j) = P(H_i)P(O_j|H_i)/[Sum_k P(H_k)P(O_j|H_k)].
Here P(H_i) is the prior probability of the hypothesis H_i, which is the probability assigned to H_i prior (in the logical sense, not necessarily in the temporal sense) to considering the data of the observation O_j, and P(O_j|H_i) is the probability of the observation O_j given the hypothesis H_i (that is, under the assumed condition that H_i is true), which is technically given the misleading name of the `likelihood’ of the hypothesis, though it is not the probability of the hypothesis but rather of the observation given the hypothesis. In the denominator, Sum_k means to sum what follows over all k, that is, over all hypotheses H_k. The denominator is a constant factor (for a fixed O_j), independent of the particular hypothesis H_i whose posterior probability is being calculated, to normalize the posterior probabilities so that for any particular fixed O_j, the sum of the posterior probabilities P(H_i|O_j) over all of them (over all i) gives unity, as the sum of the probabilities of a complete set of mutually exclusive possibilities (here the hypotheses H_I, which should be a complete set of mutually exclusive hypotheses) should do.
Since there are an infinite number of different ways the world logically could be, generically the sum in the denominator is an infinite sum. However, if one assigns positive prior probabilities P(H_k) to only a finite set of hypotheses, only those hypotheses will contribute to the sum, so that then one just has a finite sum over the hypotheses assigned positive prior probabilities. (Actually the situation can be more subtle, as the collection of possible worlds is surely not countable, so what I have written as a sum would not just be a sum over a countable set of possible complete hypotheses, each completely describing a different possible world, but at least an integral, and presumably an infinite-dimensional integral, with the dimension of the integral presumably not being countable either. However, by Occam’s razor, one might assign prior probability measures to this infinite-dimensional integral so that a countable discrete set of hypotheses H_k give the complete contribution, in which case one has a countable sum and can ignore the continua of other logically possible hypotheses as making a total contribution of zero to the posterior probabilities.)
The previous paragraph illustrates what I have emphasized, that there is no fixed rule that everyone would agree on for setting the prior probabilities P(H_i). That is, they are necessarily subjective. I have argued that these priors seem to be a major contributor to the different posterior probabilities theists and atheists get for their hypotheses, though someone like Josh might disagree with the whole Bayesian analysis (in which case I do not know how to respond, since then I don’t understand the basis for saying that one hypothesis is more or less probable than another).
Of course, the data one has in one’s observation O_j is also important for the likelihood factor P(O_j|H_i). I might say that this is how I see the motivation for preaching the Gospel, to give people the data they need to estimate (at least implicitly) the likelihood P(O_j|H_i) for Christian hypotheses H_k. However, this data in O_j does not determine the prior probabilities P(H_k), so different people can come to different conclusions even if they have the same data.
Now I agree with Paul Wright’s implicit point, that there are many different theistic hypotheses (presumably an uncountably infinite number, though here for simplicity I shall assume that only a countable number contribute positively to the sum of the products of the priors and the likelihoods), including many for what God would choose to do in various situations. But there are also many different naturalistic hypotheses (again presumably infinitely many, though I shall assume that it is countable, as the integers are even though there are infinitely many of them), including many for different laws of nature. Presumably there are also many hypotheses that are neither theistic nor naturalistic.
Consider dividing the hypotheses H_i into theistic (T), naturalistic (N), and alternative (A) hypotheses. Then one can say the total posterior probability for theism, P(T|O_j), is the sum of P(H_i|O_j) over all theistic hypotheses H_i; the total posterior probability for naturalism, P(N|O_j), is the sum of P(H_i|O_j) over all naturalistic hypotheses H_i; and the total posterior probability for alternative hypotheses, P(A|O_j), is the sum of P(H_i|O_j) over all alternative hypotheses H_i. Note that from Bayes’ theorem one cannot calculate these purely from the likelihoods P(O_j|H_i) and from the total prior probabilities P(T), P(N), and P(A) that are the sums of the priors for all the theistic, naturalistic, and alternative hypotheses respectively; one also needs P(H_i|T), P(H_i|N), and P(H_i|A), the conditional prior probabilities for the complete hypotheses H_i given that one is looking only among the theistic, naturalistic, and alternative hypotheses respectively.
There are also subsets of the three sets of hypotheses, such as the Christian subset C of the theistic hypotheses T. Different people may have different criteria as to whether a theistic hypothesis also counts as a Christian hypothesis (and indeed there may be different criteria as to whether an hypothesis even counts as theistic), but for the sake of argument let us assume some particular set of criteria so that each complete hypothesis can be uniquely determined to be either theistic, naturalistic, or alternative, and so that each theistic hypothesis can be determined to be Christian or not. I shall also assume for simplicity that each hypothesis that counts as Christian also counts as theistic.
