A New Proof

I have just discovered a new proof of the existence of God.

Consider the following sentence:

(S) If this sentence is true, then God exists.

Suppose sentence S is true. Then the first clause is satisfied, so the second clause is true. Thus, God exists.

What the preceding paragraph proves is that if sentence S is true, then God exists. But that is exactly what sentence S asserts. So that means we have proved that sentence S is true! And therefore God really does exist.

As a result of this proof I am longer an atheist. Sorry to disappoint everyone.*

* Note this proof also works for unicorns. Yay, unicorns exist!

Craig and BGV

I hate writing more posts about William Lane Craig, because I think he gets way more attention than he deserves already. But.... I can't let this pass.

I just ran across this post from Craig's website. Craig is responding to Carroll and, after quoting him, replies thusly:

Here Carroll claims that to have a singularity in the past does not mean to have a beginning; it means only that SOME [past-directed] geodesics come to an end. He says that others might not. On this interpretation, the BGV Theorem is consistent with some geodesics’ being infinitely extended into the past. But that is precisely what the theorem proves to be impossible. The theorem requires that ALL actual, past-directed geodesics eventually come to an end. In order for the universe to be beginningless, there must be infinite, past-directed geodesics. That’s why Borde, Guth, and Vilenkin take their theorem to prove that any universe which has, on average, been in a state of cosmic expansion throughout its history cannot be past-eternal but must have a beginning.

OK, so, in my last post (yeah, I know, no apologies, I'm only going to post when I feel like it, so there), I quoted the conclusion from the actual BGV paper:

... we see that if Hav > 0 along any null or noncomoving
timelike geodesic, then the geodesic is necessarily
past-incomplete.

So, it's obvious from the paper that the requirement that a geodesic ends is not applicable to geodesics that are timelike and comoving. In other words, Craig is simply wrong when he writes that BGV requires "ALL actual, past-directed geodesics eventually come to an end."

Either Craig hasn't understood the conclusion of the paper he cites so frequently, or he is deliberately mischaracterizing the paper for his readers so that they will think he has decisively refuted Carroll.

What do you think?

BGV and KCM

OK, so last time I claimed that our best, experimentally successful model of the early universe is one that is infinitely old and has no initial singularity. If you are savvy about these things (from listening to Craig debates, for instance) you are wondering, "But what about the Borde-Guth-Vilenkin theorem? Doesn't it prove that an inflating universe must have had an initial singularity?" The answer is, "No, it doesn't."

There has been a lot of confusion about this, with clip quotes from one or another of the paper's authors being traded to "prove" that the theorem does, or doesn't, prove the universe had a beginning. So let's look at what the theorem actually says.

"Any theorem is only as good as its assumptions," writes Alexander Vilenkin in a letter to Lawrence Krauss. So let's start with the assumptions of the theorem. Roughly speaking, there are two:

1. Spacetime is classical.
2. Spacetime is expanding on average.

(I say "roughly speaking" because there are all sorts of technical issues about spacetime congruences and so forth that one needs to make these assumptions precise, but I think these short versions are sufficient to understand the main philosophical issues involved.)

Now let's jump to the conclusion, which I quote from their paper:

... we see that if Hav > 0 along any null or noncomoving
timelike geodesic, then the geodesic is necessarily
past-incomplete.

Some translation: a "timelike geodesic" is simply the path that an object will travel on if it is not subject to any forces other than gravity. Similarly, a "null geodesic" is the path that a light ray will travel. "Hav > 0" is the mathematical statement of assumption (2.): the universe is expanding on average. "Past-incomplete" means that if you try to follow one of these paths backwards in time, you can only do so for a finite amount of time.*

OK, so here's my first point: the BGV theorem is not a singularity theorem!

The conclusion says nothing at all about singularities: it only says that certain paths cannot be extended infinitely backward in time. One way that this might happen is if the path encounters a singularity. But that is not the only way it can happen.

The other thing that can happen is that, as we trace the path backward in time, we encounter a region where one (or both) of the assumptions of the theorem is no longer valid.

Start with assumption (2.). The path can enter a region in which spacetime is static, or contracting, or cyclically expanding and contracting. Then assumption (2.) is violated and the theorem's conclusion is avoided. In spacetimes like these, the BGV theorem simply doesn't apply.

What about assumption (1.)? Classical spacetime is a pretty basic assumption in any sort of cosmology. But it is expected to break down in the quantum gravity regime, where we encounter "spacetime foam" of some sort. This is difficult to discuss, since in the absence of a good theory of quantum gravity, no one has any idea what spacetime foam should look like. But it's possible that the BGV theorem is pointing us to a place where quantum gravity comes into play.

So the BGV theorem does have something very interesting to tell us about the early universe: namely, that the infinitely old, infinitely expanding inflationary period that I discussed in the previous post cannot be the end of the story. Not just because of vague speculations about the Planck epoch, but because of the properties of classical spacetime itself. Here's what the authors said in the paper itself:

Whatever the possibilities for the boundary [where the geodesics come to an end - RNO], it is clear that unless the averaged expansion condition can somehow be avoided for all past-directed geodesics, inflation alone is not sufficient to provide a complete description of the Universe, and some new physics is necessary in order to determine the correct conditions at the boundary. This is the chief result of our paper.

But the BGV theorem does not say that spacetime must be singular; still less does it say that there was an initial singularity from which the entire universe arose. This is why I say that the theorem is irrelevant to the Kalam Cosmological Argument: it doesn't say anything about whether the universe had a beginning or not.

* A few more technical points: by "backward in time" I mean in the opposite time direction from the direction in which the universe is expanding. And by "finite amount of time" I mean time as measured by a clock carried along with the moving object (proper time). In the case of null (light) rays, we have to use an "affine parameter" rather than the proper time.

The Universe Is Infinitely Old (Says Cosmology)

The Secular Student Alliance at my school recently  hosted a debate on the topic "Is there a God?" The theist side was very well prepared and did a great job in the debate, as even the secular students in the audience agreed. One of the arguments they presented was the Kalam Cosmological Argument, which was presented rather the same way that William Lane Craig presents it. The discussion brought up the Borde-Guth-Vilenkin Theorem (BVG for short), which Craig has used as well, as support for the premise "The universe began to exist." I want to talk about why the BVG theorem is irrelevant to the Kalam Cosmological Argument, but first, by way of preliminary, I want to discuss the current state of cosmology.

Cosmology begins with Einstein's equations of General Relativity (GR for short), and asks whether these equations, applied to the universe as a whole, are capable of explaining what we see when we look out into deep space. GR relates the curvature of spacetime to the energy content in the universe, so in order to solve the equations we need to know what the universe is filled with. There are three basic types of energy we need to consider:

• Matter in the form of galaxies, dust, dark matter, and the like,
• Radiation, including particles moving so fast that they are relativistic, and
• Cosmological constant, aka "dark energy."

The three forms of energy behave differently, so different ones are important at different times in the evolution of the universe. For most of the last 13.7 billion years, the expansion has been matter-dominated. But in the far future, the expansion will be dominated by the cosmological constant, and at very early times (the first 50,000 years or so), the expansion was dominated by radiation.



This plot shows the "scale factor" - roughly speaking, the size of some patch of the universe, as a function of time.The universe described by this model fits extremely well with the observations of distant galaxies, supernovas, quasars, etc.

If the early universe is indeed radiation dominated, then the scale factor goes to zero at some finite time in the past: that is, there is a Big Bang - an initial singularity.

However, we now have an alternative account of the earliest moments of the universe. Inflationary cosmology, proposed by Alan Guth in 1980, then in a corrected from by Linde and (independently) by Albrecht and Steinhardt in 1982 supposes that before the radiation-dominated epoch there was another epoch, dominated by a cosmological constant - but a very much larger cosmological constant than the one we measure now. I'm not going to go into the reasons these physicists thought there might have been a very large cosmological constant in the early universe, which then "switched off" (meaning it wasn't really a "constant", obviously): you can read about it at the Wikipedia page if you're interested.

