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.

Return to BS5

Sometimes, you return to something that you worked hard on in the past and an obvious aspect leaps out at you that wasn't obvious at the time.  In The Fans of Plantinga's BS5, I was arguing against the claim:

This was primarily because this is used to claim that, since we cannot prove that (a maximally great) god does not exist, it is possible that (a maximally great) god does exist, furthermore since we cannot prove that (a maximally great) god is does not exist necessarily it is possible that (a maximally great) god does exist necessarily and it therefore follows that (a maximally great) god does exist (necessarily).  Sounds like BS, right?

Anyway, I also argued against a more complex version of the argument (raised by cpdavey):

1. ◊□A (Assumption for Conditional Proof (CP))

2. ~□A (Assumption for Reductio Ad Absurdum (RAA))

3. ~~◊~A (2 E2)

4. ◊~A (3 Double Negation (DN))

5. □| ◊~A (4 S5-reit)

6. □◊~A (5 nec intro)

7. □~□~~A (6 E1)

8. □~□A (7 DN)

9. ~◊~~□A (8 E2)

10. ~◊□A (9 DN)

11. ◊□A & ~◊□A (1,10 Conjunction)

12. ~~□A (1-11 RAA)

13. □A (12 DN)

14. ◊□A -> □A Q.E.D. (1-13 CP)

I concluded that the Reductio Ad Absurdum wasn't actually necessary, because you can do it like this:

1. ◊□A (Initial position)
2. A <--> ~B (Assumption for Logical Fiddle)

3. ◊□~B (Substitution of 2 into 1)

4. ~~◊~~□~B (3 double DN)

5. ~□~□~B (4 E2)

6. ~□~□A (Substitution of 2 into 5)

7. □A (6 n2)

8. ◊□A -> □A Q.E.D. (1-7)

But here we can see that the step between (6) and (7) is not valid (because it's reversed) - so there's a problem which is being disguised by the process of going through the Reductio Ad Absurdum.

I pretty much left it at that, inviting the reader to point out where the problem is, if they could see it.  That was five years ago.

So, what was the obvious thing that recently leaped out at me?  The proof put together, or at least presented by cpdavey relies rather heavily on the introduction of double negatives and swapping from ~□~ to ◊ and from ~◊~ to □.  Both of these latter two moves can be reversed (see Classical Modal Logic).  What it doesn't rely on, is the value of A.  Which means we can do this:

1. ◊~G (Initial weakish atheism position)
2. ~□~~G (1 classical modal logic)

3. ~~□~□~~G (2 n2, right way around)

4. □~□G (3 DN removed)

5. ~◊□G (4 classic modal logic)

This means we arrive at the same conclusion whether we assume that it is possible that there is no god (◊~G) or that it is not necessary that there is a god (~□G), namely that it is not possible that there is necessarily a god (~◊□G), which is precisely what we would expect.

Effectively all cpdavey was arguing was that if his presumption was correct, then assuming the truth of the opposite of his presumption would lead to a conclusion that his presumption was incorrect.  Which it did and which we would expect.  That's why there's no great problem within his "Reductio Ad Absurdum"  but there is when we run his proof with no RAA.  His whole argument came down to a "heads I'm right, tails you're wrong" sort of con.

The error is quite clear in Step 12 above, where cpdavey writes "12. ~~□A (1-11 RAA)".  Clearly the RAA started at Step 2, not Step 1.

Sometimes we just don't see things that are staring us in the face.  Perhaps I was trying too hard to be clever.  But then again, so was cpdavey, since the result that he needed to get his RAA to work was precisely the one he was aiming at, via use of the RAA, ie the fallacious claim that, given ◊□A, □A.

The Problem of Evil vs The Problem of Good

In response to Pre-Creation (How Good Can God Be), a reader drew my attention to the work of Brian Davies, specifically “The Reality of God and The Problem of Evil”.  A survey of the reviews of this work gives me the impression that Davies’ argument is that the Problem of Evil misses the point and that we should instead be pondering about just how much good there is in the world.  If so, then the reader appears to have rather missed the point of what I wrote in Pre-Creation.

It’s entirely possible that Davies has a different argument to the one that I’ve surmised.  If so, the publisher Bloomsbury has got it wrong too:

Finally, though many theologians argue that evil is a mystery, Davies argues that this too is wrong and a cop out. We should rather be concerned with the problem (or mystery) of good. The real issue is `Why is there not more good than there is`. From the discussion Aquinas emerges as a hero (as filtered through analytical philosophy) but many modern thinkers do not emerge so well. Davies effectively picks holes in the arguments of Peter Geach, Paul Helm, Richard Swinburne and even Mary Baker Eddy

Admittedly, my first interpretation was that Davies was arguing that good itself is a mystery as in “why is there any good at all?”  This is sometimes argued as the obverse of the anti-apologetic argument “why is there evil in a universe supposedly created by an omnipotent, omniscient, omnibeneficient god?”  At the very least it seems to be a basic assumption for many theists – if there were no god, then there would be no good.  It’s terrifying how often you hear theists argue that, without god, they would be rapists and murderers.  Our old friend WLC provides us with an example:

Today I want to argue that if God exists, then the objectivity of moral values, moral duties, and moral accountability is secured, but that in the absence of God, that is, if God does not exist, then morality is just a human convention, that is to say, morality is wholly subjective and non-binding. We might act in precisely the same ways that we do in fact act, but in the absence of God, such actions would no longer count as good (or evil), since if God does not exist, objective moral values do not exist. Thus, we cannot truly be good without God.

