The BGV Theorem Does Not Mean What You Think it Means

I’ve addressed the use and misuse of the Borde-Guth-Vilenkin (BGV) Theorem a number of times in the past (The Misquoting WLC, The Eternally Inflated (Multiverse and WLC) and Multiholes in WLC’s Physics Arguments).

The apologetic argument goes a bit like this:  Atheists are terrified by the idea the universe must have begun, because if the universe has not been in existence forever, something must have created it.  The BGV Theorem says that inflation must have had a beginning, so the universe has a beginning, therefore the universe has a creator.  Therefore god.  (Much leaping around fisting the air and yelling “OOH-ya” and “who da man”.)

To be brutally frank, Vilenkin (one of the authors of the theorem) seriously did not help when he wrote:

It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning.

Admittedly, he did write a couple of paragraphs later:

Theologians have often welcomed any evidence for the beginning of the universe, regarding it as evidence for the existence of God… So what do we make of a proof that the beginning is unavoidable? Is it a proof of the existence of God? This view would be far too simplistic. Anyone who attempts to understand the origin of the universe should be prepared to address its logical paradoxes. In this regard, the theorem that I proved with my colleagues does not give much of an advantage to the theologian over the scientist. As evidenced by Jinasena’s remarks earlier in this chapter, religion is not immune to the paradoxes of Creation.

But the damage had already been done, there was a paragraph begging to be cherry picked by apologists and they went to town.  (A search on “There is no escape: they have to face the problem of a cosmic beginning” brings up page after page of apologetic nonsense.

As an aside to very interesting video on a universe from ‘nothing’, Vilenkin makes a very clear comment to the effect that the BGV Theorem does not mean what people like WLC want it to mean.  In this part of the video, he very specifically says that the BGV Theorem does not conclude that the universe must have a beginning, it concludes only that expansion must have a beginning.

WLC will need to find a new argument for an absolute cosmic beginning.  Well, he should, but given his track record, it’s likely that he will just ignore inconvenient statements by the people whose arguments he misrepresents.

Theological Zombies to the Rescue!

I was listening to Skydive Phil’s debate with Randal Rauser recently and it occurred to me that I have a solution to the Problem of Evil.

I went part of the way in Theological Zombies already, but in that I was mostly aiming at the problem associated with the absence of compossibility, or to put it less abstrusely, the problem of a supposedly good, all-knowing, all-powerful god creating this universe in which many of the sentient beings with whom god apparently wants to have a loving relationship (being saved) will end up being damned (being sent to hell, being extinguished or merely being set apart depending on the type of god).

Phil and Randal were talking specifically about the suffering of animals and how that is inconsistent with the existence of a tri-omni god.  They danced around some of the standard defences, that animals are simply fleshy automatons (Descartes’ solution) or that animals don’t feel pain as we do (WLC’s solution) or that demons might be to blame (Plantinga’s silly argument, but only as a possible defeater raised in order to avoid a logical problem) or that the suffering of animals is somehow necessary to achieve a greater good (as I recall Randal tended to lean this way).

Now, in the Theological Zombies argument I present a way in which everyone can be saved.  The fact that there are worlds in which you may be saved but others are cannot is resolved by observing that god is not limited to creating one single universe.  As many universes as are needed can be created and largely populated with zombies that act precisely like other people would in the same circumstances, people who would either be saved in a universe with less suffering or who need a universe with even more suffering in it to be saved.  Therefore, the only beings in this universe who are not zombies are those for whom salvation is compossible with all the other real, non-zombie inhabitants.

If that means that god needs to create billions and billions of universes, that’s ok, because god is not limited in power, or by time, or anything (except perhaps logic).  But it does mean that anyone in this particular universe who is real and is being saved in it is a bit of a scumbag by virtue of it not being possible to be saved in any universe with less pain and suffering in it.

While I was specifically focusing on how Theological Zombies could avoid the problem with consigning so many people to hell or whatever, I can see now that the same argument applies to animals.  For those humans being saved in this universe, it is not necessary that real animals need to suffer.  All that is needed is for there to be theological zombie animals which act precisely as a real animal would if it were to suffer.  Which makes the people who are being saved in this universe even worse scumbags since they need those animals to suffer in order to be saved.

The positive thing though is that for the relatively low cost of accepting that pretty much nothing in this universe is actually real, and that you are a total scumbag who needs innocent animals to suffer, you can believe in whatever god you like and avoid the Problem of Evil altogether.

Plantinga, if he wants, is welcome to use this as one of his defeaters – at least it’s a lot less silly than pain and suffering demons.