The inflationary model was able to explain several features of the universe that had been puzzling in earlier cosmological models: the flatness problem, the horizon problem, and the monopole problem. In science, though, explanatory power is not enough for a theory to become accepted. In addition, a theory has to make novel predictions that are confirmed by experiment before scientists accept it as (likely to be) true.

(I can't help pointing out how different this is from theistic "explanations," in which God is claimed to be the explanation of things like life, morality, or the universe, but where there is no concern for making testable predictions about these realms.)

We now have several good reasons to think that there was in fact such an inflationary epoch. One of these is the pattern of fluctuations of the cosmic microwave background, that fits extremely well with the predictions of inflation:



Another is the very recent BICEP2 result, that seems to show the effects of quantum gravity on the polarization of the cosmic microwave background, in a way consistent with the predictions of the inflationary model.

So inflationary cosmology replaces the initial singularity with a period of exponential expansion.



How long is this inflationary period? Well, an exponential function never reaches zero, so the inflationary period is, in principle, infinitely long!

Let's sum that up: According to our best, experimentally verified model of cosmology, the universe is infinitely old and has no initial singularity! 

This is the current state of our understanding of the early universe. Now, I have to admit right away that no physicist thinks the inflationary model is the end of the story. The exponential expansion is so fast that in a very short time the scale factor reaches the Planck realm, where we expect GR to break down and quantum gravity to come into play. So most diagrams of the early universe insert a quantum gravity region before the inflationary epoch. (In this diagram from Andrei Linde it's labeled "Space Time Foam.")



There has been much discussion of what went on before the inflationary epoch: quantum foam, the no-boundary proposal, the cyclic universe, and so on. There is even a version called "eternal inflation," in which some portion of the universe goes on inflating forever, while pocket universes like ours bubble off from time to time. In some of these models, time is finite in the past. In others, it is infinite. But all of them are pure speculation: there is to date no experimental confirmation of any of these scenarios.

Does modern cosmology support the premise that the universe had a beginning? Emphatically, no! Our best model extends infinitely into the past, with no initial singularity. We know better than to take that prediction as the last word: likewise, we know better than to take models that do exhibit an initial singularity as the last word. In short, modern cosmology allows us to draw no conclusion about whether the universe has existed for a finite or infinite amount of time. And anyone who says differently is not being completely honest.

Next time: Why the BVG theorem is irrelevant to the Kalam Cosmological Argument!

Bicycles and Universes

I have often imagined debating William Lane Craig myself, and thought out the ways I would respond to his arguments. I have often, while listening to Craig's debates, wondered why his opponent didn't call him on some claim that was simply untrue. Were they just being polite, or did they not realize the falsity of the claim?

I think I may be cured of these fantasies. Sean Carroll did brilliantly in the debate - far better than I could ever have done. He didn't hesitate to say outright, "That's just false!" And his deep expertise in cosmology was the perfect counterpoint to Craig's quote-mining of partially-understood physics papers.

I have only a couple of comments on style and content. I thought Sean did a good job of pointing out where Craig failed to respond to the argument. (This is an area where Craig usually excels.) But instead of merely pointing it out, he ought to have taken the opportunity to summarize his argument again, for those who might not have understood it completely the first time.

Craig, as usual, excelled in his logical organization and presentation of his argument. His concluding summary nicely recalled his original point: not that he was out to prove God's existence, but that modern cosmology lends support to one of his premises.

Here Carroll really missed an opportunity. He ought to have said, briefly and succinctly, that modern cosmology lends no support at all the premise that the universe had a beginning. What we can say for sure is that the universe was a very different place 13.7 billion years ago. But any statement about what happened before that is very speculative and unfounded in established science. There are models in which time has a beginning, and there are models in which it doesn't: none of these models are established science, and so nothing can be deduced from them about a beginning.

One final missed opportunity: when Craig asked, quite reasonably, "If universes can just pop into existence, why not bicycles? What's the difference?" (from memory, not an exact quote) Sean could have responded that there is an obvious and crucial difference: bicycles are things that exist within time, while universes are not. On the contrary, time exists within a universe. For all Craig's bluster about simultaneous causation in the Q&A session, causality has to do with what brings about a change. And for there to be change, there must be time. Since a universe is not something that happens in time, the causality issue doesn't apply.

I think Sean probably had something like this in mind in his argument about the a cosmological model as a self-contained description needing no outside cause, but it would have been nice to respond to Craig's question with a specific difference that clearly matters.

Craig, Carroll, and Cause

Since I've been reading about causes, one part of the debate that stood out for me was the fact that neither Carroll nor Craig tried to define "cause." In terms of the debate, this was undoubtedly wise: a long digression on the different definitions of "cause" would probably have lost most of the audience. But it was bad philosophy. Carroll tried to explain that, for a physicist, having a consistent mathematical model that comports with the experimental evidence is all we need. Any discussion of causes and effects will proceed from that model. Craig simply kept repeating his argument from incredulity: a universe can't just pop into being without a reason.

But certainly, how we think about causation affect our ideas on whether a self-contained universe needs a cause.

(By the way, this issue is independent of whether the universe in question has a beginning or not. While it might seem intuitively that a universe that begins is more guilty of "just popping" into existence, it has often been argued that a universe that is infinite in time is no less in need of some sort of external cause or explanation.)

On Hume's regularity view, causation is a matter of constant conjunction: to know that A causes B, we need to know that A is always followed by B. So what we need to do is to make lots of observations of deities, and if "Let there be light!" is always followed by a universe popping into existence, then we can conclude that gods cause universes.

On Wesley Salmon's analysis, a causal process is one that can carry some sort of a mark that transmits from the cause to the effect. It would seem, though, that if God is perfect, God is impossible to mark. Thus, we could never tell if a mark can be passed to the universe.

Another modern approach is to take causation to involve the transmission of a conserved quantity, like energy or momentum. But neither the theist not the atheist would claim that a universe that has a beginning in time was initiated by a transfer of pre-existing energy, so in this case there is no possibility of a cause.

On the Aristotelian-Thomian analysis, causation involves a potentiality becoming actuality, and an external cause is necessary to tip something into actuality. A universe is obviously possible (if it were impossible we wouldn't be here), so on this analysis an external cause is needed to make the universe actual.

So it seems possible, in principle at least, that both Craig and Carroll are right: differing definitions of "cause" may yield different conclusions about whether a self-contained universe requires a cause.

Two Debates

There have been two very recent debates between high-profile Christians and scientifically-minded opponents.

I'm not that interested in the Ken Ham vs. Bill Nye the Science Guy debate, as Ham's creationist views have no credibility whatsoever. It would be interesting to see what approach Bill took. Some reviews have been positive, others not so.

I'm much more interested in the William L. Craig vs. Sean Carroll debate. Unfortunately, there doesn't seem to be video available for it yet. [ETA: Video now available here.] WLC is infamous in atheist circles for "winning" most of his debates. ("Winning" is of course very subjective in informal debates like these, but when the folks on the opposing side think you won, you probably won.) Carroll is not only a cosmology expert, he is one of the most philosophically astute scientists I know of - he's light-years ahead of Lawrence Krauss or Jerry Coyne, in my opinion. So Carroll is probably the ideal opponent for WLC. Props to WLC for taking on Carroll on his home turf: cosmology. This was either very brave or very stupid of him.

Carroll's own views on the debate are here. (I don't see any comments on it on Craig's website yet.) I think it's not just atheistic bias to assume that, where they disagree on the cosmology, the cosmology expert is probably right.

One new thing I learned from Sean's comments: Some cosmologies have a Boltzmann Brain problem and others don't. That's something I'll have to learn more about.

