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.

Misuse of the Material Conditional

I'm going to start off easy.  First, check out the wikipedia entry on the Material Conditional.

Note that there are two usages:

As a truth function, and

As a formal connective

Now, note that the truth table for one has p->q being true for all conditions except where p is true and q is false.

And then, note that the material conditional p->q as a formal connective:

can be considered as a symbol of a formal theory, taken as a set of sentences, satisfying all the classical inferences involving ->, in particular the following characteristic rules:

Modus ponens;

Conditional proof;

Classical contraposition;

Classical reductio ad absurdum.

Now, I take the use in a modus tollens to be precisely the same sort of use as in modus ponens.  You can try to argue differently, but that would put a bit of a hole into modus tollens, and how it is generally shown to relate to modus ponens.

Finally, note the truth table at the SEP entry on Conditionals.  In the Non-Truth-Functional Interpretation truth table, A->B is true when A is true and B is true, false when A is true and B is false and could be true or false when A is false (so we simply don't know).

This does not correlate with what WLC stated in his answer in his Q&A Formulating the Moral Argument (see my earlier take on this here).  He got it wrong because he tried to use the Material Conditional as a truth function when he clearly should have used it as a formal connective.  Anyone who has subsequently or coincidentally followed him on this is also wrong.

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One of the objections I got to the argument above was a little confused.  The objector complained that 1) WLC “intends the argument to be interpreted subjunctively” and 2) “(t)he truth table (Craig) gives is for the indicative mood”.

So, which is it?  Why give a truth table for the indicative mood if WLC intends the argument to be taken subjunctively?  Why not present the argument subjunctively if he meant it to be taken subjunctively?  And what does he think he's doing changing what is claimed by some to be a material conditional (which I think it probably is, but not with the truth functionality interpretation) into a counterfactual (conditional)?

If he wants to be using a counterfactual condition, and to be using the subjunctive ... he should use the subjunctive.  It's not hard, even I could do it (although I think the major premise that follows is false, because the protasis is true while the apodosis is false):

• If WLC's god were not to exist, then objective moral duties and values would not exist
• But objective moral duties and values do exist
• Therefore, WLC's god exists.

See the "were not to"?  This is a calling card of the counterfactual.

If WLC did intend to use the subjunctive mood and create a counterfactual conditional, then all talk about the material conditional as a truth function (the sin committed by the various people who thus motivated me to write this piece) is misguided. 

See also philosophical treatments of the counterfactual conditional.

Contingency

Is christianity contingent?

Of course, I think it is.  But I don't believe in the god of christian theists, so I see christianity as something largely made up by Paul, perhaps together with some advisors, partly based on a mythical or mythologised Jesus character.

My question pertains more to the world view of a christian theist.  There are problems on both sides, as I see it.

In short, if christianity is contingent, then the god of christian theists screwed up and created creatures that unexpectedly ran off the rails and had to be saved by the uncomfortable execution of the Jesus character.  The ability to screw up is not a recognised characteristic of the god of christian theists.

If christianity is not contingent, which seems to be the preferred position of christian theists, then either the Garden of Eden event was staged and the "Fall of Man" was a known outcome right from the start, which could have been prevented but wasn't (thus making the god of christian theists responsible for the event, since that god is so much more powerful and knowledgeable than its creations), or the god knew that there was "sin" built into humanity that would eventually require the uncomfortable execution event (which again could have been prevented, but wasn't, thus the god of the theists is responsible for the "sin" that is built into humanity is).

Personally, I so see christianity as contingent, even within the christian theist's paradigm.  Assuming Adam and Eve existed and had free-will, they could have chosen to ignore the serpent.  Assuming an old universe creation, events could have been different, due to small decisions anywhere in our history, such that the Jesus character never existed (or was never invented), or Paul could have decided to go to the pub for a few refreshing ales rather than head to Damascus the day that he fell over and had his vision.

This sort of contingency is transferrable to other Abrahamic, if not all religions.

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When I initially floated this argument (which I admit only hints at the problem), the primary defence seemed to be a total misunderstanding of what "contingent" means.   There was some variation in the lack of comprehension though, which was nice.  I took it to be a sign that some of the WLC fan-club were thinking for themselves rather than just following the party line.

The point that I was trying to make with this argument was that if the universe itself is contingent (per WLC), how could anything within the universe be fundamentally necessary?  If something in the universe is fundamentally necessary, then the universe itself would be necessary - so long as it's also essential to that universe and/or being in the universe is part of the inherent nature of that thing.