The No Boundary Proposal and i-Time

Skydive Phil and co recently released a couple of new videos in their Before the Big Bang series.  They have upped their tempo a little, with two episodes being released in less than four months.

I’ve not yet had time to look at “BtBB6: Can the Universe Create Itself?” (to which the answer would initially seem to be no, but I’ll reserve further comment until I’ve watched it).  I have, however, enjoyed “BtBB5: The No Boundary Proposal” and I must congratulate Phil on getting such luminaries together – including Stephen Hawking.

I do have a vested interest though, or two.

The first is that the model aligns very closely with something that I’ve pondered myself, which I’ll go into in a moment.  The second is that the No Boundary (or Hawking-Hartle) Proposal rips a hole in two of WLC’s favourite arguments, namely the one when he trundles out the BGV theorem and uses it to argue for his god and the one where he argues that the universe is contingent (while excluding necessity as underlying the beginning of the universe).

I’ll simply throw that out there and encourage the reader to watch the video.  Just keep in mind that if there is no conceptual issue with a natural universe that is not past eternal, then the BGV argument is short circuited and that if a natural universe can be necessary by virtue of physics, then the argument from contingency fails.  Or, at the very least, WLC and his ilk are constrained to a form of argument from incredulity (and/or from personal ignorance).

Now, the physics of the No Boundary Proposal.  I will say up front that I never considered an initial 4-space (ie a four-dimensional manifold) somehow transforming into a 3-space plus time, but I certainly have considered i-time.  Let me start from somewhere close to the beginning, or perhaps a long way before the beginning.  Bear with me if it seems like I am taking a weird detour.

One of the characteristics of a black hole is its density.  Density is simply the mass of something divided by its volume, so a very heavy (or, more correctly, very massive) thing in a small volume has high density, and something with mass spread out over a large volume has low density.  Lead is dense, air is not.

We tend to think of stars as very dense, and they certainly have a dense core, while black holes are thought of as either collapsed stars or, in the case of a supermassive black hole, many stars crushed together so tightly that nothing emerges from them – not even light.  So you'd be forgiven for thinking that black holes are very dense.  Not so fast ...

A star has a fuzzy boundary, so the answer to how dense it is is not as simple as with something more distinct like, say, a lump of granite.  Our sun has a core with a density in the order of 150 g/cm³ (liquid water is about 1 kg/litre, or 1 g/cm³) but if you measure from the “surface” of the sun, the photosphere, the average density is only 1.4 g/cm³ which is one quarter the density of the Earth at 5.51 g/cm³.  But at the photosphere, the sun has a density of 0.0000002 g/cm³ compared to the density of the atmosphere at sea level of 0.001225 g/cm³.  Only above 60km above sea level do you start to see atmospheric density in the order of the density of the sun at its "surface" (and then there's another 40km further to go until you are officially in space).

The sun doesn't really stop at the photosphere though, because there is also the corona, which extends out millions of kilometres from the sun (and is actually hotter than the "surface" of sun, up to 450 times hotter).  Note that the radius of the sun is a little under 700,000km, so the corona covers a much greater volume.  Then there is also the area in which solar wind is a factor, which could be argued as being the heliosheath and is sort of equivalent to the atmosphere of a planet (it's a "protective" bubble against the interstellar medium).  This heliosheath extends far out beyond Pluto or about 120 au (astronomical units, so 120 times further out than Earth).

Unlike a star, a black hole has a very well-defined boundary, known as the event horizon which itself can be defined by the Schwarzschild radius or the distance from the centre of the mass of a (non-rotating, spherically symmetric) black hole at which a photon can only just escape (because the escape velocity is the speed of light).  The Schwarzschild radius is directly proportional to the mass (M*2G/c²).  The volume defined by a radius is, however, proportional to the inverse of the radius cubed (4/3.π/r³).  The upshot is that the density of black hole is proportional to the inverse square of the mass – as the mass increases, the density of the black hole goes down (proportional to the square of the increase of the mass).

If you plug in the mass of the universe into the equation (3c⁶/(32G³.M²), you get a density in the order of the density of the universe – implying that we may be in a black hole.

(Note: if the black hole in question is rotating or not spherically symmetric, the argument that we are inside a black hole only improves.)

If we are indeed inside a black hole, the question then arises as to what is outside the black hole.