Craig has employed modern cosmology extensively in the past, both in debates and in his published papers. I was glad to see that Sean brought up the big problem with this: some cosmological models have an infinite past. Others don't. None of these models is considered established physics. So cosmology tells us nothing (yet!) about whether the universe had a beginning or not.

I really like Sean's five responses to the fine tuning argument - especially his #2, which is basically the same as my Fine Tuning Argument for Naturalism. Craig apparently had no response to this point.

There's been a lot of discussion about whether these debates are a good idea or not, from the point of view of promoting science and rational thought, much of it focussed on whose resume will be enhanced and whose pockets will be filled. From the purely intellectual point of view, I'm all for them. It's true that debates are a poor format for getting to the truth, but they're a great format for exposing folks to ideas  they might not have encountered otherwise.

More Detuning

If my Fine Tuning Argument for Naturalism (FTAN) is going to work, it needs to be supported with examples. To recap: the FTAN notes that, because God is (by supposition) all-powerful, there are many ways he could have created the universe other than by naturalistic methods. If we assume that the probability of any of these methods is equal, then there is a very small probability that we will discover that God has chosen a naturalistic method. (The assumption that "probability is equally spread over the various possibilities" is analogous to the assumption made in the usual Fine Tuning Argument for God (FTA for short).) If we find that observations agree with naturalistic methods, then we have a strong presumption against theism.

I already admitted that the FTAN in its original form doesn't quite work, because many instances of God intervening in a naturalistic process would be indistinguishable from a (somewhat different) naturalistic process. So what I need is to show explicit examples where a miraculous intervention would be distinguishable from a naturalistic process, and where the evidence available points to the naturalistic process. I gave a few in the earlier post, here I want to add to the list. (I won't make any attempt to estimate the degree of detuning here.)

1.) Age of the universe - If life evolved through naturalistic processes, then the universe must be old enough for evolution to have happened. If God created the universe, this need not be the case: there is no reason the universe couldn't be, say, 6000 years old. God could have placed humans, animals, plants, etc., on a ready-made earth, and human history could have proceeded in just the way it has.

In fact, we know the universe has been around for about 14 billion years - plenty of time for evolution to have happened.

2.) Age of the earth - Even if the universe is old, there is no reason the earth itself needs to be more than 6000 years old. God could have inserted an earth into a pre-existing universe, complete with animals, humans, etc.

Naturalistically, of course, the earth must be old enough for evolution to have happened. In fact, we know the earth is about 4.6 billion years old - plenty of time for evolution to have happened.

3.) The earth is dateable - Actually, if the earth was created separately by God, there is no reason for it to be any age at all. What I mean is this: The age of the earth can be determined by comparing the ratios of different isotopes in radioactive decay cascades. If God created the earth out of whole cloth, as it were, then comparing these ratios for different cascades would not lead to a sensible determination of the earth's age. Those ratios could have had any values God chose. Unless God was trying to fool us by carefully adjusting the ratios to give a particular, consistent, age for the earth, those ratios need not point to a single particular age.

In fact, we find that the isotope ratios do point to a consistent value of about 4.6 billion years. Once again, naturalism wins.

4.) Age of life on earth - Even with an old universe and an old earth, God could have simply zapped life into existence. He could have done this at any point in the evolutionary history of life, and evolution could have proceeded from that point. Or, he could have simply created all species in their present forms.

The fossil record shows that life has been on earth at least a billion years, and likely as much as 3.6 billion years. Needless to say, this is consistent with the naturalistic evolution of all current life forms.

5.) Common descent - If God created life on earth, there is no particular reason all life forms would be related to each other. He could have created each species individually (as indeed Christians thought for centuries), in which case there wouldn't be any relationship-through-descent.

Naturalistically, it need not be the case that all life is descended from a single common ancestor, either. In principle, life could have arisen on earth more than once. (Here I need to assume that life can arise naturalistically, which we do not know for sure yet.) However, given what we know about evolution, we can be sure that, in time, many different but related species will arise. Think of Darwin's Galapagos finches - many different species but all descended from a single ancestral species that somehow found its way to the islands. So, under naturalism, we expect to find many different species that are related by common descent.

In fact, we have strong reasons to believe that all life on earth is related by common descent from some original self-replicating life form. The evidence comes through the study of the anatomy of living organisms, through the fossil record that reveals the slow modification of life forms over vast periods of time, and through genetics that confirms the relationships deduced from anatomy and the fossil record. This is of course consistent with naturalism, but highly unlikely under theistic assumptions.

I should say again that I don't think this is a very good argument for naturalism. What I hope is that, by turning the fine tuning argument around, I can get you to see the problems with it. In my view the main problem is the assumption that probability is equally spread over the conceivable options. In the FTA, these options are the various conceivable values of the fundamental constants of nature. In the FTAN, the options are the various conceivable ways God could have created life on earth. In neither case do we have any good reason to think the probability is equally spread among  the conceivable options.

Can you think of other examples of ways God could have chosen to create life, but didn't?

What's Wrong With Fine Tuning?

I've been saying for a while that I think fine tuning arguments are bad arguments. I want to explain that.

Suppose I shuffle a deck of cards and let you draw one. It is the queen of hearts. What was the probability that you would draw that card? Think carefully before answering!

Pruss, PSR, and QM

In the discussion of the Leibnizian cosmological argument for God, Tyler mentioned a book by Alexander Pruss (of Prosblogion fame), The Principle of Sufficient Reason, A Reassessment. In particular, Tyler said he thought Pruss had answered all the possible quantum mechanical objections to the Principle of Sufficient Reason (PSR). I have finally gotten a chance to look at Pruss's chapter on QM. It seems to me that he succeeds - much too well.

Pruss has a good grasp of the quantum mechanical objection. He even presents a version of the famous EPR-Bell inequality paradox. He goes on to suggest several ways of reconciling QM with the PSR, including non-local causation, or backward-in-time causation, and hidden variable theories. With regard to the latter, he acknowledges that Bohmian theories run into problems with relativity, and are not a really satisfactory replacement for standard quantum field theory. But, he says, it is possible to show that some such theory could, in principle, explain the QM results.  

For instance, take a neo-Leibnizian theory that says that every point of space is a monad, and this monad has encoded within it a list of all the events that will happen throughout time at that point and through an internal causal process it goes deterministically through these events as time passes. 

Now, it seems obvious to me that this solution achieves too much.  For this could be said of any conceivable pattern of events in any conceivable universe. No matter how random, lawless, and chaotic, those events could be described in Pruss's monad theory as deterministic and causal. So this solution makes the PSR trivial, and therefore uninteresting. If every possible pattern of events satisfies the PSR, then the PSR has no content.

If the PSR means anything at all, then it needs a more rigorous notion of "reason" and "causality" than Pruss is employing here.

Cosmic De-tuning

I really appreciate all the comments on my Fine Tuning Argument for Naturalism (FTAN). Ben Yachov made the excellent point that a constant tweaking by God of the natural laws would itself appear to be a sort of natural law, and not a miracle. Tyler asks about the amount of parameter space that would be gained by God's intervention, and would it really be as large as I am suggesting. He writes, "...we need the numbers to argue concretely." Together, these two criticisms make a serious challenge to my argument. I have tried to answer them in brief in the comments, but here I will try to give a fuller account, complete with numbers.

Ben's point is a very cogent one, and requires careful consideration. If, for example, the strong force were too weak for atomic nuclei to hold together, and yet God held them together, how could that be seen by physicists as anything but a natural law - a strong force, or an additional force, strong enough to hold nuclei together? I feel that, in principle, an omnipotent God ought to be able to allow life to exist in a non-law-like way. But as I have nothing other than a law-like universe to refer to for examples, I think it would be hard to argue this point. So, I will (partially) concede Ben's point. Unfortunately for me, this means my FTAN in its generic form can't go through. Still, I think I can save the argument by appealing to particular cases where Ben's complaint can be circumvented.