That might take some explaining.  Say we have a thing "P in a bucket", say that this "P in a bucket" is necessary, there is no world in which there is no "P in a bucket".  It would therefore follow that there is no world in which there is no bucket just as much as there is no world in which there is no P – because in any world that exists, there would be P and that P would be in a bucket.

The question that could be raised is whether, given our universe, is X necessary (is X like "P in a bucket" or is X like a different type of P, P that may be in the bucket, but might easily be somewhere else, like in a can, or lying on the floor)?  Note that X can be "something", "anything" or "a specific thing", like christianity for example.

The necessity or otherwise of X, given my caveat above (“given our universe”), would depend on the nature of the universe, would it not?  And what is responsible for the nature of the universe?  In a sense, what the objections to the argument revolved around was what could be called “the contingency of necessity”, because the theist’s god apparently gets to choose what is and what is not necessary.

On the grand scale, what that means is that what some theists consider as "necessary" is, in fact, contingent.  Unless, of course, their god is not omnipotent.

A Problem with Theodicies

 A problem with theodicies, as I see it, is that (some) theists will initially accept – for the sake of the argument – the notion that their god does some bad things.  Then they'll spend a lot of time justifying why their god does those bad things (better goods via evil, inability to do the logically impossible, necessity of evil for good by comparison, etc).  They'll reach a conclusion that their god could in fact be justified in doing some bad things, and they will confidently declare that their god hypothesis is not invalidated by the problem of evil (so long as a long list of caveats are satisfied).  Then, finally, they'll forget all about the mental gymnastics that they just went through and will go back to believing in a god without all the caveats that those mental gymnastics resulted in, a god that they had previously accepted as invalidated by the problem of evil.

There's also the problem of using logic in a theodicy.  Certain logical truths – for example the Law of Non-Contradiction – are features of this universe ("as created", in the world view of a theist).  We use these logical truths to arrive at the conclusion that, for example, action X is not "logically possible".  This makes the impossibility of action X a secondary feature of this universe ("as created"), because that logical impossibility is a consequence of the logical truths which are primary features of this universe.

There's nothing that implies that logic transcends this universe such that a sufficiently powerful, knowledgeable and good god could not create a universe without logic – at least nothing beyond our inability to imagine such a universe, but we live in a universe in which logical truths pertain, so we are naturally limited in our imagination.

Perhaps the theist might wish to argue that logic does transcend this universe and that "prior to the creation of the universe" (whatever that means) the creator god was limited by logic and was obliged to create a universe in which logic necessitated suffering and evil.  The problem here is that the theist is therefore suggesting that the creator god is transcended by logic, is less powerful than logic.  And we know that logic is ultimately imperfect (per Wittgenstein and Russell).  Thus, the creator god is diminished and becomes a mere vassal of imperfect logic.

Is this not a problem for the theist?

The Logic of Theological Zombies

Sometimes, rather than accepting an argument in words, an apologist will demand that an argument be presented as a series of premises and conclusions.  So here is the formal argument for theological zombies (and a little beyond):

P1 – Everything a maximally excellent being (MEB) wants is a thoroughly good thing (TGT)

P2 – The saving of a soul is a TGT

P3 – The MEB wants to save more than a single soul

P4 – That which is thoroughly good cannot saturate

C1 – Therefore, the MEB must want an infinite (or maximal) number of saved souls (from P1, P2, P3 and P4)

P5 – If the MEB wants an infinite (or maximal) number of saved souls it can achieve that by means of theological zombies

P6 – With the option of theological zombies, it not necessary that the MEB send any soul to hell

P7 – To be a maximally excellent being it must be impossible for there to be a superior being

P8 – If the notional MEB were to send any soul to hell, when it is possible to not send any souls to hell, then there would be a possible superior being to the notional MEB (meaning that the notional MEB is not an actual MEB)

C2 – No souls are sent to hell by the MEB (from C1, P5, P6, P7 and P8)

P9 – If the MEB will not, and cannot, send any souls to hell, then Jesus (as, or as a representative of, the MEB) was lying about hell (from C3)

P10 – A being that lies and lets its representatives lie is a lesser being than one that is always truthful and does not let its representatives lie

C3 – Therefore, there is no MEB associated with Jesus (from C2, P10, P11 and P7) and therefore christianity is false.