Let’s leave that question aside for a moment and consider instead what happens to time as you approach the Schwarzschild radius (or event horizon) of a black hole.  The equation for this is given by t_o = t_f.√(1-r_s/r) which basically tells us that, as your distance from the centre of the black hole (r) approaches the Schwarzschild radius (r_s), the time you experience (t_o) decreases as compared to that of a distant observer (t_f) – or time slows down as you approach the event horizon.  This is a phenomenon referred to in the movie Interstellar where travellers deep in the gravity well of a very heavy (massive) planet left their buddy up in space alone for ages while they only experienced a relatively short time on the (liquid) surface.

But this is all about what happens outside the black hole, on the “safe” side of the event horizon at r_s.  If you look at that equation again, you’ll see that something funky happens with time when r < r_s.  You get the square root of a negative number, which is imaginary time, or i-time.  Inside a black hole, time shoots off orthogonally from time outside the black hole, and it does so with no limit because as r->0, r_s/r->infinity (and (1-r_s/r)-> negative infinity and √(1-r_s/r)->i-infinity).

There’s a spatial effect as well.  Compared to a distant observer, rulers in a gravitational well (as in close to a black hole) shrink and once, inside past event horizon, they expand out into i-space.  In other words, within a black hole, there is effectively infinite space and infinite time, but it’s all orthogonal to what is outside.

Now consider the view from inside a black hole.  The entire history of the universe outside will effectively happen instantaneously at t=0, everything that is ever sucked into the black hole will appear instantaneously, having been ripped apart by the transition through the event horizon, with no information remaining in it. There will, be at t=0, basically no space (there’s a limit to how little space there is due to how much mass-energy can fit into it) but as space expands out (orthogonally to space outside the black hole) you basically end up with a Big Bang.  There is a natural correlation between a t=0 and a severely limited amount of space, there’s also a natural arrow of time, and a natural expansion.

So that’s basically how I think of the Big Bang, with each universe eventually (after an eternity) ending up ripped apart inside a new black hole which has a new Big Bang and the routine keeps going, with multiple eternities (and maybe even multiply infinite space, although that is less certain to me, particularly given the initial non-zero space condition).  The thing that I find so interesting with the No Boundary Proposal is not so much that it parallels my model (which it only does to some small extent), but rather that there is a willingness to consider what I call i-time especially given that it is an unavoidable consequence of my model.  There’s also the fact that, as far as we inside our black hole are concerned, the universe outside is as good as a four-dimensional manifold – what happens (or rather happened) out there is all done and dusted, set in stone in a way because it’s all in the past from our perspective (and it all happened instantaneously at t=0) and, from our perspective, the entire history of that external universe is in imaginary time, since that time is orthogonal to our time.

The benefit of my model is there’s a clear explanation as to the transition to our time and our space.  The down side is, well, there are truly brilliant brains looking at the maths behind the four-dimensional manifold and they seem to think that it works.  There’s just my brain looking at my model.

Seems Implausible

I've often been curious as what precisely is meant by the term “plausible” in apologetics.  WLC and his ilk* frequently bang on about how their arguments build a cumulative case based on their being "more plausible than not".  I wondered whether they have looked a dictionary (my emphasis):

plausible (google)

adjective

(of an argument or statement) seeming reasonable or probable.

"a plausible explanation"

(of a person) skilled at producing persuasive arguments, especially ones intended to deceive.

"a plausible liar"

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plausible (merriam webster)

1:  superficially fair, reasonable, or valuable but often specious <a plausible pretext>

2:  superficially pleasing or persuasive <a swindler… , then a quack, then a smooth, plausible gentleman — R. W. Emerson>

3:  appearing worthy of belief

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plausible (dictionary.com)

adjective

1. having an appearance of truth or reason; seemingly worthy of approval or acceptance; credible; believable:

a plausible excuse; a plausible plot.

2. well-spoken and apparently, but often deceptively, worthy of confidence or trust:

a plausible commentator.

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plau·si·ble (thefreedictionary)

adj.

1.    Seemingly or apparently valid, likely, or acceptable; credible:

a plausible excuse.

2. Persuasive or ingratiating, especially in an effort to deceive.

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It seems odd to me that the term "plausible" should be used so frequently by WLC when it is so tightly linked to the mere appearance of truth, validity and reason and also to deceptiveness.

Why not avoid that problem by using the phrase "more likely than not" or "more reasonable than not" or "more consistent with the facts than not"?

And yes, I know, Blackwell gives "plausible" a specific philosophical meaning, but even that should be read carefully (my emphasis again):

A claim is plausible if it subjectively seems worthy of belief even if we have not necessarily studied its objective ground

This doesn't really do much more than say that something is plausible if it's superficially convincing or comes from a subjectively credible authority.  And it includes a caveat such that when we have a claim that is “plausible”, we have not fully (or properly) investigated the evidence in support of it.  A claim that is completely wrong can still be plausible, and an (apparently) implausible claim can be right.