First let me point out that, although science has revealed a unified and consistent picture of natural laws, that need not have been the case. A  couple decades ago there seemed to be a developing contradiction about the age of the universe. Astrophysicists modeling the evolution of stars were coming up with ages for those stars that were longer than the age of the universe that cosmologists were suggesting. Of course, creationists got very excited about this and began crowing about how the Big Bang model was inconsistent and so forth. In the event, the star ages got revised downwards and the universe age upwards, so that today there is no longer any contradiction. But that need not have happened. It could have happened that astrophysicists, applying their methods, came up with ages that were much larger than the age that cosmologists, using their own distinct methods, allowed for the age of the universe. Thus science would have had a conundrum. Methodological naturalism would prevent scientists from resolving this conundrum by postulating supernatural intervention. But the conundrum would be available for anyone who wanted to argue for a supernatural being or cause.

What does this have to do with Ben's point? Well, in a universe that runs by rigid natural laws, there is nothing surprising in the fact that the laws give consistent answers to questions like "How old is the universe?" But in a universe created by an omnipotent being, such consistency is surprising - because there are so many other ways God could have created the universe. For instance, by injecting stars that are already in an advanced stage into an already-expanding universe. In this, the young earth creationists are logically correct: God could have created a universe that was only 6000 years old, but which had the "appearance of age." And there is no particular reason that the ages, as deduced from different sources using the (incorrect) naturalistic assumption, would agree with each other. So, in addition to Ben's suggestion that miraculous intervention appears as natural law, there is another possibility:  that a miraculous intervention would show up as a conundrum, i.e., an apparent contradiction between natural laws. I will give some other examples below.

The second general point to make is that there is nothing in our known natural laws - apart from the supposed fine tuning of the parameters of those laws - that seems to prefer life to non-life. Given an omnipotent God, it is possible that there would be either special natural laws for life that differ from those for non-living things, or special exceptions to otherwise uniform natural laws that permit life in places where it would otherwise be impossible. The latter would (per Ben) appear as natural laws - but laws of a very particular type (see below) and of a type we do not see in our actual universe.

OK, now on to three specific examples to show what I mean, and to give some numerical values to answer Tyler.

In discussing these examples, I will use the term de-tuning to describe the amount of parameter space that is opened up by the God hypothesis. Let's call the naturalistically life-permitting range of the parameter the n-range, and the range of the same parameter for which an omnipotent God could allow life (like ours) to arise the g-range. Then define the de-tuning to be the ratio n-range divided by g-range. According to the assumptions of the Fine Tuning Argument, taken over into the FTAN, this ratio represents the probability that the parameter will fall in the naturalistically life-giving range, assuming theism to be true, and all other things being equal.

(Of course, God could presumably allow life unlike life on Earth to arise in a much wider range of parameters, so this ratio is a conservative estimate of the de-tuning.)

1. Cosmological Constant: The cosmological constant is a favorite target of fine-tuning arguments. It is a constant that appears in Einstein's General Relativity equations. A non-zero cosmological constant acts like a uniform energy density spread throughout space, and therefore is a candidate for the so-called "dark energy" of the universe.

If the cosmological constant is large and negative, the universe will re-collapse on itself too fast for galaxies, and therefore life, to form. If the cosmological constant is large and positive, the early universe will expand too fast for galaxies to form - the primordial hydrogen spread throughout space will not have time to collapse under its own gravity.

Now, it turns out that no matter how large the cosmological constant is, the expansion will not tear apart structures that have already formed. So, an omnipotent God could create a universe with a positive cosmological constant, then miraculously collect enough primordial matter into one place for a galaxy to form. Life could then evolve naturalistically without any further intervention. It doesn't matter how large the constant is, this scenario remains possible for any positive value. Thus, the g-range is, in principle, infinite. But if we follow Collins and use the Planck scale as the reference range, then we get a conservative estimate for the de-tuning that is essentially the same as his result for the fine-tuning, which he gives as one part in 10¹²⁰.

This example shows that the de-tuning is not just a matter of slightly expanding the range of some parameter, as Tyler seems to suggest. The g-range is vastly larger than the n-range, and therefore (by the logic of the Fine Tuning Argument) the probability of finding our universe lying in the n-range is vastly smaller under the theistic assumption.

2. Origin of life on Earth: It is possible that natural laws allow life to exist, but don't allow life to arise from non-life. In this case, God could initiate life on Earth by "seeding" Earth with the original life-form(s), which then could go on to evolve into a variety of different forms in a naturalistic way.  There is obviously an infinite number of ways this could happen: God could start with just a single reproducing cell, or she could seed the earth with a whole range of flora and fauna.

There is no way to capture the infinite possibilities in a single number, but we can get a sort of very conservative limit on the de-tuning by considering the age of the Earth. It seems that naturalistic processes required 3 billion years to produce complex life. The Sun is expected to shine for about 10 billion years before becoming a red giant. Naturalistically, then, we should expect the age of the Earth to be between 3 and 10 billion years at the time intelligent life arises. But under theism, it could be anything from nearly zero to 10 billion years. This gives a not-very-impressive detuning of 0.7.

3. Distance of the Earth from the Sun: The earth-sun distance doesn't make a good candidate for a fine-tuning argument: given the large number of planets in the galaxy it is highly likely that some of them will be at the "right" distance from their star for life to arise: the region called the "habitable zone."  (Nonetheless, some folks still cite it.) However, we can turn it into a de-tuning parameter as follows.

A planet too close to its star for life could be miraculously protected from the excess radiation by a sort of blanket surrounding the planet. At this blanket, energy disappears from the universe. Elsewhere, I assume, the laws of physics are the same as in our universe, so energy is conserved everywhere except at this blanket. Thus, the planet could be much closer to the star than the habitable zone, and still contain life. Moreover, the blanket could instead provide energy to the planet, and so life could exist on a planet farther from the star than the habitable zone, too. Indeed, such a planet would not need a star at all, so it could be wandering through interstellar space.

To estimate the de-tuning in this case, note that the Wikipedia page cites the habitable zone as about 1.4 AU wide, providing the n-range. The g-range extends from the surface of the star out into interstellar space; we can take it be half the average distance between stars, or about 2 light-years. So the de-tuning is about 10^-5. (Again, I am making a very conservative estimate. There is no reason such a planet couldn't wander about in inter-galactic space. Allowing that scenario would give a much more impressive de-tuning factor.)

4. Chemistry for life:  Lastly, consider the possibility that the laws of chemistry are not (fine) tuned for life, but God changes the rules so that atoms and molecules behave differently when in living things than in non-living things. Per Ben's dictum, this would appear to us as a natural law: the chemistry of living things is fundamentally different from that of non-living things. (It would give rise to conundrums, too. Molecules are constantly passing from inside the body to outside via respiration, perspiration, etc., and we would have no naturalistic way of explaining the chemical change when they do.)

I don't know how to put a de-tuning value on this possibility, but obviously there are many more ways life could exist under this scenario than in a world with a single unified set of chemical laws.

I think I have shown that divine interventions vastly expand the possibilities for life to exist in the universe. These interventions could show up either as conundrums - apparent contradictions in the laws of nature, as in the first two cases above - or as natural laws that single out living things in a special way. Strictly speaking, only the former count as expanding the parameter ranges that allow for life to exist, since the latter may be considered as "naturalistic" scenarios. But special natural laws for life is just what we don't see in our universe: we don't see planets wrapped in energy-destroying bubbles, or see molecules that behave differently inside a living thing than outside.

Put the point the other way around (and more in the spirit of the FTA), and ask what would we expect to see under the theistic hypothesis? Other things being equal, we would expect to see lots of conundrums and lots of special-exception type laws that allow life to exist, because there are many more ways to make a life-containing universe that include those than there are ways that exclude them. The fact that we don't see such laws and conundrums, then, is evidence against the theistic hypothesis.