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Support and clarification for various premises and explanations for conclusions are as follows:

P1 – if the MEB wants anything that is less than a TGT then it is not omnibeneficient and not thoroughly good in itself (which would defeat the moral argument)

P2 – this could be argued from at least two perspectives.  Firstly, unnecessary damnation for anyone is not a thoroughly good thing.  Secondly, there are claims that the MEB wants humans to enter into a personal relationship with it, which saves the soul and must be a thoroughly good thing (along with the consequential saving of the soul).  Note that “soul” here could just mean “individual”, the precise mechanism of individuation post death is immaterial to the argument

P3 – the MEB apparently wants not only more than one saved soul but also more than one of each type, since that limited requirement could have been satisfied by just saving Adam and Eve.  The need to procreate and fill the planet with billions of people would indicate that the MEB wants many saved souls

P4 – that is to say that there is no value of N such that N is the optimum number of TGTs, because if N+1 TGTs is less good than N TGTs, then the TGT is not thoroughly good, because it can be bad under certain circumstances.  In other words, if you can say there is too much of a good thing, then that good thing is not a thoroughly good thing

C1 – infinite seems better when it comes to thoroughly good things since, as per P4, they cannot saturate, so for every value N, N+1 TGTs is better than N TGTs.  Perhaps there could be a "maximal number" of saved souls that is finite, but this eats away at both the omnipotence of the MEB and the thorough goodness of saving souls

P5 – see Theological Zombies

P6 – see Theological Zombies

P7 – seems quite self-evident to me

P8 – that is to say that given that theological zombies are not impossible, there is a way to avoid sending any soul to hell (noting that there is no commitment from the MEB that all experiences of humans must be both authentic and veridical – the non-veridical experiences of someone in a universe which is otherwise inhabited by theological zombies are still authentic experiences in that they are identical to the experiences they would have had in interactions with real others, they just have the benefit of being authentic without necessitating the condemning of any of those others to hell)

C2 – otherwise it would not be maximally excellent

P9 – the Jesus character mentions hell a few times, admittedly mostly in relation to parables, for example the Parable of the Net (Matt 13:49-50): “This is how it will be at the end of the age. The angels will come and separate the wicked from the righteous and throw them into the blazing furnace, where there will be weeping and gnashing of teeth.”  One might argue that this is just a parable, but earlier in the chapter, another parable, the Parable of the Weeds, was explained (Matt 13:41-42): “The Son of Man will send out his angels, and they will weed out of his kingdom everything that causes sin and all who do evil.  They will throw them into the blazing furnace, where there will be weeping and gnashing of teeth.”  There’s little space for misinterpretation there.

P10 – if there are two paths to the same objective and the only consequential difference is that one involves a lie and the other doesn’t, then the honest path is the better of the two

C3 – an MEB would not lie or permit lies on its behalf and it would not send souls to hell.  Therefore, there is a dilemma with respect to the Jesus character’s pronouncements on hell.  Either these pronouncements are factual and the supposed MEB sends souls to hell (and therefore it cannot be an MEB and therefore christianity is false) or these pronouncements are false and the Jesus character is lying about it (and therefore Jesus cannot be representing an MEB and therefore christianity is false).

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I listed the ways that theists might try to avoid the difficulties that follow consideration of theological zombies in WLC – A Hole:

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)

I think here there is another issue that one might need to keep in mind given the argument above.  If the MEB did use theological zombies to ensure that no created soul would be unsaved, then it would not necessarily need to send an actual avatar to Earth to speak on its behalf.  A madman who thinks that he is the earthly representative of the MEB would do, or a group of people with runaway imagination who create a fictional character who thinks he is the earthly representative of the MEB (or even knows it, given that he is fictional).  That is to say, the apparent lies of Jesus would only be lies if Jesus were divine or divinely inspired.  If they are the ravings of a madman or the words put into the mouth of a fictional character, then the MEB is neither lying nor allowing its representatives to lie.

A Good Reason for WLC's Modus Tollens

I've railed elsewhere about the fact that WLC's morality argument is posed confusingly; in modus tollens form rather than the (more standard) modus ponens form.  To clarify, the argument:

• If P then Q
• P
• Therefore, Q

is more straightforward than:

• If not Q then not P
• P
• Therefore, Q

So, why use the latter rather than the former?

I've also pointed out that WLC himself torpedoes his own argument when appealing to vacuous truth (which he calls "trivial truth", perhaps because it thus seems as if he is referring to a Nils Bohr quotation).