Now I would agree that the total prior probability of the Christian hypotheses, conditional upon their being theistic, that is
P(C|T) = (sum of prior probabilities of Christian hypotheses)/(sum of prior probabilities of theistic hypotheses),
is low. In an earlier comment (May 3, 2015 at 1:17 pm), for the sake of giving an example, I suggested the conditional probability of the data D, assuming theism T, of the historical records one has for the claims that Jesus’ apostles saw Him alive again after the Crucifixion, is P(D|T) = 0.001. (This is of course just my subjective guess for the probability I might personally assign to this if I could understand all the different detailed theistic hypotheses.) This is indeed low, but I might similarly guess that the probability of this data D given naturalism N is something like P(D|N) = 0.000001. Then from just this data, the posterior probability for theism would be higher than it is for naturalism unless the prior probability for naturalism were at least 1,000 times the prior probability for theism.
Even leaving aside the data D for claims of the Resurrection, one might consider data D’ for the laws of nature. There are so hugely many different possible laws of nature, even very many laws simpler than we think the actual laws are that would be consistent with our data D’, that I would guess that a plausible but subjective probability for our data D’ given naturalism is very low, say P(D’|N) = 0.000001. It is presumably harder to estimate P(D’|T), but I might personally (and of course subjectively) guess that the prior probability, conditional upon theism, that God would choose the actual laws of physics that are consistent with our data D’ (including the existence of ordered sentient experiences), would give something like P(D’|T) = 0.001. Again, this time using just the data D’ for the form of the laws of nature, one would get a higher posterior probability for theism than for naturalism unless the prior probability for naturalism were at least 1,000 times higher than the prior probability for theism.
One difference between the two data, D for claims of the Resurrection and D’ for the form of the laws of nature, is that while I believe the latter alone rather strongly support theism over naturalism, D’ does not give particular support for the Christian subset of theistic hypotheses, whereas D does.
Paul Wright also mentioned “Raphael Lataster’s paper on Craig’s argument for the Resurrection,” which unfortunately it seemed that my university does not have a subscription for an electronic version for me to access. However, I could access the abstract, which says in part, “there is no confirmed empirical evidence for the existence of God, nor can there be any good historical evidence; sound historical methodology necessarily being dismissive of supernatural claims.” This shows that the Lataster seems to be effectively assigning very low or zero prior probabilities for supernatural events.
Don/Paul,
It wasn’t that I was just blatantly against using Bayesian thinking. Rather my argument was basically that it’s only useful when it’s useful, and that requires being able to calculate likelihoods which Don can’t do for this specific inquiry. It doesn’t provide any meaningful mathematical answer then (which is the whole point of dong it), and so in that context I argue to not prop oneself up with Bayesian thinking if, in effect, one really isn’t doing meaningful calculations.
I think that people build worldview as time proceeds by processing consecutive experiences and modifying tentative beliefs, or even revising previous strongly held convictions. Therefore something along the lines of a Bayesian approach may be a good model for how we build beliefs. However putting agreed upon numbers on many areas of it, and that probably includes the resurrection, is more or less impossible.
It is true that one cannot do a full Bayesian analysis if one does not have the prior probabilities and the likelihoods to enter into the calculation. However, one can sometimes still use it as a framework for making qualitative arguments. For example, it seems pretty clear to me that relative to the data D of reports of claims of witnessing the resurrected Christ, the likelihood of Christian theism is a lot higher than that of naturalism. (That is, the probability of this data would be a lot higher if Christian theism were true than if naturalism were true.) But of course one also needs the prior probabilities, so if someone thinks that Christian theism is a priori a quite a lot less probable than the particular naturalism that would fit other observations, then for that person the posterior probability for Christian theism can be less than that of naturalism even if the likelihood is much higher for the former.
Josh’s comments about skepticism led me to think of one way that one might in general choose more skeptical priors by an algorithm that is not specifically focused on either theism or naturalism. This relates to the fact that even if one has only a countable number number of hypotheses under consideration, has a definite ordering of the hypotheses in increasing order of complexity, and has decided to use Occam’s razor in the sense of ordering the prior probabilities so that they monotonically decrease as the complexity increases, then one still has the ambiguity of what algorithm to use to determine the particular prior probabilities.