This doesn't, subjectively speaking, seem to be the best of grounds on which to argue for the existence of one’s god.  Belief in maybe but, honestly, is minimal justification for belief all the theist is after?  This doesn’t seem plausible.

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Examples of use of the phrase “more plausible than not” but WLC and his ilk:

William Lane Craig - apologist

William Dembski and Bruce Gordon - IDiots

Steven Dunn – apologist

WLC actually seems to be one the most frequent users of the phrase.  Here’s what he had to say in a booklet, Five Arguments for God:

In fact, if the premises, taken together, are more plausible than not, then the conclusion is guaranteed to be more plausible than not, and so you should believe it.

Apparently, WLC believes that there is an obligation to believe that which is plausible.

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There’s an interesting effect of negation in English which I suspect sneaks past many people.  Naively it seems that the use of “not” or negating prefixes such as “im-” imply some sort of negative reflection of the concept in question.  But this is not the case.  Consider the words “possible” and “impossible” in the following context:

It is ____________ that X (where X = (X is true)).

If we think of a phase space, mapping out the modalities of X, there might be only a very small area in which X is possible meaning that everywhere else in that phase space, X is impossible.  If there is no part of the phase space in which X is necessary (where is it not possible for X to be impossible), then across the entirety of that phase space, it is possible that not-X = (X is not true).  In other words, impossible, or not possible, is a much stronger concept than a “possible not”.

This imbalance in the strength of a term and its negation applies also to plausible (and implausible), perhaps even more so.  Because the bar for being plausible is set so low, it becomes a major issue if a claim fails to clear to that bar – so that a claim is “implausible” is a very strong statement.  When saying that a claim is “implausible”, you are not implying that it’s plausible that the claim isn’t true, you’re not even implying that the claim doesn’t seem reasonable or probable, but rather you are implying that it’s not possible for the claim to seem reasonable or probable.

I note that WLC does not shy away from appealing to the (apparent) implausibility of competing hypotheses, sometimes saying they are “extraordinarily implausible”.  I suspect that these sorts of claims are quite effective as rhetoric, in part because of an implicit understanding of how strong an appeal to implausibility actually is.

That all said, I detect a bit of manoeuvring on the part of WLC to avoid any problematic claims to certainty.  For example, from the WLC-Tooley debate:

Now I'm not claiming that I can prove that God exists with some kind of mathematical certainty. I’m just claiming that on balance the evidence is such that theism is more plausible than not. Let me present, therefore, six reasons why I think it’s more plausible that God exists than that atheism is true.

I think what WLC is doing here, consciously or not, trying to eat his cake and eat it too.  He first claims to not achieve an unrealistic standard of proof (some kind of mathematical certainty) and then he compares a plausibility claim with an implausibility claim.  Such a comparison is a rhetorical cheat.

The theist should not really be comparing the plausibility of her belief claims again their implausibility.  She should instead be digging deeper into those claims and going beyond questions of plausibility, beyond questions of appearance, seeming and subjectivity and looking at the objective grounding of her particular form of theism.  But of course, this is unlike to be an approach that an apologist would promote.

Turning Fine-Tuning on its Head

The existence of you and me is, in a sense, fine-tuned.  This statement might come as a surprise to anyone who has noticed that I am vehemently against the fine-tuning argument, but I can explain.  The fine-tuning argument goes a little like this:

Fine-tuning,

Therefore, god.

I've stripped it down a bit, but those are the basics of the argument.  I don't have much against the first line, given the inherent (often ignored) caveats, but I do have problems with the second as I would have problems with the first premise of an expanded fine-tuning argument, namely the assertion "If fine-tuning then god".  The stripped-down but deluxe version of the argument, which I also have problems with, is:

If there is fine-tuning, then either god or something else,

Fine-tuning,

Not something else,

Therefore, god.

My problem is with the third line of this version.  When argued by such luminaries as WLC the main thrust is that the idea that we should be here purely by chance, when the odds against are so staggeringly high, beggars belief.  The problem is that there remains a gap between unlikely and impossible.  The answer "something else" remains possible, and to some it is believable despite being unlikely, while the god solution is simply not believable. 

What I don't argue against is the line "Fine-tuning", so long as that line is short-hand for "if things were slightly different in this universe, then intelligent life would almost certainly not exist".  If "fine-tuning" is short-hand for "this universe was designed by a divine being of some sort", then of course I have a problem but then the whole fine-tuning argument resolves down to begging the question, "god, therefore god".