What I have come to realise is not only that WLC possibly was aware of what he was doing when he presented his argument in the form that he did, but also that the problem that he was trying to avoid possibly applies to all arguments for the existence of god.

You see, if WLC had presented the moral argument in the standard modus ponens form, it would look like this:

• If objective moral values and duties exist then god exists 
• Objective moral values and duties do exist
• Therefore, god exists

The issue that WLC was aware of, I think, is that people who are not theists are not as enamoured with "objective moral values and duties" as theists are.  Sure, we agree that if a god of the sort that WLC believes in were to exist, then it would follow that objective moral values and duties would exist, somehow rooted in the existence of that god.  But this is just saying "if a god existed, then the sort of objective moral values and duties that only would exist if a god existed would exist" and non-theists simply do not believe that "the sort of objective moral values and duties that would only exist if a god existed" exist.

So, for us, "objective moral values and duties" of the sort that WLC is referring to constitutes an empty category and therefore it becomes perfectly clear that the major premise of the modus ponens is only vacuously true.  The argument becomes:

• If the sort of objective moral values and duties that would only exist if a god existed existed then a god would exist
• The sort of objective moral values and duties that would only exist if a god existed do exist
• Therefore, a god does exist

We can live with the major premise, since it's vacuously true, but we disagree with the minor premise.

Now, the thing with the vacuously true premise is that it effectively begs the question.  The (actually empty) category that is in question is assumed to not be empty on the basis of an assumption that the conclusion is true.  This is the case, even when you shuffle the terms around and present your argument in modus tollens form.

The trick the WLC then plays, by shuffling his terms around, is to imply that the major premise of his modus tollens is vacuously true:

As you can see, p → q comes out false only when the antecedent clause is true and the consequent clause is false. (I know that seems weird, but that’s the way “→” is understood logically.)

So what does this imply for the first premise of the moral argument?

1. If God does not exist, objective moral values and duties do not exist.

Well, since God does exist, the antecedent clause is false. Therefore, no matter what the consequent clause is, (1) comes out true! (Look at our truth table above.) So it is also true that

1′. If God does not exist, objective moral values and duties do exist.

A falsehood implies anything! So for the theist, (1) and (1′) are said to be trivially true or vacuously true.

Again, can you see?  WLC is pointing out that he is begging the question here (see WLC Being a Duffer for more).  His argument only works for theists who have already committed to the truth of what he is ostensibly trying to prove.  It's a worthless argument.

If an argument is begging the question in its modus ponens form then the argument is begging the question in all correctly stated equivalent forms, including the modus tollens form, such as WLC's stripped down version:

• If god did not exist then objective moral values and duties would not exist
• Objective moral values and duties do exist
• Therefore, god exists

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My other realisation was that this applies to all arguments for god.  If you shuffle the terms around and find that there is begging of the question happening in one (correctly stated) form of the argument, then it's happening in all correctly stated forms of the argument.

This is not a huge realisation on my part, since I thought that was the case in an informal way.  It's just nice to know that it can be shown formally.

Of course, if there is an argument for god which does not include any begging of the question, you are welcome to present your case.

A Powerful Argument

In Hands Off Our Logic, God-Boy, I mentioned the fact that Craig refers to his god as “enormously powerful”.  I noted that “power” is time related and want to address a possible wriggle manoeuvre that Craig and his disciples might try.  Possibly, they might argue, Craig is using a different definition of “power”, the “power” that would be necessary to make the universe out of nothing:

If Craig is using a magic version of these concepts, then he’s doing an argument like this:

In The Last Day of the Dinosaurs, the renowned palaeontologist Mathew Wedel holds forth on “how these majestic creatures went extinct”.

(Note that there is no clear indication that Wedel is responsible for the quote that I attributed to him.  Even if he is, it’s a mine-quote, and more than likely it’s a misattributed mine-quote that I took from an inappropriate source, namely tvtropes.org in an article which has a link to a complaint by Wedel that he had been totally misquoted by the production company responsible for the Discovery channel show mentioned.)

“Majesty” derives from the existence of royalty, but where did this “majesty” come from?  It couldn’t have come from human kings and queens because they were not around during the time of the dinosaurs, and dinosaurs had no kings and queens.

(Note that this is a misuse of the term “majestic” and of authority.)