Collins vs. Stenger

Robin Collins has written a paper responding to some criticisms Victor Stenger made of the Fine Tuning Argument.

Collins starts out by conceding to Stenger that many of the claimed fine tunings do not qualify  as such. He focuses on a few examples where he thinks Stenger's arguments fail, basing his argument on a close consideration of the physics involved. Collins is a philosopher but, according to his CV, did some grad work in physics.  Stenger is himself a physicist. Collins accuses Stenger of getting the physics wrong. So who's right?

For this post, I'm only going to consider their remarks about the relative strengths of the various physical forces. I haven't read Stenger's book, The Fallacy of Fine Tuning (FOFT), so I'm basing my comments on this paper and Collins's claims about FOFT. I also should make clear that I think the Fine Tuning Argument is a bad argument overall. But I think it might be worthwhile for me as another physicist to try to evaluate the physics part of these arguments.

On the strength of gravity, Stenger writes,

The reason gravity is so weak in atoms is the small masses of elementary particles. This can be understood to be a consequence of the standard model of elementary particles in which the bare particles all have zero masses and pick up small corrections by their interactions with other particles.

Collins responds,

Although correct, Stenger’s claim does not explain the fine-tuning but merely transfers it elsewhere. The new issue is why the corrections are so small compared to the Planck scale. Such small corrections seem to require an enormous degree of fine-tuning, which is a general and much discussed problem within the Standard Model.

Collins is correct: the only natural energy scale in terms of fundamental physical constants is the Planck scale, and we have as yet no understanding of why the proton and neutron masses should be so small compared to the Planck scale. (I should point out, though, that when physicists talk of a parameter being "fine-tuned" it has nothing to do with being fine tuned for the existence of life. Rather, it is a matter of fine tuning for the observed physics of the universe.)

With regard to the relative strength of gravity compared to other forces, Stenger writes,

The gravitational strength parameter α_G is based on arbitrary choice of units of mass, so it is arbitrary. Thus α_G cannot be fine-tuned. There is nothing to tune.

Now, I have to say I find this statement very unclear.  α_G is a dimensionless parameter: it doesn't depend on any choice of units. It is defined as

α_G ≡ G(m_p)²/ℏc,

where G is the gravitational constant, m_p is the proton mass,  ℏ is Planck's constant, and c is the speed of light. No matter what system of units you use to measure those quantities,α_G will have the same value.

Collins, who has read FOFT, says that Stenger means the we can replace the proton's mass in α_G by the mass of some other fundamental particle. Collins, correctly, points out that this is irrelevant to the question of whether α_G as defined is fine tuned. In the absence of any reasonable alternative interpretation I have to agree with Collins again: changing from one parameter to a different parameter can't save you from fine tuning of the original parameter.

Collins goes on to give a rather involved discussion of how various physical properties scale as we allow α_G to change. This is a sophisticated bit of argument; Collins pulls in arguments based on biology, plate tectonics, and planetary science. I tried hard to find some flaws in this analysis, but only came up with a few minor quibbles.

Stenger does make an important point that Collins simply ignores. He points out that if we just change one parameter, that parameter might appear to be fine-tuned. But if we allow for two (or more) parameters to vary at the same time, there might be a much wider range of values that allow for life. For instance,

The relative values of α and the strong force parameter α_S also are important in several cases. When the two are allowed to vary, no fine-tuning is necessary to allow for both nuclear stability and the existence of free protons.

As I said, Collins makes no comment about this claim. There is an obvious counter to it, though: if we increase the number of parameters that vary, we also increase the available parameter space. Even if the life-permitting range of some value is increased in this way, the relative volume of parameter space might still be small.

What's worse, Stenger goes on in the very next paragraph to step on his own toes:

There are two other facts that most proponents of fine-tuning ignore: (1) the force parameters α, α_S, and α_W are not constant but vary with energy; (2) they are not independent. The force parameters are expected to be equal at some unification energy. Furthermore, the three are connected in the current standard model and are likely to remain connected in any model that succeeds it.

If Stenger is right here, then the values of α and α_S cannot be varied independently. So which is it?

First off, I don't know what Stenger means by, "the three are connected in the current standard model." In the current standard model, the three are independent parameters and can be varied independently.

Second, it is true that these couplings change with the energy scale at which they are measured: physicists call this "running coupling constants." But it's not clear to me why Stenger thinks this is relevant. Is he suggesting that at some vastly different energy scale, they might again have the correct ratios to allow for life? I'm not sure what the point of this remark is.

Thirdly, "The force parameters are expected to be equal at some unification energy." This is true in grand unified models (GUTs) and in some supersymmetric models, but these have not been verified experimentally and so remain highly speculative. Anyway, this causes problems for Stenger, because if these parameters are related by physical theory then they can't be varied separately and so his argument about varying two parameters at the same time is no longer available. 

Finally, let's return to Collins. He writes,

Next, I define a constant as being fine-tuned for ECAs [embodied conscious agents] if and only if the range of its values that allow for ECAs is small compared to the range of values for which we can determine whether the value is ECA-permitting, a range I call the “comparison range.” For the purposes of this essay, I will take the comparison range to be the range of values for which a parameter is defined within the current models of physics. For most physical constants, such as the two presented here, this range is given by the Planck scale, which is determined by the corresponding Planck units for mass, length, and time.

Taking the Planck scale as defining the comparison range is badly wrong, for two reasons.

First, the Planck scale sets a limit on current physics in the sense that we expect it to break down around that scale. But in fact we have good reason to think current physics breaks down very much before that scale. Physicists have high hopes that the LHC will reveal "new physics," at an energy that is a factor of 10¹² below the Planck energy. This has not yet happened, unfortunately. But to suppose that we can understand physics at energies all the way up to the Planck energy is just way off.

Secondly, even apart from the issue of new physics, it's absurd to suggest that we can determine whether ECAs are possible for values of parameters that differ greatly from the values we know as the actual ones. Think about it like this: if someone handed you the equations of the Standard Model and of general relativity, together with the values of the constants therein, would you be able to predict the existence of complex life forms? Certainly there are some ranges of some parameters that let us rule out complex life. For instance, if the cosmological constant is to big, then the universe will expand so fast that matter will never be able to clump together into stars and planets. But changing the ratio of (say) electromagnetic to gravitational force is a very delicate matter, and all sorts of unforeseen possibilities might arise, especially for values very far from the true values. Sure, you could say that life like ours would be impossible under those parameters. But the argument is supposed to be about embodied conscious agents in general, not just life like ours.

What's strange is that Collins himself took a much more modest view of the comparison range in a previous paper. There he showed a sophisticated appreciation of both of the points I just made. For example, he writes,

One limitation in the above calculation is that no detailed calculations have been performed on the effect of
further increases or decreases in the strong and electromagnetic force that go far beyond the 0.5 and 4 per
cent, respectively, presented by Oberhummer et al. For instance, if the strong nuclear force were decreased
sufficiently, new carbon resonances might come into play, thereby possibly allowing for new pathways to
become available for carbon or oxygen formation.

He introduces the "epistemically illuminated range" for a parameter: that range for which we can calculate with reasonable assurance of success whether a given value allows the formation of complex life. He applies this procedure to the fine tuning of the strong force for carbon and oxygen production in stars, and comes up with a not-very-fine-tuned value of 0.1. Here, too, he treats only of the possibility of there being life like ours, and makes no attempt to address whether some very different sort of complex life might arise.

