Another Chance of Design - Response to Travis R

There's been a short exchange in the comments following Chance or Design:

measureoffaith - FYI, the objections you list here appear to have been sourced from WLC rather than Robin Collins, and the accompanying reference to Penrose is on pages 762-765 of TRtR (The Road to Reality).

neopolitan - Thanks, I've updated accordingly. I don't think that pages 762-765 say what you want them to say. Penrose is arguing against the anthropic principle. Towards the end of an earlier section, "28.6 The anthropic principle", he writes (having linked the strong anthropic principle with a creationist god hypothesis):

"My own position is to be extremely cautious about the use of the anthropic principle, most particularly the strong one. My impression is that the strong anthropic principle is often used as a kind of ‘cop-out’, when genuine theoretical considerations have seemed to reach their limit. I have not infrequently heard theorists resort to saying something like: ‘the values of the unknown constant parameters in my theory will be ultimately determined by the anthropic principle’. Of course it might indeed ultimately turn out that there is simply no mathematical way of fixing certain parameters in the ‘true theory’, and that the choice of these parameters is indeed such that the universe in which we find ourselves must be so as to allow sentient life. But I have to confess that I do not much like that idea!"

Note that he moves from having particular issue with the strong anthropic principle to just referring to it as the anthropic principle. Thus, when he's protesting strongly against the anthropic principle in a later section, he is most particularly protesting against the strong anthropic principle, and thus against your god. Given the context, it's a little disengenuous to call upon Penrose in support of your case.

I see no strong objection in Penrose's book against multiverses. Even when we limit ourselves to the very specific thing that WLC could be thought of as honestly referring to - the extravagance associated with having such a large, long-lived universe when perhaps we need a much small(er) region of order, no more than one galaxy, with the current laws in place only for as long as required for humans to evolve - we see that Penrose is arguing that for the purpose indicated (creating us, apparently) there would have been 10^10^123 more options that were significantly less extravagant. This is a strong argument against god, not a strong argument against multiverses. If anything, it implies that if there are multiverses (and thus more likelihood of the initial conditions from which intelligent life might spring) then the argument against god only increases.

measureoffaith (writing as Travis R): You assume too much. I don't "want" Penrose's argument to say anything in particular, nor am I making a case for any particular view. I was simply skeptical of the story put forth in your original version and so wanted to inform you of the correct sources after locating them for myself. Perhaps I should have been more explicit - it is WLC, not me, who refers to pages 762-765 of Penrose'sTRtR in the context of the quote. So the point was that your remarks about WLC presumably (and amusingly) referring to pg 784 is a strawman and is probably best exorcised from the post. As far as I can tell, WLC accurately characterizes the cited argument from Penrose, though he simultaneously fails to acknowledge the accompanying implications for theism that you outlined.

You are right, Travis, I assumed too much and misspoke (or miswrote).  I perhaps should have written " I don't think that pages 762-765 say what WLC wants them to say" or " I don't think that pages 762-765 say what John Piippo wants them to say" or " I don't think that pages 762-765 say what the theist might want them to say".  Probably, however, I should have just stuck with the facts and avoided speculation as to what other people want.

My point was that John Piippo was presenting arguments against the multiverse and had quoted WLC who made reference to Penrose.  And in the Penrose book, the word multiverse is only used once, on page 784, after which he uses the term "omnium".

It is true that WLC, as you linked, was referring to a different section of Penrose's book.  The questions then are whether WLC was "accurately characterising" Penrose's argument - and whether John Piippo was accurately reporting WLC's case.  WLC seems to have used Penrose repeatedly, in his book On Guard, on the page you linked and also at his Defenders podcast.  Here's what WLC had to say in the last of these:

Moreover, thirdly, the Many Worlds Hypothesis faces what may be a truly devastating objection. Do you remember when we talked about the thermodynamic properties of the universe, we discussed Boltzmann’s Many Worlds Hypothesis? You will remember that the Austrian physicist Ludwig Boltzmann tried to explain away the current disequilibrium of the universe by a kind of Many Worlds Hypothesis. He said that the universe as a whole really is in a state of equilibrium but there are just little pockets of disequilibrium throughout the universe, and these are different worlds. He called them “worlds” and we are one of these little pockets. We are one of these worlds. You will recall what sank Boltzmann’s hypothesis was that if our world is just a random member of a World Ensemble like this, then it’s vastly more probable that we should be observing a much smaller region of order than the vast universe that we do. In order for us to exist, all you would need would be a small fluctuation from equilibrium, say, enough to produce our solar system and not an entire universe which exists in such a state. It turns out that a parallel problem faces the Many Worlds Hypothesis as an explanation of cosmic fine-tuning.

The Oxford University physicist Roger Penrose has pressed this objection with great force. Penrose points out that the odds of our universe’s initial low entropy condition existing by chance alone are somewhere on the order of one chance out of 10^10(123). A truly incomprehensible number. By contrast the odds of our solar system’s forming by just a random collision of particles, Penrose calculates to be about one chance out of 10¹⁰⁽⁶⁰⁾. A number which is so tiny in comparison to 10^10(123) that Penrose calls this number “utter chicken feed” in comparison with 10^10(123). What that implies is that it is far more likely, incomprehensibly more likely, that we should be observing an orderly universe no larger than our solar system, since a world like that would be unfathomably more probable than a finely tuned universe like ours.