This is the same person who argues that without his god, and “objective” morality, the torture of babies for fun would not be wrong.  Personally, I like to comfort myself with the notion that the theists making these sorts of comments are doing so for rhetorical purposes and that, if they were convinced that their god does not actually exist, they would not immediately commence a campaign of rape, torture and murder.

There’s a major difference between the anti-apologetic argument from evil for the non-existence of a god and the apologetic argument from good for the existence of one’s god.  The argument from evil is a type of reductio ad absurdum in which one starts from the assumption of the existence of a specific type of god and end up with an impossibility – the god of that type would not permit the sorts of evils that we find in the universe, therefore it does not exist.

The argument from good, on the other hand, does not truly start from the assumption of the non-existence of any god whatsoever.  Instead, there is an inherent assumption that the universe could only have good in it if there were a god, as per WLC’s argument above.

There’s a reluctance on the part of the theist to honestly consider whether the “good” observed in the universe could arise without their god.  Note that by “good” here, I refer to the actual act, intent or situation that is considered to be good, not the attribution “good” that is assigned to that act, intent or situation.  Perhaps I should explain …

An act can be good in itself – say it reduces or prevents harm, involves some real self-sacrifice (even if minor) or adds to the well-being of others.  Alternatively, an act can be labelled as “good” – going to church, abstaining from pre-marital sex or obeying some rule (don’t mix linen and wool in one garment).  Labels can be assigned pretty much arbitrarily, but once you have a method of deciding what is and isn’t good (increased harm bad, improved well-being good), then you have an objective measure by which you can judge whether an act is good.  But even aside from that, we do have measures for judging whether acts are good or not, we can basically list which acts are thought of as good and we can consider those acts.

Could the acts that we consider to be good arise in a universe without a god?

The theist, at least the christian theist, tends to think not but the reason for this is tied up in theology, in the theist’s assumptions about the basic (and base) nature of humanity.  Man is born of and in sin, humanity is depraved, atheists (according to many a theist) are atheists because they don’t want to believe there is a god so they can continue to sin.  If you take this view of the universe and only do one thing, remove god, then of course, it’s going to be dark.

To be more fair, the theist needs to place his argument in a universe which has no god and never had a god, in which the nature of humanity is not presumed to be sinful and depraved.

So, the Problem of Good … could the godless universe produce the acts that we call “good”?  I certainly think this is possible.  There’s no Problem of Evil for an atheist, but equally there’s no real Problem of Good either.  In the Morality as Playing Games series, I explain how the (western, judeo-christian) morality that we currently espouse can arise from pretty solid self-interest.  To the best of my knowledge here’s no “good” act which cannot be explained in terms of the ethical structure that I arrive at.

Some might complain that this is a “just so” story, but that’s not the point.  Perhaps our morality, our sense of what is good and what is wrong did not arise the way that I have laid it out, but even so, I do demonstrate that it could arise without a god.

This is all that is required to refute the argument that, for there to be any good, there must be a god.  There’s a way without god, therefore god is not necessary in moral terms.

SSMD Down Under

There is one English speaking nation in the OECD which has not (yet) legalised same-sex marriage, at all.  (I use the term nation to include the UK, which is a union of four countries, of which one has not legalised same sex marriage.)  In that nation, Australia, there has been a protracted debate, or discussion (the SSMD of the title) and, most recently, a voluntary, non-binding postal survey on whether or not the law should be changed to permit same-sex marriage (SSM).

This was quite odd because the primary argument against legalising SSM seemed to be fundamentally religious – it’s just not the way things should be.  The old chestnut – “God made Adam and Eve, not Adam and Steve” – encapsulates the notion.  But of the English speaking OECD nations, Australia is the second least religious (after the UK).  So, perhaps it wasn't a religious thing after all.

However, the Australian parliament seems to have a high proportion of god botherers and dyed-in-the-wool conservatives than the average population and some of them were getting desperate in their attempts to stave off the inevitable (polls consistently indicated that majority of Australians, and the vast majority of younger Australians, are in favour of legalising SSM).

For example, one member – Senator Paterson, was the front man for a bill that would legalise SSM, but would enshrine protections for religious freedom.  It seemed like Australia might well be heading towards its own version of the gay wedding cake debacle, depending on how you interpret the right of people to “refuse to participate in a same-sex wedding”.