To sum up, I think Collins has done a pretty good job of pointing out problems with Stenger's analysis. His treatment of the physics here is a big improvement over some of his earlier work. But his arguments aren't enough to establish his claim. Collins's chosen "comparison range" is certainly too large to be reasonable. And his arguments only address the possibility of life that is substantially similar to ours. Yet vastly different forms of life might be possible in other parameter regions: we simply don't have the sophistication to predict their existence from bare physical laws. (It's possible that life-permitting regions might be scattered, fractal-like, through the parameter space, so that at any life-permitting point small changes don't allow life, while overall the probability of life is quite large.)

Contingency

Tyler has brought up the cosmological argument from contingency and linked to a Philosophy of Religion (POR) article and a paper by Alexander Pruss. The latter is a long article and will take me a while to read and digest. So I'm just going to post some comments on the first article by way of starting (I hope) a discussion.

The argument runs like this:

(1) Everything that exists contingently has a reason for its existence.
(2) The universe exists contingently.
Therefore:
(3) The universe has a reason for its existence.
(4) If the universe has a reason for its existence then that reason is God.
Therefore:
(5) God exists.

I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.

Cosmological arguments always begin by implicitly carving out a "God exception."

• - "Nothing can be beginningless - except God."
• - "Nothing can exist without a cause - except God."
• - "Nothing can be undesigned - except God."

Here we have "Nothing can exist necessarily - except God."

Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today.

The argument from contingency rips these terms out of their proper context and attempts to apply them to things. It asserts that there are contingent things - those that could possibly have not existed - and necessary things - those that could not have not existed. The problem is, no one ever seems to be able to point to something that exists necessarily - except God.

"Exists necessarily" is supposed to mean "exists in all possible worlds." But what is a possible world? Philosophers distinguish different types of possibility. Physical possibility means that which, according to the laws of nature, could happen. Logical possibility means anything that is not logically incoherent. (There are other types of possibility, but these are enough for discussion.) In making a modal argument - one based on what might happen in other "possible worlds" - it makes a big difference whether we are talking about physically possible worlds or logically possible worlds. So, it might be logically possible for the universe not to have existed, while at the same time it is physically impossible for the universe not to have existed. (That would be the case if the laws of physics somehow guaranteed that a universe spring into existence. I'm not claiming that they do guarantee this - only saying that some set of laws might do so.)

The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe.

But also, no God. Because when necessary existence is construed according to logical possibility, it is an empty concept. Nothing exists in the empty world. So there is nothing that exists in all possible worlds. So there is nothing that exists necessarily.

The Nature of Necessity objection was articulated by Bertrand Russell a long time ago, so I'm sure someone has thought up a response to it. If you know of one, let me know!

... We Have Heard On High

Ed Feser has a new paper out explaining why Newton's First Law of Motion is not incompatible with Aquinas's principle that "whatever is in motion is moved by another." In it he expands on some comments he made in response to my criticism of his book, The Last Superstition.

Newton's law states that anything that is in motion will remain in motion unless acted on by an outside force, so the two principles seem to be directly contradictory, at least at first glance. Newton says that an object that is completely isolated, so that it has no external influences on it, will continue to move. Aquinas denies this.

So how does Feser resolve the conflict? Easy! The object in uniform motion is moved along by....

(wait for it)

ANGELS!

Yes, angels are necessary to keep a moving object moving. I'm not making this up, he really says it:

So, it is difficult to see how inertial motion, when interpreted as involving real change, could have a physical cause. But as we implied above, even if its lacks a physical cause, there is nothing in the principle of inertia that rules out a metaphysical cause. Indeed, if inertial motion involves real change, then given the principle of motion together with the absence of a physical cause, such a metaphysical cause is necessary.

Of course, that raises the question of what exactly this metaphysical cause is....

If inertial motion involves real change, then, only a metaphysical cause external to the moving object could be the ultimate source. And we already have a model for such a cause in the Aristotelian tradition. For the motions of celestial bodies were in that tradition regarded as unending, just as inertial motion is (barring interference from outside forces) unending; and while this view was associated with a mistaken astronomy, a metaphysical kernel can be extracted from the obsolete scientific husk. Now the causes of celestial motion in this earlier Aristotelian tradition were, of course, intelligent or angelic substances....

Hence the only possible cause of inertial motion—again, at least if it is considered to involve real change—would seem to be a necessarily existing intelligent substance or substances, of the sort the earlier Aristotelian tradition thought moved celestial objects. (Unless it is simply God Himself causing it directly as Unmoved Mover.)

Here Feser is considering inertial motion as "real change." He also considers what happens if you consider inertial motion as a "state" that doesn't involve any real change: no actualization of a potential. Feser seems to be getting confused by the way physicists use the term "state": the "state" of a (classical) object refers to its location and its rate of change (velocity), so by definition it involves change. Ultimately, though, the question of whether inertial motion is or is not "real change" is not a physical question but a metaphysical one. One would think that Feser's Aristotelian-Thomian metaphysics would tell us which it is. That it cannot just shows how useless that metaphysics is.

The idea that angels are responsible for inertial motion raises a whole (heavenly) host of questions. Presumably, an object at rest doesn't need any angelic mover. However, in Newtonian physics, any uniformly moving reference frame can be considered to be at rest (Galilean relativity). If we have two objects in uniform motion relative to each other, which one does the angel need to guide? If we consider object A at rest, then the angel must move B. But if we consider object B at rest, then the angel must move A. What's a poor angel to do?

And how many angels are needed for this heavenly guidance? If an asteroid is being guided by an angel, and suffers an impact that splits it in two, does the angel recruit another angel to guide the second piece? Or can the first angel handle both pieces? What if the asteroid gets shattered into smaller and smaller fragments? Maybe each elementary particle has its own angel? How many angels are needed to guide a fragment the size of a pin? (And do they dance?)

Once again we see the Sophisticated Theologian in action. When the world doesn't work the way you want it to, just invent some invisible, undetectable beings to fill the gap.

I have to thank Prof. Feser for this paper; it shows more clearly than anything I could write what absurdities result when you try to force the world into a pre-conceived metaphysics.

Assumptions, Assumptions

So, I pointed out my FTAN (Fine Tuning Argument for Naturalism) to Alexander Pruss of Prosblogion, who was kind enough to respond in the comments of his post on fine tuning vs. the problem of evil. Alexander is not just some random blogger. All the folks at Prosblogion are Genuine Sophisticated Theologians - philosophy professors, no less. So, I was glad to get the opinion of an expert on my version of the fine tuning argument. Here's what he wrote (in part, I think I am fairly representing his responses with my excerpts here, but see the original post for his full remarks):

The FTA needs an assumption that there is a significant value to a universe that with very few exceptions, if any, follows orderly and elegant mathematical laws of nature. Such an assumption is compatible with miracles.

Now, this is exactly the sort of thing I was complaining about in my Purple Pachyderm post, and that Carl Sagan was complaining about in his Dragon in the Garage, and so on. For any argument against the existence of God, the theist simply introduces an arbitrary and unfounded assumption in answer.

So I pointed out that in a universe with any miracles at all, my FTAN would still work. For instance, on an earth that was too close to its sun for life to exist, God could prevent the excess radiation from reaching earth, thus allowing life to exist. The exception to energy conservation would be localized, satisfying the "few exceptions" assumption.

Alex responded:

Leibniz argued against Newton/Clarke that it would be inappropriate for God to rely on on-going miracles for the ordinary operation of the universe.
One way to defend this is to say that God has reason to avoid miracles. This reason can be overridden, of course.

OK, so now we have a new assumption: that miracles should not be on-going. Dragon in the garage once again.

 Unfortunately for Alex, this new assumption still doesn't answer the objection. Even with one-time miracles, there will still be infinitely more possible life-containing universes if there is an omnipotent God than if there is not. One example I pointed out was if the laws of chemistry don't allow for chemical evolution of life, but do allow for the existence of life. Then a single miraculous intervention by God could get life started. But there are infinitely many ways God could make this intervention, so there are infinitely many more possible life-containing worlds under the theistic assumption. So my FTAN still works.