For example, one of the simplest algorithms to use after ordering an infinite countable set of hypotheses H_n so that each H_n is simpler than any H_n’ with a larger index n’ (n’ > n) is to set the prior probabilities to be P(H_n) = 1/2^n. That is, the nth hypothesis is assigned the prior probability that is the inverse of the nth power of 2, so that the simplest hypothesis H_1 is assigned the prior probability of 1/2, the next simplest N_2 is assigned 1/4, the next 1/8, etc., which all sum up to 1 when one does the infinite sum. This set of priors drops off fairly rapidly with n, tending to give a rather strong preference for simpler theories (though the simplest ones, such as the one that nothing concrete exists, which would be my H_1, lead to zero probabilities, P(O_j|H_n) = 0, for our concrete observations and hence end up having zero posterior probabilities despite having the highest priors).
However, one could choose a more skeptical set of priors, such as saying P(H_n) = N/(N+n)^2 (approximately), for N a large integer, say N = 1000. Then none of the infinite countable set of hypotheses would have priors higher than 1/N (say 0.001), and one would need a set of at least N of the hypotheses before one could say that the total prior probability for all the elements in the set is greater than 50%. So this procedure would lead to a high degree of skepticism for any particular hypothesis.
Relative to the simpler algorithm P(H_n) = 1/2^n, I don’t know whether this more skeptical algorithm of saying P(H_n) is about N/(N+n)^2 would give more or less favor to theistic or to naturalistic hypotheses. The more skeptical algorithm would tend to disfavor simple specific hypotheses, but when one considers to total prior probability of whole sets of hypotheses, such as theism or naturalism, it is not yet clear to me.
TY
(referring to God of the gaps) ‘That is not what Don has in mind. God is integral to the Laws of Nature and the complete model, and therefore not ad hoc, which goes all the way back to St. Augustine.’
I think God is integral to the creation because of his omnipresence and omniscience. I don’t think he is constrained by it or otherwise defined by it though. The Shorter Westminster Catechism has
‘Q. 4. What is God?
A. God is a Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth.’
Regarding ‘infinite’ one source scripture is from Kings where Solomon is dedicating the Temple:
But will God indeed dwell on the earth? behold, the heaven and heaven of heavens cannot contain thee; how much less this house that I have builded?
(1Ki 8:27)
Regarding QM and indeterminacy, Don sees the universe as wholly deterministic concerning actions of sentient beings other than God himself. That is my recollection of his tentative choices from his 52 hypotheses. I assume that is what he means in your quote of him,
“God could determine (and would, in my view) what is left undetermined by the incomplete theory. So at one level (that of the incomplete indeterministic quantum theory) there would be indeterminacy, but at a higher level (that of a complete description of world) there would be determinism.”
I don’t actually understand the second part of this statement, but in the first part, Don seems to perhaps support my ‘permeable to God’ idea of physics? Perhaps Don believes that God intervenes by this ‘permeability’ but our own actions are fully determined by God and physical law? Here I disagree, believing that any ‘permeability’ or ‘slack’ in physics allows for the expression of our own wills, as well as that of God.
To summarize my own opinions:
I believe physics is completely ordained by God and not ‘stand alone’, something God stumbled across and decided to play with. That seems to be the ‘God of the gaps’ perspective.
I also believe he can perform acts which violate our understanding of its constraining effect on reality.
I believe even when our physics is observed as conserved, God can still be acting ‘underneath’ it.
And I believe God himself, infinite and eternal, is fundamentally greater than the physical laws he ordained for us at this time, and therefore free to change them.
I have no fear that ongoing human discovery will undermine this set of beliefs.
Don,
I think trying to cast Bayesian inference as a qualitative model is a bit like trying to force a square peg in a circular hole and, in the least, does not serve well here. To do so would require you picking your likelihoods as well as your priors which tells you nothing other than to remind you that your priors effect your outcome. And we don’t need Bayesian inference to tell us this! Common thought recognizes we have biases which serve much the same effect. Meanwhile, Bayesian inference on this can obfuscate the issue for those who don’t understand how it works (sometimes discussing things mathematically takes far longer to explain than it does to discuss it in plain terms). It also might help legitimize ideas that otherwise wouldn’t hold against the typical cognitive selection we might employ (having a specific number for our probability is very attractive, and thinking about things so narrowly avoids other contentions). Whereas I might wish we had a mathematical way to go about this, we’re just not there yet (if we ever will be). And so sometimes, trying to force the math brings more obfuscation than it does clarity.