Therefore, when seen as part of a cumulative argument, this shows that there must be a beginningless, uncaused, spaceless, timeless, immaterial, enormously powerful, and sovereign, Personal Creator of the universe!

(Note that this is a very minor change from Craig’s own words as uttered during his debate with Stephen Law.)

In his argument about the creation of the universe however, Craig is specifically talking physics.  In physics, power is the rate at which energy is transferred, used or transformed.  So “enormously powerful” means having the capacity to transfer vast quantities energy (or, alternatively, more modest quantities of energy over very short periods of time).  Hang on a second though … what is energy?  Energy has the SI unit “joule” and 1 joule is 1 kilogram multiplied by the square of 1 metre divided by the square of 1 second.  Both power and energy imply the existence of time and space.

So how did we end up with a spaceless and timeless being who is also “enormously powerful”?

I’ll leave it up to the apologists to provide an answer.  I won’t try to stuff more words in their mouths.

(And, if I am to be completely fair, I have to acknowledge that this simple physics based critique may be unreasonable since I am taking Craig’s gibberish far more seriously than is truly warranted.)

Metaphysical Necessity

Yesterday, I asked whether it is a strict logical possibility that William Lane Craig is a lying doofus.  Today, I want to ask whether it is a metaphysical necessity that William Lane Craig is a lying doofus.

Some may be sad to learn that I think that the answer is a resounding "No", but please stay with me as I try to explain how I reach this conclusion.

When reading the Wikipedia page on "metaphysical necessity", we immediately come across words that are faintly familiar:

In philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological (or physical) necessity.

Compare this with the words of WLC:

… The answer is “metaphysical possibility.”  This is a modality in between physical possibility and strict logical possibility and is often called “broad logical possibility” by contemporary philosophers.

So, it would appear that WLC took the notion of "broad logical necessity" (likely coined by Plantinga in The Nature of Necessity in 1974), twisted it into a new form, that being "broad logical possibility", and claimed that contemporary philosophers were already talking about it.  I saw the term "metaphysical necessity" in one of the very early documents that refer to "broad logical possibility", the transcript of a talk by … yep, William Lane Craig (The Coherence of Theism).

In this document, you can see evidence of the switch from "broad logical necessity" to the new term "broad logical possibility":

Furthermore, the modality operative in possible worlds semantics is not strict logical necessity/possibility, but broad logical necessity/possibility. Strictly speaking there is no logical impossibility in the proposition The Prime Minister is a prime number; but we should not want to say, therefore, that there is a possible world in which this proposition is true.

It is true that people have been talking about metaphysical necessity for a very long time, but what exactly do we mean by "people" here?  Most of these people have been theists talking about god, or talking about Saul Kripke (who in turn was talking about what was referred to in Strict Logical Possibility as "metaphysical possibility").  Again, when we try to consider things that fall into this category, now considered in terms of necessity, rather than possibility, we can find only one thing that is claimed to be "metaphysically necessary" - and that is a god, most specifically the god of the ontological argument.  There's a neat little Venn diagram on this page that sums things up nicely.

Let us put Kripke's modal logic tautologies aside (ie put aside notions similar to it being "metaphysically necessary" that water is H₂O and vice versa (at which point we need to also put aside the confusion of people who don't accept that ice is also water, despite it having a different name and being a lattice rather than liquid form)).  Other than a god, what does anyone claim to be a "metaphysical necessity"?

When I first started developing the idea for what became Strict Logical Possibility, I was very much thinking about the awkward negation of "strict logical possibility".  People tend to get confused about how modals are negated and casual modern English (particularly as used by Americans) only makes the confusion worse.

For example, if I were to say that "not all" cats are grey, I am not suggesting direct opposite of "all cats are grey" - that is I am not say that all cats are not grey.  If I wanted to say that, I would say "no" cats are grey (or all cats are "not grey".  In clumsy usage, "all cats are not grey" is often meant to say "some cats are grey, but not all of them" - rather than "every single cat that exists is some colour other than grey".  (I'm somewhat ambivalent on the grey/gray divide, although I do see Gray as more of a surname than a colour.)

This confusion carries over to considerations of what is possible/necessary and not possible/necessary (see Plantinga and His BS5).  In brief: that which is not possible cannot be necessary, but that which is not necessary can be possible.  In other words, a lack of necessity is consistent with both possibility and impossibility.  WLC does not fall into the trap of saying explicitly that the non-existence of god is metaphysically impossible, but others certainly do:

William L. Rowe has challenged my claim that there are only two kinds of impossibility, logical and physical, by introducing the concept of metaphysical impossibility — the impossibility which obtains just in case nothing has the power to bring about an individual’s non-existence — and by maintaining that, though God’s non-existence is metaphysically impossible, it does not follow that it is logically impossible as well.