Now, about you and me being fine-tuned - let's get all excited about it!  Think about how amazing it is that we exist on one little planet in such a massive universe.  What are the chances of that?  If we go by volume, we can see that the Earth is only about 10^-56 of the observable universe's volume.  If we were just about anywhere else, we'd be dead. 

But of course it'd be silly to compare our location with a random spot in intergalactic or even interstellar space.  It's pretty cold out there, and we need to be a bit warmer than that, without being too warm.  So we could consider how remarkable it is that we are in orbit around just this star, one that is so suitable for intelligent life to develop.  While our sun is one of about 10²¹ stars, it's a pretty common type of star - roughly one in five is a G-class star.  And about one in five of those is estimated to have an "Earth-like" planet in orbit around it - in the habitable zone.  So about one in twenty-five stars are of the right type with the right type of planet in orbit around it.  (ed. - these numbers have changed with more observation, but not in a direction that helps the apologists)

Not that amazing after all.  Although, to get the one in twenty-five figure we are assuming that once we've got the right type of star, and it's got the right sort of planet in the right sort of zone, then we get that one automatically.  That's a little unreasonable.  Our solar system is jam-packed with planets, moons, asteroids and comets (by which I mean generally "very sparsely packed, but with more than half a million objects").   The chances of ending up on the one habitable object out of all of those is about, well, one in half a million (after we've select the right star, with the right planet in orbit around it). 

If we did limit ourselves to a suitable planet in orbit around a suitable star though, the fact is that we are on a very privileged part of that planet - standing somewhere close to the surface (ISS residents aside, plus anyone currently on a high-altitude international flight).  We're sitting or standing rather comfortably on the surface instead of floating high in the atmosphere, floundering at the bottom of an ocean or being crushed and then burnt to a cinder in the core.  And we live in a community that is relatively well placed on that surface: not in a volcano crater, not in Death Valley, not in Antarctica, not just below the summit of Everest.  What great fortune!  However, only about one sixth of the Earth's surface is habitable (half of the land mass).

Then there is timing.  This is a rather good time for intelligent life.  The planet that we are on has sufficient oxygen, not too much carbon dioxide, it still retains enough of the ozone layer that we don't die too quickly of cancer and the temperature is about right - not too cold that we freeze to death and not too warm that we are constantly flayed by killer storms or reduced to desiccated husks.  We have flowering plants, most importantly variations of grass that permit large populations to feed themselves, and they have only been around for about 55 million years, so 1.4% of the time that the Earth has been a planet.  Humans (as Homo sapiens) have only been around for about 200,000 years, or one thousandth of one per cent of the age of the Earth.  Genetic research indicates that humanity has gone through a few bottlenecks, the most recent may have been about 70,000 years ago - meaning that we were lucky, as a species, to not go extinct at that time.

It's remarkable that we're alive at all.  It's in the order of one in a billion, even aside from all the unlikeliness of one particular human meeting another particular human and producing a specific human at a specific time (with none of them being killed by any of the lethal flora and fauna that is abundant on this planet).  So … sure, we're fine-tuned, in a sense.

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The thing is that what I have just provided is a continuous stream of indicators that our universe is not finely tuned for human life.  Our planet is not finely tuned for human life – there’s a very narrow band geologically and temporally.  We are finely tuned to exist in that very narrow band and the fine-tuned-ness of a biological organism to its environment is far more elegantly explained by evolution than it is by the introduction of a creator being.

The bottom line is that fine-tuning is not a challenge to naturalism or evolution or atheism, the real challenge is to the creationist or intelligent design theorist to explain why the universe is so unrelentingly hostile to humanity.

WLC - A Hole (Through which Theological Zombies Emerge)

The following sequence is from about minute 54 in the debate between Raymond Bradley and William Lane Craig, although the text is taken from the transcript at Reasonably Fallacious - so be aware that this is the version sanctioned by WLC:

Dr. Bradley:

I'll return to this microphone, if I may, okay? Now let me try to get my point across on this because this is crucial. And we both agree that Dr. Craig's strategy has been to try to prove that propositions (1) and (2) are compatible on the grounds that there is a third proposition which is consistent with (1) and with together with (1) implies (3). I've said that (3) . . .

Dr. Craig:

Entails (2).

Dr. Bradley:

Entails (2). Sorry! I've said that his (3) is all by itself inconsistent with (1).

Let's look at it like this [draws circle on the overhead]. Let that circle represent the set of all possible persons that God could have created with free will and of whom He knows in advance from the very beginning, in the words of the Bible, what the outcome of their choices would be. Okay? Now that set of possible persons, possibilia as you call them in one of your works, can be subdivided more or less arbitrarily, we'll say, into those who would be saved if He were to create them and those who would be damned as a consequence of their free choices [divides the circle into two halves labeled "sacred" and "damned" respectively]. All right?