As I argued way back previously though, I think your saying of:
“For example, it seems pretty clear to me that relative to the data D of reports of claims of witnessing the resurrected Christ, the likelihood of Christian theism is a lot higher than that of naturalism.”
is your real argument or reason for buying into theism. It’s certainly not a Bayesian analysis at least, as this is where you “pick” your likelihood. Even if you say you employ Bayesian just to see how the priors would play out when you pick a likelihood (which is pretty meaningless as discussed above), you wouldn’t actually arrive at a conclusion this way (as you would need acknowledge having stacked the deck through picking both priors and likelihoods). Something else is causing you to actually “decide.” Your theism then must live or die based on the veracity of Christ’s story (which we’ve previously discussed), but yet you spend far far more energy playing the Bayesian game for theism without building this crucial leg it would need stand on, and so the game is, in many ways, wasted, even though it might be much more attractive. The claim you make here then, that “it seems clear [that the Christian story of Jesus is correct]” is the most contentious, important, and ironically least defended.
Don,
Simple question: How will you know if you’re wrong? Claiming a deity exists is a claim about objective reality. What objective evidence would demonstrate that your claim is wrong?
Thanks
Surprised to see this conversation still going. Well, maybe not so surprised.
Just some comments about Don’s countability comments:
“Since there are an infinite number of different ways the world logically could be, generically the sum in the denominator is an infinite sum.”
I don’t know if a world of finite size can have an infinite number of configurations. If any of the state space variables (space, time, energy, etc.) are infinitely divisible (or there are an infinite number of such variables), then yes. Otherwise, no, unless there are an infinite number of finite sizes that a universe can have. But if there are, why is ours so small? Most finite numbers are much, much larger than the 10^80 or so count of particles in our universe. There may be a finite limit to how big a universe can be.
“Actually the situation can be more subtle, as the collection of possible worlds is surely not countable, so what I have written as a sum would not just be a sum over a countable set of possible complete hypotheses, each completely describing a different possible world, but at least an integral, and presumably an infinite-dimensional integral, with the dimension of the integral presumably not being countable either.”
Maybe an infinite-dimensional integral, but uncountable dimensions? I’m doubtful.
“Now I agree with Paul Wright’s implicit point, that there are many different theistic hypotheses (presumably an uncountably infinite number, though here for simplicity I shall assume that only a countable number contribute positively to the sum of the products of the priors and the likelihoods), including many for what God would choose to do in various situations.”
Assuming each hypothesis can be expressed by a finite string of symbols taken from a countable set of possible symbols, the number of possible hypotheses is countable. If a sufficient description of, say, Christianity requires an infinite string, then your chances of getting Christianity right are exactly nil.
In short, although I don’t think it modifies the argument in any substantive way, I think it is a safe assumption that we are dealing with countable cardinalities when talking about possible hypotheses and possible universe configurations.
Simon Packer, you asked (May 9, 2015 at 1:00 am) the following:
“Do you believe, in your tentative world(s)view, that a mathematically realizable construct leads necessarily to a substantiated reality? For us? For God? If you believe in many worlds, are they all real just because they are mathematically realizable?”
No, I do not agree with Max Tegmark that a mathematically realizable construct leads necessarily to a substantiated reality. I take a rather platonic view of mathematics, that it largely consists of logical truths (theorems, statements of what follows from certain axioms, though I think the axioms, such as the axiom of choice, need be neither true nor false) that could not possibly be false, so that these truths are logically necessary and cannot be created or destroyed by anyone, even God. However, they are abstract and not substantial, and I believe all of reality other than logical truths and the abstractions needed to express them, which I call concrete reality, is not logically necessary. I believe that both God and the physical universe are concrete and not logically necessary. (I think most philosophers today agree that God is not logically necessary, that there is no logical incoherence in atheism. Many Christian philosophers say that God is metaphysically necessary, but I don’t understand what that is supposed to mean beyond saying that God exists in the actual world, with which I do agree.)
I consider causality to be part of concrete existence and hence also not logically necessary. However, I do believe that causality exists in the concrete part of the actual world (let me call this the concrete world, leaving out the abstract platonic world of mathematics and other logical truths). Then I believe each basic entity in the concrete world either has no cause or is completely caused by other basic entities. (There can be composite entities that are composed of basic entities that are uncaused and other basic entities that are caused by yet other basic entities not in the composite entity.) Differing from many (probably most) Christians, I believe that the only uncaused basic concrete entity is God, and that all other basic concrete entities are totally caused, created, and determined by God.