And the ontological argument is based very much on the notion that the non-existence of the god in question is metaphysically impossible - which is to claim that the existence of god is metaphysically necessary.  WLC certainly makes the claim that the existence of his god is a metaphysical necessity:

(blah blah blah, blah blah) … Thus, it is metaphysically necessary that God exists.

But now we are back to the question of what things are metaphysically necessary - if there is nothing else than god in this category (and possibly all those tautological claims that things are the things that they are), then surely the claim that god is "metaphysically necessary" has no teeth whatsoever.  God would have the precisely the sort of "metaphysically necessary" existence that god has (which could easily be no existence whatsoever) and god would have the precisely the same characteristics that god has (being spaceless, timeless, immaterial and non-existent).

WLC goes on in the article linked above to write:

We have here the germ of the ontological argument for God's existence. For if it is possible that God exists, there is a possible world in which God has necessary existence. But then He exists in every world, including this one. Thus, the atheist is thrust into the awkward position of having to say that God's existence is impossible. It is not enough to say that in fact God does not exist; the atheist must hold that it is impossible that God exists—a much more radical claim!

He's claiming here that, because the atheist disagrees with the claim that the existence of god is a (metaphysical) necessity, she needs to hold that existence of god is a (metaphysical) impossibility - perhaps even to the extent that the non-existence of god is a metaphysical necessity.  This is a false dilemma built on a(n implied) begged question - buried in the fact that the only object that is asserted to have a metaphysically necessary existence is a god.  The atheist is quite entitled to allow that gods are a metaphysical possibility, whatever is actually meant by that, while holding that none actually exist (for reasons other than metaphysical necessity/possibility).

Finally, I did say that I did not want to claim that is a metaphysical necessity that WLC is a lying doofus.  I think it's quite reasonable to be averse to putting the assertion "god exists" on a par with "WLC is a lying doofus".  After all, I am quite convinced that god does not exist.

Strict Logical Possibility

Is it a strict logical possibility that William Lane Craig is a lying doofus?

While this might seem like a totally uncalled for attack on WLC's person, it is merely meant as an example of how we might think about "strict logical possibility".

First we need to define our terms.  When we look up "strict logical necessity" we might be disturbed to note that there are only 35 hits (excluding the hits that result from this post - update, as of 6 June 2018, there are now 75).  The majority of them (including this post) make reference to WLC or Plantinga.

This led me to believe that "strict logical possibility" is another taxi-cab, a vaguely impressive sounding piece of nonsense created by William Lane Craig.  A bit more manipulation of Google reveals that the phrase might actually have been a William Dembski original from a 2003 document on the flagellum, a phrase that was then resurrected by WLC in 2007.  Dr Glen Martin used the words in that order in 2004, but the use doesn't appear to be intended as a phrase.  I'm not entirely certain that Demski meant it to be a specific phrase either, since he also used "strict logical certainty", "strict logical deduction" and "strict identity" in the same document - so I think we would not be far off the mark if we were to award authorship of this nonsense to WLC.  I was inclined to be generous.  However, I found that there was an earlier clear use of the term, in 2006, by Sean Michael Campbell (nestled in a reference to "strict and broad logical possibility") - but this was in an overview of WLC's Kalam argument and, in the footnotes, Campbell acknowledges helpful conversations with WLC.

Since WLC was likely the person ultimately responsible for the coining of the phrase, we can look to him to see what it means.  WLC first uses the term in "Causal Premiss (sic) of the Kalam Argument":

Your first question is, “What is the sense of ‘possibility’ here?”  The answer is “metaphysical possibility.”  This is a modality in between physical possibility and strict logical possibility and is often called “broad logical possibility” by contemporary philosophers.  To illustrate, it is strictly logically possible that “The Prime Minister is a prime number” (there is no logical contradiction here); but, notwithstanding, such a thing is metaphysically impossible (incapable of actualization).  There are all sorts of truths—like “Everything that has a shape has a size,” “Nothing can be red all over and green all over,” “No event precedes itself,” etc.—which are not strictly logically necessary but are, I think, metaphysically necessary.  I think that the first premiss of the kalam argument is a metaphysically necessary truth.