Dr. Craig:

I don't want to be difficult, but I think that's too simplistic because some people might be damned if created in some circumstances but saved if they were created in other circumstances. So you can't just divide the line down the middle and put people on either half. It depends on what world these possible persons are put into.

Dr. Bradley:

So we can shift the line wherever you wish according to which actual world God chooses to create. All right?

Dr. Craig:

All right.

Dr. Bradley:

Now He creates an actual world [designates a segment of the circle overlapping both halves]. These are just possible individuals up here, the whole domain of possible individuals with free will [designates individuals outside the segment]. Here we've got the actual ones [designates individuals in the segment]. And, as you can see, some of them on this have been assigned to heaven because God knew in advance that if He were to create them in these circumstances, they would be saved. And, here we have those He's consigned to hell. In fact, I've been generous to God and you here because I've created equal parts. And, of course, Jesus says it's going to be pretty rough on most of them.

Now the point is this. Why did God have to create just this subset of possible individuals with free will? [designates segment of actual individuals] He could have sliced the pie a very different way. He could have sliced the pie so that there weren't any in this segment at all, the segment of hell [shades sub-segment of actual, damned individuals]. He could have chosen to create a world in which no actual individuals like you or me were existent [draws another segment outside the segment of actual individuals].

Dr. Craig:

Right.

Dr. Bradley:

After all, there's nothing all that great about us, is there?

Dr. Craig:

Right.

Dr. Bradley:

So He could have created all these possible individuals . . . [ticks new segment]

  

Dr. Craig:

And my point is He wouldn't be able to guarantee--so long as those people have free will--that they would FREELY RESPOND TO HIS OFFER OF SALVATION AND BE SAVED.

Dr. Bradley:

But if He knows in advance that these will in those circumstances be saved by virtue of freely accepting God's offer of salvation through the blood of Jesus, then why not?

Dr. Craig:

Because there may not be a compossible set of individuals such that if you put all of them together in a world, all of them freely receive God's salvation and are saved. It may be that individual "S" would only be saved in a world if in that world individual "S-prime" were lost …

So that it's impossible for God to … or infeasible for God to create a world in which all are saved …

Dr. Bradley:

I understand quite well about them having to be compossible. And, let's just say that out of the set of all possible inhabitants of this world that God is going to choose to create, only some are compossible. So let's make it a subset. We now have a subset of compossible individuals all of whom would be saved.

Dr. Craig:

But, see, my point is that you don't know that such a set is not the empty set. It could be the empty set.

Dr. Bradley:

Well, look, you play with possibilities. You talk about it's possible that this, it's possible that that. . . I'm asking you to confront some actual examples of possibilities. Heaven is allegedly a state of affairs in which God exists and the only other persons to exist are people who either have been saved because they believed in Jesus' name or would have believed in Jesus' name and have been saved or you could throw in a few of those who get there by general revelation.

Dr. Craig:

But that in itself presupposes there was an antecedent pre-mortem world …

Dr. Bradley:

It doesn't logically presuppose it. Causally perhaps. But you understand the distinction between causal ties and logical ones as well as I do. [long pause]

Dr. Craig:

You've still got three minutes.

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There's a lot of evasion from Craig in this sequence, and many appeals to ignorance.  The debate has been discussed previously by others such as Jonathan Pearce (who argues that WLC's argument violates the ontological argument, because we can conceive of a better god than WLC's god, one that is not obliged to create a world in which a significant proportion of the inhabitants would be consigned to hell) and Luke Muehlhauser (who applauds Bradley for being prepared for the debate, unlike many other atheists who meet WLC on the debating podium), but I want to take a slightly different tack.

My ears pricked up when WLC opened up this hole in his world view:

I don't want to be difficult, but I think that's too simplistic because some people might be damned if created in some circumstances but saved if they were created in other circumstances. So you can't just divide the line down the middle and put people on either half. It depends on what world these possible persons are put into.

Now, note that WLC is not arguing for divine ignorance, by which I mean the idea that free will might preclude a god from knowing whether a given person will be saved or not.  Bradley gave him the opportunity (a few times) to make such an argument and instead of doing so, WLC gave a "compossibility" argument.

Dr. Bradley:

But if He knows in advance that these will in those circumstances be saved by virtue of freely accepting God's offer of salvation through the blood of Jesus, then why not?