Also, this new assumption flies in the face of an argument that theists have been making for centuries:  that it takes God's on-going miraculous intervention to sustain the universe. Here, for example, is Pope John Paul II discussing proofs of God's existence  (emphasis added):

Without such a supreme Cause, the world and every movement in it would remain "unexplained" and "inexplicable", and our intelligence would not be satisfied. The human mind can receive a response to its questions only by admitting a Being who has created the world with all its dynamism. and who continues to maintain it in existence. 

The theist wants to have it both ways. On-going miracles? Proof of God! No on-going miracles? That's proof of God, too!


Alex answered:

• 1. Dougherty and Poston in the paper I linked to argue that one can't consistently run both the FTA and ID-type biological design arguments. Your point is similar, though not the same.
• 2. I think both your and their point is somewhat weakened, but not destroyed, on the supposition that God would have good reason to minimize the number of miracles, subject to other desiderata.
• 3. But in any case, I think many of the proponents of the FTA would say that a number of the constants going into the FTA are such that not only need the values be "just right" (tough making sense of that rigorously, but there is an intuition there that many theists and non-theists find compelling) for life to begin, but for life to persist.

In (2) Alex is saying, I think, that God would prefer to create a life-containing universe without using miracles rather than one that requires miracles.Yet another new assumption. But Alex recognizes that that even this assumption does not "destroy" my point.

Anyway, isn't God supposed to want us to know about him? Wouldn't these miracles be evidence of a God? So why would God want to avoid them?

In (3), Alex is just saying that you can run the FTA (for God) on those parameters that allow life to persist. But this is irrelevant to my argument, which takes precisely the fine-tuned nature of those parameters as an argument against God.

So I have to say, I'm not too impressed with the Sophisticated Theologian's response to my counter-argument. Of course, with enough additional assumptions you can neutralize any argument. But the very need to make those logical contortions reveals how weak the theist's position is.

RP: Fine Tuning Supports Naturalism

The following seems worth re-posting, as some folks still seem impressed with the fine tuning argument. It seems like a fairly obvious point, yet I haven't seen it mentioned much in the fine tuning discussions I've read. I'd be grateful if anyone can show me the glaring flaw in the argument that I'm missing. At the Prosblogion link, Alexander Pruss kindly responded to my remarks; I'll have some comments on his response soon.

I should say again that I don't think the following is a very good argument for naturalism - it's just a way of showing why the fine tuning argument for God is hollow.

Originally posted on Thursday, October 13, 2011.

Garren's comments on the previous post got me thinking more about fine tuning. There are lots of reasons to dislike fine tuning arguments for God, but it occurred to me that we can turn the fine tuning argument around and show how it actually supports naturalism, not theism. Let me explain.

The usual fine tuning argument goes like this: Our universe is governed by natural laws that involve certain numerical parameters - the cosmological constant, the strength of the nuclear force, etc. Some of these parameters must lie in a very narrow range in order for life to exist:

PU = Possible Universes
FTU = Fine-Tuned Universes

So, given a naturalistic hypothesis (N) and general background knowledge (K), the probability of a fine-tuned universe is small:

P(FTU|N&K) = Area(FTU)/Area(PU)  << 1

On the other hand, given the theistic hypothesis (T), we would expect the universe to be suitable for life: P(FTU|T&K) is not small, or at least not as small as P(FTU|N&K).

One of the (many) problems with this argument is that we can't assert that the probability is given by the ratio of the areas without making many additional assumptions: that the values of parameters 1 and 2 are randomly chosen from the space of all parameters, for instance. But that's not the objection I want to pursue. Rather, I want to point out that the probability envisioned in the fine tuning argument is a sort of prior probability that ignores some of our background information: namely, the fact that life actually exists. That is, we have to take (K) to mean "general background knowledge not including the knowledge that life exists."

But we actually do know that life exists (L), and it is perfectly legitimate to include this knowledge along with our other background knowledge. If we add this knowledge back in, then trivially P(FTU|N&K&L) = 1: under the naturalistic hypothesis, the only way that life can exist is for the universe to have parameters that allow the existence of life.

But that is not true if God exists! Indeed, under theism, there is no reason to expect that the universe will be fine-tuned.

Remember that God is, by hypothesis, omnipotent. That means that God could  have caused life to arise by miraculous means, even in a universe that was not fine-tuned. Say, for example, that the universe had a value of the cosmological constant that caused it to expand too fast for galaxies to form. God could have prevented a galaxy-sized region from expanding in order to allow our Milky Way to form. Or God could have inserted a pre-made galaxy. Or he could have inserted an additional force that operated only within our galaxy and that countered the effects of the expansion. Or any number of other possibilities, because God can do anything.

So, under theism, the diagram looks like this:

That is, the probability of a fine-tuned universe under the theistic hypothesis is:

P(FTU|T&K&L) = Area(FTU)/Area(PU)  << 1

Conclusion: given that we know that life exists, the probability of discovering we are living in a universe with parameters fine-tuned for life is much higher under the naturalistic hypothesis than under the theistic hypothesis.

Space elephants! Space elephants!

 Can you prove there is no god?

From the point of view of argument, it seems like a big mistake to take on the task of disproving the existence of God. After all, if someone is making the claim that there is a God, then the burden of proof is on them. Also, I don't think it's possible to disprove the existence of God any more than it is possible to prove it.

Still, there are very many people who believe in God, and so we atheists are often in the position of explaining why we don't think that a god of some particular description is at all likely or possible. The inevitable response from the theist is that my argument doesn't apply, because God is some sort of special exception.

Take, for instance, the claim that God is a person. Most Christians, at least, are committed to this claim. (Worse, they are committed to the claim that God is three persons, though only one being, something that seems incoherent on the face of it, and even sillier when they say in addition that God is "simple". But let's not go there....) What is a person, though? We usually think of a person as a being possessed of  intelligence, capable of thinking and reacting in complex ways. But God is supposed to be somehow outside of time, so she can't react to anything. Nor can she have thoughts in the sense we do: a succession of mental states that relate to a person's situation at a particular time.

And what is intelligence but the ability to process information in complex ways? But God, being omniscient, can never receive any new information, and, being outside of time, cannot process anything: a process is something that takes place over time.

So how does the theist respond to these challenges? Ed Feser has helpfully given examples in some recent posts.  He agrees that God canot have the same sort of consciousness as we do:

There’s nothing it’s “like” to be God if we mean by that a certain kind of stream of thoughts and conscious experiences, like ours but (say) more vivid and encompassing a perceptual awareness of every part of the world at once.

But, he says, God's intelligence is "analogous" to ours.

OK, sure - if by "analogous" you mean "utterly and completely different from." God doesn't have perceptions, or mental images, or thoughts, or emotions, God can't gain new knowledge of anything, or change Her mind. God is, in fact, incapable of pretty much everything we associate with personhood.

So is God less than a person? Of course not!

Similarly, to say that it is a mistake to try to grasp the divine intellect by modeling it on our thought processes does not entail that God is less than “personal” in the sense that we are personal (as contrasted with impersonal objects and forces like stones and gravity).  Rather, God is more than personal, in that everyday sense of “personal.” His intellect is not inferior to our conscious thought processes (as a stone, gravity, or even the unconscious informational states of a computer are to that extent inferior to our conscious states) but on the contrary beyond and higher than them, just as divine power is beyond and higher than the relatively trivial capacities in created things that we characterize as “powers.” 

Oh, I see: our poor human personhood is but a pale shadow of Her perfect Personhood.

The only thing that can be said about arguments like these is that they are so clearly born of desperation, so clearly instances of equivocation and special pleading, that they hardly require a response. Any more than the Purple Plutonian Pachyderm.

Sensus Elephantiasis

I have to apologize that posting has been so slow of late. Sometimes real life intervenes.