In my way of putting it, I think most Christians today believe that humans are composite concrete entities that are partially caused by God but also have basic entities of libertarian freewill choices that are not caused by God. This certainly seems to be logically possible. I even think it is consistent with total foreknowledge by God, including middle knowledge of what the freewill choices would be in various hypothetical or counterfactual situations God might consider choosing to create. That is, there could be potential humans with potential freewill choices, not caused or created or determined by God, of what they would do if they had actual existence and were put into certain situations (and even if God knew what these choices would be). God could then choose to `adopt’ these uncaused potential humans into a universe that He otherwise creates, so that they become composite beings partially determined by God and partially determined by their uncreated freewill choices.
So I think this is a logically possible view, but to me it just does not seem so simple as the view that God alone is the complete Cause, Creator, and Determiner of everything concrete other than Himself (who is the ultimate Brute Fact, even if not logically necessary). So I take creatio ex nihilo in a very strong sense, that God totally creates, causes, and determines (from nothing) everything concrete other than Himself. I believe that other than the result of God’s creative activity, nothing concrete other than God exists in the actual world. Therefore, if we imagine God’s creative activity occurring in some divine `time’ (which should not be confused with physical time within what God creates, which could run from minus infinity to plus infinity in our universe even though totally created by God), then `before’ God created anything, there was nothing else concrete in the world. In particular, there were not potential humans with freewill choices of what they would do if God `adopted’ them within a universe He otherwise creates. Without such freewill choices existing independently of God, I don’t think it is even logically possible that He could create them, since the very meaning of libertarian freewill choices (as opposed to compatibilist freewill choices, which I do believe in but think it can be confusing to call them freewill) implies that there is something about them that is not created and determined by God.
I also don’t understand how it can be logically possible for God to create something from nothing without completely determining it. We partially create things that are mainly created by God (in my view ultimately totally created by God, when I consider His ultimate total creation of us who in some very limited sense partially create entities within the universe, such as this comment I am writing). But since even in the limited sense in which we partially create the entities, we do not totally create them, and so we do not totally determine them. However, if God has to create everything else concrete from absolutely nothing apart from Himself, I don’t see how it would be even logically possible for these concrete entities not to be totally determined by God.
I might further note that I do not see any strong evidence for libertarian freewill in the Bible. There is of course much emphasis on choice, but no clear statement that I can remember saying that our choices are truly free in the libertarian or incompatibilist sense (incompatible with determinism, that is). We indeed have responsibility, but I take that to mean respond-ability, the ability we have to respond to the commands and precepts of God, governments, society, conscience, etc., which to me does not imply that we have libertarian freewill.
In fact, the one time I remember that the Bible directly discusses the issue, in the Apostle Paul’s Letter to the Romans (one of the most theological book in the Bible), in Romans 9:19-21 (New International Version), Paul seems to accept the idea that God does determine our choices: “One of you will say to me: `Then why does God still blame us? For who is able to resist his will?’ But who are you, a human being, to talk back to God? Shall what is formed say to the one who formed it, `Why did you make me like this?’ Does not the potter have the right to make out of the same lump of clay some pottery for special purposes and some for common use?” Now the Apostle Paul might just be answering the objector on his or her own terms, without really accepting the objector’s assumption of determinism by God, but if God wanted us to know that we had libertarian freewill, this would have seemed to be an ideal place where He could have inspired the Apostle Paul to write that the objector’s assumption to the contrary was false.
On the other hand, I do think it is at least logically possible (though not so simple, and not clearly taught in the Bible) that God does not create everything concrete other than Himself from nothing, but instead that there are uncreated libertarian freewill choices that God `adopts’ into His universe. This would not seem to fit into a straightforward interpretation of creatio ex nihilo, but I do recognize that this is a concept that theologians have developed to summarize this aspect of their interpretation of Scripture and is not expressed explicitly in Scripture itself (though it does seem to be strongly suggested by Scripture).
Thus I am not claiming that it is unbiblical to deny total creatio ex nihilo, but it does seem to me rather surprising that most Christians who believe in libertarian freewill do not face up to the fact that this belief does seem to water down the doctrine of creatio ex nihilo. I would think this should be more seriously taken into account by Christian philosophers.