Oddly enough, I find myself in the position of partially agreeing with the idea of protecting the freedoms of people with religious belief.  I am very much opposed to the idea that a priest should be forced to conduct a same-sex wedding against his convictions (I’m going with the percentages here and making the priest a “he”).  If religious people object to a same-sex wedding being conducted in their church, then those people should be able to shop around for a priest or pastor who shares their prejudices.  If a religious person doesn’t want to attend a homosexual marriage ceremony, then nobody should be forcing them to attend.

I find it a little odd that homosexual people (men in particular) would want to get married by an organisation that is guided by a book in which it is clearly stated that men who lie with men should be put to death.  But if a particular church is going gloss over that minor detail and put their god’s seal of approval on an SSM, then I suppose that’s fine.  And if a deeply (or indeed shallowly) religious person doesn’t want to attend a homosexual marriage ceremony, then nobody should be forcing them to attend.  (Were I planning to get married, I would prefer not to have people there who want to kill me.  It’d rather put a damper on things.)

But outside of that, it starts getting a little more complicated.  Should an artisan be required to produce a work of art celebrating an event that they have religious objections to, if asked to?  Should a more mundane craftsperson (like a baker) be required to produce some product for such an event?  Should the owner of an events locale be required to host the reception of newly wed homosexuals, despite religious misgivings?

Probably no.

I don’t agree that people necessarily should be stupid enough to believe that there’s some sort of god who was the ghost writer of a poorly-written instruction manual that is, in parts, thoroughly homophobic, but the fact is that we still have such people in our world.

My suggested solution is quite simple.  Private organisations should be permitted to discriminate when offering services for payment.  But only if they make it perfectly clear that this is their policy, including in any and all marketing they conduct.  If they don’t make it clear or make it insufficiently clear that they are prejudiced, then they must accept all comers.  And if their objections are religious, then they should have the courage of their convictions and be consistent in their prejudice.

So, for example, a reception hall who are discriminating on the basis of their religion would be required to have a prominent sign outside saying that they don’t permit receptions for anyone who has broken the laws of their god.  So no receptions for homosexuals, no receptions for brides who are not virgins, no receptions for people who work on the sabbath, no receptions for people who wear clothes of mixed fabric.

If a baker was discriminating on the basis of his conservatism, the same would apply, although the sign (and associated marketing) would probably have to make clear the full range of his prejudices: no homosexuals, no mixed-race unions, no drifters, no Irish, no atheists, no muslims, no gypsies and no jews.

Sometimes it will just be a single issue, non-affiliated prejudice.  But if a provider of products or service wants to systematically discriminate, why not let them – so long as they clearly indicate that they are carrying out that discrimination?

The result should be that the significant percentage of us who are not so prejudiced would then know where to not spend our money and whose weddings to not attend (because they are holding their reception at the Fifth Reich Resort which clearly advertises its “whites only” policy).  If the more reasonable among us are indeed in the majority, then market forces will come into play and the prejudiced will be dealt with via a form of economic Darwinism.  If we are not, then we need to do some more work and should not be resting on our laurels.

Barely hidden prejudice is, after all, still prejudice.

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Note: I am not being entirely serious here.  A little bit, but not entirely.  If the powers that be in Australia are going to permit discrimination against anyone on religious grounds, then I do believe that those who intend to take advantage of it should be willing to pay the price of being open about their prejudice.  And I reckon that they should be consistent, even if that were to mean that in future my atheism might exclude me from enjoying the fruits of certain bakeries … but consistency has never really been a strong point with the average religious bigot. 

Note also that the wording of a store's prejudiced objection should still be respectful, I am not suggesting a return to days when shops hung out signs blandly saying "No Irish, No Blacks, No Dogs".  Perhaps something more honest like:

"The proprietor of this store is legally airing his prejudices in accordance with the Bigoted Bastard Act (BBA 2017) and wishes all patrons to be aware that he is prejudiced against the following groups of people: [strike out all not applicable]

Women/Men/Children/Teenagers/Old People/Single People/Married People/People Living Together in Sin/Heterosexuals/Homosexuals/Metrosexuals/Whites/Blacks/Asians/Orientals/Hispanics/Indigenous/Canadians/Red Necks/Intellectuals/Geeks/Jocks/Feminists/Manpriders/Liberals/Conservatives/Football Fans/Hockey Fans/Soccer Fans/Baseball Fans/Star Wars Fans/Grammar Nazis/Plain Old Nazis/Conspiracy Nuts/Others (as listed below)

Furthermore, this prejudice will take the form of [strike out all not applicable]: No Soup For You/No Drink For You/No Cake For You/No Food For You/No Accounting For You/Other (as listed below)"

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I wrote this a week or so ago, and have thought further on the risks of forcing an artisan to create a piece of art against his or her religious beliefs.  I suspect the artist was not forced to take on this commission, but the artwork below hints at some sort of disagreement about the values involved:

The statue was commissioned for a Catholic school with some, ahem, shall we say "history".  Amusingly, the statue is now covered - with the child still in there, snuggled up to the saint's loaf, but now hidden under the cassock (well, it looks more like a burka than a cassock, but hopefully the allusion isn't entirely lost).