The argument from "sensus elephantiasis," refers, of course, to Plantinga's claim to have a sensus divinitatis, a direct sense of the divine. I previously called this "the worst philosophical argument ever."  Commenter Garren pointed out that there definitely are differences in people's perceptive abilities: if 99% of us were blind, the 1% would seem to have an amazing ability unavailable to the rest.

I can't fault the logical point here. Yet, it seems to me, by now we pretty much have agreement on what powers people possess and what powers they don't. Sight, smell, touch, hearing, taste, proprioception, yes. ESP, telekinesis, channeling, no. Any claim to further powers would seem to carry a large burden of proof.

Garren goes on to point out that the hypothetical blind scientists would easily devise tests to see whether the strange faculty of "sight" corresponded to the real world - i.e., did their perceptions agree with what could be sensed via the "normal" senses of touch, hearing, etc.? Religious claims of special senses fail the corresponding tests rather spectacularly: people differ greatly on the number, attributes, and powers, of gods.

Commenter c emerson has a response to my purple pachyderm argument at his own blog, Random Walk: first part, second part, third part.

The Purple Pachyderm Argument

Pachydermist: I believe there are purple space elephants living on the planet Pluto.*

Apachydermist: Um, OK, what evidence do you have for that belief?

Pachydermist: I have the ability to sense them directly. Whenever I feel a tingling in my left little toe, I know that these elephants exist. I call this my sensus elephantiasis, because everything sounds more impressive in Latin.

Apachydermist: And you feel this tingling...?

Pachydermist: All the time.

Apachydermist: Riiight....

Pachydermist: Well, can you prove that there aren't any purple Plutonian pachyderms?

Apachydermist: I know I'm going to regret this, but here goes. Let's start off with the easy stuff. There can't be any elephants living on Pluto, because Pluto has no air and elephants need air to breathe.

Pachydermist: Ah, but you don't understand. These are space elephants, they don't need air to breathe.

Apachydermist: Well, they wouldn't have anything to eat or drink on Pluto.

Pachydermist: Space elephants! Space elephants! They don't need any stinkin' food or water!

Apachydermist: OK, but look: if these things don't eat or drink or breathe air, and they're not related to Earth elephants by descent or ancestry (how would they have gotten to Pluto from Earth, or vice versa?) then they can't in any meaningful sense be elephants, can they? I mean, if these things are so utterly different from anything we know as an elephant, then there's no sense in calling them elephants.

Pachydermist: Ah, but these are the true, essential elephants. Our Earth elephants are but a pale shadow of their perfect pachydermic nature.

Apachydermist: And you learned all of this from a tingling in your toe?

Pachydermist: Yes, and through pure logic.

Apachydermist: Uh, right, logic. I knew I was going to regret this. Well, just to prove you wrong, I'm going to build a spaceship and travel to Pluto and search for these elephants.

Pachydermist: OK, sure, but it won't do any good.

Apachydermist: Huh? Why not?

Pachydermist: You see, these space elephants are invisible.

Apachydermist: Invisible? You said they were purple!

Pachydermist: Yes, but they are the essence of true purple. The color we know as purple on Earth....

Apachydermist:  ... is but a pale shadow, yeah OK I get it. But I'll make a huge cordon across the entire planet and corral the elephants...

Pachydermist: Sorry, they're not only invisible, they're intangible, too.

Apachydermist:  Intangible, too? What are they made out of?

Pachydermist: An immaterial substance.

Apachydermist:  Immaterial substance? It seems to me that translates as "immaterial material", or "substance which has no substance." I think I've finally found something we can agree on. Your pachyderms are oxymoronic!

Pachydermist: Actually, they're very smart. They have a level of intelligence compared to which human intelligence is just ....

Apachydermist:  (Exits stage left, shaking his head sadly.)

Very silly, I know. But these are the same arguments  theists use against atheists, as I will demonstrate over the next few posts. I don't know when I'll get to those posts, so in the meantime, you can try to guess whose arguments I'm thinking of. Have at it!

* Pluto is now considered a dwarf planet, but a dwarf planet is a planet, too, right? So no complaints about "Pluto is no longer a planet! Aaaugh!"

Act and Potency in Physics

A while back, BeingItself commented on this post by quoting Ed Feser:

The Aristotelian theory of act and potency is the classic example of such a piece of middle ground knowledge. It is grounded in the basic empirical datum, the fact of change. But it is not a description of this or that particular change or this or that particular kind of change but rather of all change as such. Hence while empirically grounded it is not subject to falsification by theorizing in physics, chemistry, etc., because the phenomena dealt with in all such theorizing, since they all involve change, implicitly presuppose the theory of act and potency.

BI then asked,

Do you think that is correct? Do physicists presuppose this metaphysics?

This is a great question, and I thank Mr. Mosis for bumping it back to my attention. I really have no idea what the answer is. Although I've read a fair smattering of philosophy of science and philosophy of physics, I can't recall ever coming across a discussion of the metaphysical assumptions underlying physical theories - not even in discussions of the foundations of quantum mechanics, where some sort of metaphysical groundwork would really be useful. As Feser points out in the linked article,

[F]or most of its history the philosophy of science was essentially concerned with questions about the methodology of science, the logical structure of scientific theories, the meaning of scientific assertions, and the like...

Feser says there has recently been a return to metaphysical issues, and links to some relevant books. Not having read these, though, I'm going to plunge in and try to give you an idea of how physicists go about their business.

(I suspect one reason philosophers avoid these issues is the fear of having the rug pulled out from under them by physicists. Anything any philosopher wrote on time, for instance, probably sounded remarkably silly after Einstein revolutionized our concepts of space and time.)

Let's start with classical mechanics. (Quantum mechanics is a whole different ball of wax, and its interpretation remains very controversial.) The basic entities we work with are:

• Space - the three-dimensional continuum that is the stage on which everything takes place.
• Time - is what keeps everything from happening all at once.
• Point particles -  the actors on the stage. They are idealized objects that have a location in space at a given time. 
• Fields - extended entities that exist at every point in space. They are produced by (certain types of) particles and they exert influence on  (certain types of) particles.

(Of course, after special relativity we had to stop talking about space and time and start talking about a unified spacetime as the stage on which everything takes place. And after general relativity, we had to get used to curved spacetime. But the basic picture remains the same.)

We then proceed to write equations for how the particles and fields change in time. (Newton's laws for motion of particles, and Maxwell's equations for the changes of fields, for example.) Here the possibility of change is implicit in the fact of a time coordinate: there is no reason to assume that what obtains at one time also obtains at some other time. So, my first reaction to BI's question was to think that of course there's nothing like act and potency in physics. We just talk about change as a fundamental fact about the universe.

When I read Feser and his Aquinas quotes on actuality and potentiality, it seemed as though they were saying that the actual is real, and the potential was sort of real, too, as if it were sitting around somewhere waiting to be pushed into actuality. This seemed like a quaint, medieval idea that had no relevance to modern physics. But the more I thought about it, the more I began to realize that we actually have an approach in physics that very closely resembles this. That is the idea of a state space.

The state space is the collection of all possible states of the system. For a point particle, the state consists of its position and its velocity, or state of motion. For a single particle moving in one dimension, the state space consists of the two-dimensional plane (x,v). The particle's motion is then envisioned as a path in this plane. So, we do indeed think of the possible states of the particle as sort of existing "out there", and the (actual) particle as moving from one of these states to another.

So is Feser right - does modern physics presuppose the notions of actuality and possibility? I'm not convinced. For one thing, the whole notion of state space wasn't developed until the 19th century (by Hamilton, I think). And for another, the state space picture doesn't remove the need for a time coordinate. As I said before, the existence of time already allows for the possibility of change. And we can't even talk about the state space without the notion of velocity, which itself requires time. So it seems to me that the concepts of time and change are metaphysically prior to those of potentiality and state space.