To me, this is not an "accurate characterisation" of what Penrose had to say.  Craig was very clearly implying that Penrose was pressing an objection to the "Many Worlds Hypothesis as an explanation of cosmic fine-tuning".  It's very difficult to interpret what was written here differently. 

Now, Penrose did write:

Much more problematic are versions of the strong anthropic principle, according to which we try to extend the anthropic argument to determine actual constants of nature (such as the ratio of the mass of the electron to that of the proton, or the value of the fine structure constant §26.9, §31.1). Some people might regard the strong anthropic principle as leading us to a belief in a ‘Divine Purpose’, whereby the Creator of the universe made sure that the fundamental physical constants were pre-ordained so as to have specific values that enable sentient life to be possible. On the other hand we may think of the strong principle as being an extension of the weak one where we broaden our questions of ‘where’ and ‘when’, so that they apply not just to a single spacetime, but to the whole ensemble of possible spacetimes (Fig. 28.13b).27 Different members of the ensemble might be expected to possess different values for the basic physical constants. The where/when question now also involves a choice of universe within the ensemble, so again we must find ourselves in a universe which permits sentience to come about.

Penrose is not necessarily talking about a multiverse here, but of an ensemble of "alternative universes", which involves a range of possible universes - not necessarily a range of instantiated universes.  The difference here is subtle.

Put roughly, we arrive at the idea of a multiverse via three possible paths, none of which involve thinking about a god: there is something like string theory in which each universe is a different solution to the equations, none of which has a higher likelihood than any other; there is the patchwork greater universe, in which for one reason or another, the laws of physics and the fundamental constants vary from region to region (eternal inflationary theory fits in here); and, some sort of cyclical or branching multiverse, like Penrose's CCC or a mother-daughter relationship between universes mediated by black holes, in which the constants are randomised in each cycle or branch.

The ensemble of worlds idea is a little different, especially as it pertains to the strong anthropic principle.  The basic idea is that not only is it a truism that we live in a universe in which life of our sort is possible, but also that sort of universe must also be possible - our sort of universe is a necessary member of any set of possible universes, by virtue of the fact that at least one example of our sort of universe exists.  If you come up with a theory that expressly prohibits a universe of the sort we live in, then your theory is wrong.

Just in case it is not entirely clear, the difference between the multiverse and the world ensemble is the direction from which the idea is approached.  As I wrote in Chance or Design, consideration of fine-tuning resolves down to chance or design.  If you find design to be unpalatable, then you are left with the question of how it could be that a universe so (apparently) unlikely as ours should exist.  A potential solution hangs on the notion that our universe, however unlikely, is still possible (and necessarily so, since it is existent).  This is the point at which you might posit a world ensemble, an array of possible universes, all slightly different and numerous enough to drive the posterior likelihood of our sort of universe towards unity … Pr(our sort of universe|world ensemble) -> 1.

What you can't do, legitimately, is suggest that there is a world ensemble purely on the basis of finding design unpalatable.  What you can do, legitimately, is look around and see whether there is any good reason for thinking a world ensemble exists.  It is at this point that you might meet up with multiverse theories coming in from another direction.  Some theists might not believe that multiverse theories arose independently of apologetics, but there are some who are becoming aware that this is in fact the case.

Another approach is Bayesian in nature (the equation above should have given this away).  We are considering a posterior, P(U|WE) which is given by the prior P(U) multiplied by the likelihood P(WE|U) divided by the marginal likelihood P(WE).  If we were to erase all knowledge of there being any universe in existence, what is the (marginal) likelihood of a world ensemble?  I'd suggest that this would approach zero, since the absence of any universe doesn't move us anywhere close to thinking there should be many of them (that are possible).  Therefore, we have a very low number, according to fine-tuners, for P(U) divided by a very low number.  This is rather arbitrary, but we could say that it's close to zero - especially if we were to stipulate that this world ensemble should be very highly populated given that the more highly populated it is, the lower P(WE) would be.

So, P(U)/P(WE) ≈ 1 and therefore P(U|WE) ≈ P(WE|U).  We need to consider how likely a world ensemble is, given the existence of our universe.  We could consider this in terms of how likely it would be that there is no world ensemble, given the existence of our universe - in other words, how likely would it be that, if there were only one universe, this would be the universe that came into existence?  If you say "very unlikely", then you are saying that a world ensemble, given the existence of our universe, is "very likely".  Once we've accepted that a world ensemble is highly likely, we need only to work out how populous this world ensemble would be.  With nothing else to guide us, we find ourselves being driven towards an infinite number of universes - because there is one population size for the world ensemble to the left of three and an infinite number of sizes to the right, so it's more likely to be a population size to the right of three.  Keep going (forever) and you'd eventually arrive at the conclusion that infinity is the most likely size.

I'm aware that this argument is a little dodgy, but fortunately, we don't need to rely on Bayesian skulduggery nowadays because we have pretty clear indications that the multiverse is an actual thing.

Anyway, it is very clear that, in pages 762-765, Penrose was forcefully dealing with a theistic version of the strong anthropic principle because he kept mentioning a Creator.  WLC cannot be thought of as "accurately characterising" Penrose's position when he fails to mention that.