I found it interesting that in his paper, “God and Abstract Objects,” William Lane Craig wrestled with the challenge that the abstract objects in platonism seem to violate creatio ex nihilo, concluding, “the Christian theist cannot consistently embrace platonism because such a doctrine compromises creatio ex nihilo and divine aseity by its postulation of uncreatables.” Personally I find it easy to accept that besides not saying that God created Himself, creatio ex nihilo does not imply that God created what is logically impossible to be created, namely the abstract objects and logical truths in platonism. Although all the different nuances of the alternatives to platonism Craig discusses are very subtle, it does seem to me that he rather denies the true reality of abstract objects, making it appear to me a bit paradoxical that a leading Christian apologist seems to be denying the reality of truth, which certainly seems to me to be an abstract entity. Be that as it may, I find it even more surprising that closer attention has not been paid to the challenge to creatio ex nihilo by the common Christian assumption of libertarian freewill, which, because it deals with concrete entities that are not logically necessary as the platonic abstract objects seem to be, appears to be a much more serious attack on creatio ex nihilo.
PedroJesus asked (May 12, 2015 at 8:01 am) the following:
“Simple question: How will you know if you’re wrong? Claiming a deity exists is a claim about objective reality. What objective evidence would demonstrate that your claim is wrong?”
If a deity other than the Christian God exists and resurrects me, that true God could show to me that I am wrong about Jesus’ being the Christ, the Son of God. If the Christian God exists and resurrects me, He could confirm that Jesus is the Son of God. (He would probably also show me that I am wrong about a lot of other beliefs that I mistakenly have.)
The situation does seem to be a bit asymmetrical in that if no deity exists, it seems rather implausible that I would have any conscious afterlife at all to learn that I was wrong, though it might be logically possible.
Within this life it does seem very difficult to prove that there is no deity. However, I do think in principle (though perhaps not in practice) one could prove that Jesus is not the resurrected Son of God if one could find His body still buried somewhere. The difficulty would be in proving that it was Jesus’ body, though it is remotely conceivable that if His body and that of enough relatives were found to have matching DNA, this could be strong evidence that Jesus was not resurrected. However, because of the strong historical evidence that He actually was resurrected, I would think it improbable that there actually exists strong evidence (such as an identifiable body) that Jesus was not resurrected. But if anyone sees any hope of finding it, it would definitely be worth looking.
I misunderstood Ty’s “ONE Mathematician who made it” (calculus) comment. My explanation for my mistake is that the assertion that a god made calculus did not occur to me as a possible interpretation (wrongly, however). It raises the following questions:
For something to have been made, i.e. invented, originated, fabricated, or created, a thing must have not existed prior to some time at which it was made. When did your god create calculus? Why did it need to create calculus since it is omniscient? Mathematics in general are the tricks we have evolved to calculate things like the slope of the tangent to a parabola of specific parameters at a specific coordinate. Doesn’t your God already know that answer without having to calculate it?
Calculus specifically involves a set of definitions and theorems – the Chain Rule, the Mean Value Theorem, L’Hopital’s Rule, and so on. Did your god write down these definitions and theorems somewhere? Again, when, why, and how?
I don’t expect understandable answers to these questions, I list them only to show how such assertions about an unknowable god sound to a skeptic (baffling). Any answers I get will probably only confuse me more. I think it boils down to this: “All things are possible, to him who believes.” In other words, there is no such thing as truth based on evidence and reason, because any and all evidence could have been miraculously faked by a god to test our faith. Example:
“Carbon dating, all these things, really doesn’t mean anything to a God who has the ability to create anything at any point in time.”—GOP presidential candidate Ben Carson, discussing his rejection of evolution theory.
Further to Dr. Page’s point about standards of proof in legal trials, I (dangerously) did some more Googling, this time on the “history of the early Christian martyrs”. The best reference I found (in a rather short survey, however) was this:
European Institute of Protestant Studies, History of the early Christian martyrs: “It should be understood that the accounts of the martyrdoms of apostles are mainly traditional.”
In others words, such accounts would not be admissible in a court of law (either criminal or civil), similar to the traditional accounts of Zeus, Apollo, Ra, Odin, Krishna, the angel Moroni, Paul Bunyan, et cetera. (Although such accounts may be entertaining and promote the cultural values of the cultures which produced them.)
Examples of Mormon martyrs: “In the Book of Mormon, several persons die and are honored as martyrs. The prophet Abinadi is the most notable example (Mosiah 12:1-17:1). Others include the women and children of Ammonihah who were burned to death for their beliefs (Alma 14:1-10).” (More dangerous Googling.)
All of which has been said over and over again here, in better words than mine, so I am wasting the time of whoever reads this. Believers will take the word of modern apologists versus centuries of Judaic scholars (on the issue of animal sacrifice), since “all things are possible.” Well, at least it’s an ethos.