Dr. Craig:

Because there may not be a compossible set of individuals such that if you put all of them together in a world, all of them freely receive God's salvation and are saved. It may be that individual "S" would only be saved in a world if in that world individual "S-prime" were lost …

So that it's impossible for God to … or infeasible for God to create a world in which all are saved …

I'm willing to accept that WLC misspoke and that he was not suggesting that his god could find certain acts impossible (as opposed to infeasible) and instead I'll focus on what he is saying about the possible lack of compossible sets.

What is being suggested here, by WLC himself, is that there is a possible world in which S-prime is freely saved although in that world, S would be lost, as well as a possible world in which S is freely saved while S-prime is lost.  Conceivably there would be another world in which both would be lost.  Think about that for a moment.

No matter how you want to paint it or buff it, this is predestination.  The claim entails a situation in which a god chooses which world to implement, notionally allowing either S or S-prime to freely choose to satisfy the requirements for salvation (although another optimum solution could have both S and S-prime being lost so that T, U and V together with their primes might be saved).  And this is despite there being possible worlds in which one or another of S and S-prime might be saved.  Therefore, the salvation of S and damnation of S-prime is purely the result of god's decision.  From the very moment of creation, S-prime is excluded, despite being able to act freely.  And therefore, god consciously places S-prime into the (future) eternal flames of hell.

Bradley's argument, which I agree with completely, is that an omnibeneficient god would not and could not consciously choose to create an intelligent being knowing (via omniscience) that that being would be tormented forever.  WLC also agrees (at least where bunnies are concerned).

Remember that we are talking about a maximally excellent being (MEB) here, which incorporates omnipotence - unlimited in power, unlimited by time, unlimited by space, although apparently limited by logic (the logically impossible is not required of an omnipotent god, according to WLC and his ilk, which is strange, since they could bypass such objections as the problem of evil in one fell swoop if they only allowed their god to be immune to logic).  An omnipotent MEB is not restricted to creating a single world in which all its playthings interact in such a way as to enable the salvation of one at the expense of another.

Remember that this MEB knows the outcome of all your freely made decisions, and knew it before you were created.  It already knew all your choices, all your interactions, all your innermost thoughts and the same applies to every being around you.  So, as far as you are concerned, from the perspective of the MEB, it doesn’t matter whether you interact with actual free acting lesser beings or theological zombies (soulless automatons which merely act out the behaviour of those who would otherwise be damned).  The priority of this MEB (according to WLC) is to ensure that the maximum number of humans come to freely choose to know and love it.  It's not to minimise the number of worlds created, or to maximise the actual interaction between lesser beings, or to not create theological zombies.

Therefore, an MEB of the sort that WLC believes in would choose to create a possible world in which S would be saved (largely inhabited by theological zombies, including a theological zombie playing the role of S-prime), a possible world in which S-prime would be saved (in which the damned S would be portrayed by a theological zombie) and so on such that each and every created soul would be saved.

That's a rather terrifying idea.  For each and every believer, there is a possibility that this universe is created just for them and people like them, because in any other configuration they would be damned.  While it might be comforting to know that there might be a number of actual, predestined-to-be-saved people in amongst all the theological zombies - you could never know which is which.  Your mother, zombie or real person?  Your child, zombie or real person?  Your partner, zombie or real person?

But it gets worse.  This world would be the one, presumably the best one in which these people would be saved.  Everything that goes on around them would be contributing to that salvation and every bad thing that happens would (due to the thorough goodness of the MEB) be necessary.  Therefore, for these people to be saved, it is necessary that three quarter million people die each year from dysentery.  It was necessary for journalists to be beheaded in Syria.  The tsunamis in Japan and Indonesia were necessary.  Droughts and floods and fires and earthquakes and mudslides and mental illness and drug addiction, the election of Trump and all sorts of social chaos - all are necessary to save these people.

These are not good people if they could not possibly have been saved in a better world.  Apparently WLC is one of these people (although I freely admit that, within this premise, it's much more likely that he is a theological zombie).

What does the theist have to do to escape this conclusion?  I see a few options:

Reject maximal excellence (although WLC argues that a less than maximally excellent being is not god)

Reject the arguments of WLC and people like him (a very good start on the road to reason and intellectual freedom)

Appeal to ignorance (the standard fall-back option)

Argue that the theological zombie is logically impossible (this would have to be a valid argument, of course, otherwise it's just another appeal to ignorance hidden behind a veil of rhetoric and hand-waving - of the sort that I'd expect WLC to embark upon)

Finally, I would ask any theist who is accidentally convinced by my argument to treat any and all theological zombies with the utmost care and respect.  It seems that we're here - dying and suffering, putting up with you, or at least simulating it - just to help you get into heaven because you failed to manage it in any better world.