Josh,
I agree with most of what you wrote May 12, 2015 at 6:19 am. I feel convicted in not being a very good witness for the evidence for Jesus’ divinity (such as the evidence for the Resurrection) from your frank and helpful criticism: “Your theism then must live or die based on the veracity of Christ’s story (which we’ve previously discussed), but yet you spend far far more energy playing the Bayesian game for theism without building this crucial leg it would need stand on, and so the game is, in many ways, wasted, even though it might be much more attractive.”
For example, I need to finish reading Michael R. Licona, The Resurrection of Jesus: A New Historiographical Approach. At present, perhaps the best I can say is that we have historical documents from within a generation or so of Jesus’ death that His apostles were preaching that they had personally seen Him resurrected after claiming to be the Son of God. Most of these apostles were put to death for their preaching. If these apostles who claimed to be eyewitnesses to the Resurrection persisted in their claim even to the point of death, that strongly suggests to me that they were convinced they had seen Jesus alive again after His crucifixion.
Richard,
When I was talking about possible worlds and possible complete theories for them, I was considering all logically possible worlds, which could include universes of infinite size, infinite numbers of dimensions, infinite numbers of fields, quite different physical laws (perhaps something quite different from spacetime), etc. Surely the number of logically possible worlds has no limited cardinality.
However, I would agree to use Occam’s razor ruthlessly to assign zero total prior probability to the whole hugely infinite collection of uncountable worlds and just consider countable worlds, those that are each in principle describable by a finite string of bits. So I think that if we all agree on at least that much of the assignment of prior probabilities, then we have only a countable set of hypotheses to consider.
Of course, since we don’t even have one single good complete hypothesis for just our universe, never mind God or any other possible universes, there is still a huge gap to a countably infinite set of hypotheses for possible worlds simple enough for each to be completely described by a single finite string of bits.
By the way, even though in some sense the roughly 10^80 atoms (and roughly 10^90 photons) in our observable universe seems large, in another sense it is small. Not only is it infinitesimally small compared with nearly all integers, but also it is far too small to expect to see within it exact copies of any of us humans, though one would if one had a far larger universe (which our universe may well be, since it seems to extend far beyond what we can see). One would need what one might call an exponentially large universe (having an number of particles that is some exponential of the number of particles in each of our bodies) to be able to find duplicates of us humans. I think it may be because our observable universe is not exponentially large in this way that we normally consider each of us humans to be unique, whereas the universe is exponentially large compared with an electron, so we recognize that electrons are not unique.
If Bayesian inference was all that supported our Christian faith, we’d be in bad shape, but thankfully our belief rests rock-solid on the fact that we experience God’s power in our lives. Now, those of the atheistic camp either won’t accept, or do not understand the principles of Bayesian Epistemology. See http://plato.stanford.edu/entries/epistemology-bayesian/#OthPriBayEpi
And so we spin our wheels on certain technicalities and some silliness:
1. The data or information set (what counts as evidence)
2. Admissible data or information
3. The nature of the prior probability
4. Evidential support for the prior probability
5. Why one God and not many (or lumps of charcoal from Newcastle)
There is also this argument against the subjectivity of Bayesian Theory as if the Frequentist approach has no inherent subjectivity. So it is argued that because the priors are subjective degrees of belief (what’s wrong with that?) the application of this type of statistical inference is flawed, and since it is flawed, all hypotheses of God, Jessus of Nazareth, and miracles are nonsense. But, along this chain of reasoning, it has not been shown convincingly, it seems to me, that Bayesian analysis is invalid for this type of hypothesising. One thing for sure the theist sets his priors explicitly, and considers the possibility of his bias upfront.
Both atheists and thesis are agreed that the cosmos or the universe did not come out of the void all by itself. So how was it created? The atheists have long argued the universe doesn’t need a creator because it was always there – eternal. We have no physics model describing the creation of matter out of no-thing. Some brave atheistic physicists say that over and over but repetition doesn’t make the claim true or scientific.
The theists argue, going back to a long line of thinkers, that God is the best hypothesis explaining the cosmos and, in this blog, we have provided a variety of arguments (most convincingly the religious experience) that God the creator exists. No special pleading included. I can anticipate the next question: if God created the Universe, who created God? That will be another blog or you can participate with the same fervour in Aron Wall’s blog: http://www.wall.org/~aron/blog/
The theists argue God is the best hypothesis explaining the cosmos and we have provided a variety of arguments (most convincingly the religious experience) that God the creator exists. And we have personal accounts to tell, which we have been doing for over 2,000 years.
That’s not a bad record based on alleged lies and superstition.
Don,
That was a noble response. And I’ll give you that the things you listed could be considered evidence for the Christian resurrection in a way. I think the hurdle you’d run into though, if using only the bits you mentioned (basically the documented story of Jesus), is that they are not exclusive to Christianity (i.e. a purely naturalistic world also contains them as we see happening in the other faiths). We’ve brought up before thinking about which is more likely to end up with a world with these documented stories, but I think that’s really a gargantuan task. It seems the atheist response to that quandary is skepticism. I think the Christian response would have to be pretty novel to how we typically go about it so as to be convincing on any objective level. Anyways, if there’s something fantastic along those lines in the book, maybe you’ll spread the word.
JimV says: May 12, 2015 at 12:12 pm: “I misunderstood Ty’s “ONE Mathematician who made it” (calculus) comment. My explanation for my mistake is that the assertion that a god made calculus did not occur to me as a possible interpretation (wrongly, however). It raises the following questions.”
Hi Jim, not to worry about misinterpretation. That’s the drawback of written communication. What I mean was that maths, regularity, etc were part of nature that God created. And if you have a bit of time read “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner. https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html. Here is a preeminent physicist talking about “discovering” — not creating — the laws of nature.
Wigner ends the article with this:
“Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”
By the way, he used the word “miracle” 25 times in that essay. Wonder what he was thinking about?
Simon, on your comment May 12, 2015 at 12:18 am. I’m with you on the summary points. Especially this:
“And I believe God himself, infinite and eternal, is fundamentally greater than the physical laws he ordained for us at this time, and therefore free to change them.”
That what we mean by miracle: not the abrogation of the Laws of Nature but God intervening in nature.
Thanks.
Don, my purpose was mainly to point out that, if all hypotheses are finite in length, but there is no upper bound among the natural numbers on that length, then the number of possible hypotheses is at most countable.
I’d go even further and say that, for human endeavors, there is an upper bound to hypothesis length, since any hypothesis that can’t be communicated to and processed by a person during his/her lifetime is not of any use to humanity. And given an upper bound, the number of possible hypotheses is finite. (An objection is that it may be possible for humans to build a computer powerful enough to generate and interpret very large hypotheses, and possibly even to devise and run tests of those hypotheses so that very advanced theories, which only the computer can understand, can be constructed. But suppose the computer executes its program and reports back to the human race that they should do X to save the planet. If humans then do X because of this, then they are acting, not on an understanding of what they are doing, but on faith. The computer may have decided that humans are evil and recommended X knowing that X will destroy all humans — Bender’s dream come true!)
TY (and Don, thanks, but yours, at 10.59am May 12, will take longer to properly reply to!)
You quoted me;
“And I believe God himself, infinite and eternal, is fundamentally greater than the physical laws he ordained for us at this time, and therefore free to change them.”
That is actually the easy one, because physics has normally been about the concrete. Don and I have both discriminated between potential, and concrete, or realized, realities, as both are described by platonic constructs.
It seems to me that an atheistic means of substantiation, rather than a mere description/modelling, of an abstract or platonic construct, is not available. This is also implicit in a statement made by Don in his reply to me: “I consider causality to be part of concrete existence and hence also not logically necessary” (i.e. not implicit in the platonic construct). Causality for the concrete implies creator (One who substantiates). But both causality and concrete are not logically necessary in platonic reasoning. But the concrete is, seemingly, observed and experienced. Why?
Now faith is the substance of things hoped for, the evidence of things not seen. Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear.
(Heb 11:1,3)
So thanks TY for affirming my statement, and I stand by it.
But Don for me raises another question, one Lane Craig touches on in Don’s link. Are the abstract mathematical and logical constructs we take to be immutably true (I am calling these platonic entities), say for example e^(i*pie)=-1, not necessarily true for God unless he ordains them to be true? If not, then God is not the final author, definer and source of all truth. He is then seen as being on the same level as, or perhaps even subject to, ‘platonic logical/mathematical entities’. Lane Craig discusses the difficulties in reconciling his idea of creation from nothing with the existence of immutable platonic logical entities.
It seems to me that even the smartest of us can, beyond a certain point, only accept, by faith, what God says. It seems from the verses above, that when God says something, it is. Very very simple, a child can ‘get’ it, but quite impossible to understand the mechanism involved. So God declared some logical and abstract truths. They are now true. And we proceed from there.
So we can simply say:
“There are certain abstract logical and mathematical truths which derive from the nature of God and exist as truths independent of any physical reality.”