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More zombies and the logic thereof.

WLC's Mistake in Formulating the Moral Argument

Actually, there is more than one mistake that WLC made in his formulation of the moral argument and there is more than one mistake that WLC made in his Q&A response, Formulating the Moral Argument.  I've addressed the moral argument a few times already; in The Modified William Lane Craig Moral Proof, The Logic of an Apologist, WLC3: When Morality Arguments are Bad, The Moral Argument in Graphical Form and WLC Being a Duffer.

In the first, I show how the same argument can be used to argue for the existence of a god via the existence of Kim Kardashian (if there is a better way to highlight how trivial an argument is, I'd like to know it).  I'll get to the second in a moment.  In the third, I summarise the first and second arguments and go into a little detail as to why I think WLC's formulation of the moral argument is questionable. In the fourth I demonstrated, in a diagram, the circularity of the moral argument.

The fifth is more about his Q&A response to a question about … well, it should be reasonably clear already -  it's the formulation of the moral argument, which I too questioned in The Logic of an Apologist.

Now, The Logic of an Apologist got some attention recently at Craig-Land, in a thread dedicated to lampooning my arguments, eventually focussing in on the moral argument and my assertion that WLC presents the moral argument oddly and, as I interpreted it in WLC3: When Morality Arguments are Bad, deceptively.

There's a bit of noise in the discussion, but through it is an interaction between me and the thread's originator, λ-calculus, that I want to use as my launch-pad to discussing WLC's errors.  Reasonably late in the thread (post #86) I challenged λ-calculus to answer the question I effectively posed in The Logic of an Apologist: why did WLC formulate the moral argument the way he did, if not to deceive?  I also reframed the question, to make it easier for him: Why did he word it in the form (~A->~B;B;∴A) rather than in the form (A->B;A;∴B)?

Someone else immediately chimed in and referred to WLC's Q&A response, Formulating the Moral Argument.  And this led me to take another look at the piece that was the inspiration for WLC Being a Duffer.

What a treasure trove!

My original comment on it was that WLC effectively torpedoes his own argument, but that is only one of many problems.  Here are the ones that I have identified:

Problem 1 - Equivocation on the term "objective"

This is a problem with the content of the argument.  By "objective" WLC really means "absolute", as opposed to "relative".  But he equivocates, perhaps unintentionally, when he tries to persuade atheists to accept that there is such a thing as "objective moral values and duties".  We can use metrics, generally agreed principles and cool reason to work out this action is better or worse than that action - that would be objective - rather than letting ourselves be swayed by personal opinion, hyperbole and how we felt on the day - which would be subjective.  When WLC gives examples of "objective values" saying this or that is "simply wrong", you can tell that he's really talking about absolute morality, rather than objective morality - or he wouldn't be raising emotive topics like rape or torturing children for fun.

Problem 2 - Equivocation on the term "conditional"

This is a problem with his explanation for formulating the argument the way he did.  He writes "Since, as our truth table reveals, the whole conditional statement comes out true if the consequent is true, then it doesn’t matter whether the antecedent clause is true or false."

Here he is mixing up what is known as a material conditional with what is known as a conditional sentence.  He's helped in this in that the terms both contain the word "conditional" and they can be symbolised the same way (A->B).  Wikipedia will explain the potential for confusion better than I:

The material conditional is used to form statements of the form p->q (termed a conditional statement) which is read as "if p then q" or "p only if q". It is conventionally compared to the English construction "If...then...". However, unlike the English construction, the material conditional statement p->q does not specify a causal relationship between p and q. It is merely to be understood to mean "if p is true, then q is also true" such that the statement p->q is false only when p is true and q is false.

These are quite different understandings of the construction "if … then …".

Problem 3 - Equivocation on the term "true"

When, in general parlance, we say that something is "true", we do not mean that it is "trivially true" or "vacuously true" - we mean that it is actually true such that its negation is not true.  WLC is equivocating by presenting as "true" something which is only vacuously true.

Problem 4 - Lack of specificity to morality (if Problem 2 is ignored)

This argument works (to the extent that it works) with anything, including the existence of Kim Kardashian.  It's not really a moral argument at all.

Problem 5 - Triviality due to negation (if Problems 1, 2 and 3 are ignored)

WLC himself points out that, from his point of view, his first premise is trivially true - because he believes that his god does exist.  But this isn't actually just from his (or any other theist's) point of view.  In terms of the argument, if it were to succeed, it makes its major premise trivial.

There may well be other problems, feel free to point them out.