I note that "broad logical possibility" was not a term used often by "contemporary philosophers".  It was a term used once, by one guy, after chatting with WLC.  Making such a statement is what contemporary philosophers refer to as "a lie".

Sadly, WLC doesn’t really define "strict logical possibility".  Although he does hint that something has "strict logical possibility" when it doesn't entail a logical contradiction, it isn't clear whether this is key to defining the term or merely a feature of things that have "strict logical possibility".  Fortunately, we have a later reference to the phrase to work from, a quite recent one - In what sense is it impossible for the universe to come from nothing? - 11 September 2016.

When the atheist professor says that “it may be possible that something began to exist out of nothing because that statement did not involve a contradiction,” he is talking about strict logical possibility. He’s quite right that “The universe began to exist out of nothing” involves no logical contradiction and is therefore strictly logically possible. Where he errs is thinking that this is of any philosophical significance.

So, "strict logical possibility" equals "not entailing a contradiction".  This is a construction that is bound to end in tears, since it's hiding a negation in a phrase with two adjectives and a noun - a noun that is conjugated from yet another adjective (ie possible).  And WLC just leaps right in to discuss the impossible, negation of the possible.  He's canny though, since he doesn't talk about "strict logical impossibility" - he merely talks about "broad logical impossibility" (and "metaphysical impossibility", more on that in a moment).

WLC makes clear that "strict and broad logical possibility" (the original phrasing from Campbell) are distinct, meaning that "strict logical possibility" is distinct from "broad logical possibility" and "broad logical possibility" is distinct from "strict logical possibility".  Therefore, we are led to conclude, something that has "broad logical possibility", since it is not "strict logical possibility" can entail a (logical) contradiction.  Read the paragraph above again.  WLC wrote "(X) involves no logical contradiction and is therefore strictly logically possible".

Bizarrely, WLC then writes:

It’s also strictly logically possible that “John is a married bachelor” or that “The Prime Minister is a prime number.” So what? That goes no distance toward showing that married bachelors are metaphysically possible or that it is metaphysically possible that the Prime Minister is a prime number. What we want to know is whether such states of affairs are realizable or actualizable. Could John really be a married bachelor or the Prime Minister a prime (or any other sort of) number?

What the …?

A married bachelor is a classic example of a logical contradiction.  The very term "bachelor" means "unmarried male person".  It is, strictly speaking, logically impossible for John to be a married bachelor.  The only way around this is to get into pointless semantics, to suggest that married does not have to mean what it means, that bachelor could (in an alternate world) mean "person with a big nose" rather than "unmarried male person" - to suggest that, strictly speaking, language is fuzzy and we don't know for sure what any of the terms we are using mean and therefore anything is possible.  This is a very clear indication that WLC is being a doofus.

In the midst of this doofusness, WLC uses the term "metaphysically impossible":

What your theology professor rightly argues is that the universe’s coming into being from nothing is metaphysically impossible. Philosophers typically call this sort of possibility broad logical possibility, in order to distinguish it from strict logical possibility. Speaking in terms of broad logical (or metaphysical) possibility, we claim that coming into being from nothing is broadly logically impossible, just as it is broadly logically impossible that something is colored but unextended or that gold has the atomic number 13.

Note that he's tried to tie "broad logical possibility" to "metaphysical possibility", and claim that "the universe's coming into being from nothing" is "broadly logically impossible" because it's "metaphysically impossible".

Nonsense.  There are two ways of looking at metaphysical possibility.  One is encapsulated in Kripke's classic statement "Water is not H₂O" - this is metaphysically impossible because, by composition, water is H₂O.  This is closely linked to the other way of looking at metaphysical possibility, because there is no possible world in which water would be anything else than H₂O, because that's what water is.  The other view on metaphysical possibility is such that we might discuss other possible circumstances - so it's a metaphysical possibility that this would have been written in German, had the Allies not won World War 2, or in Russian if the USSR had won the Cold War.

For something to be metaphysically impossible (and thus "broadly logically impossible"), it could not have been - even if the world were different.  Examples that we can conjure up for this category are usually the logically contradictory (the time traveller who accidentally kills his mother when she was a toddler), definitional (a sunny day with full cloud cover (our definition usually means at ground level, but above the clouds it is likely to be as sunny as any other day)) or mathematical (1=2).  An example that doesn't quite fit into any of these is the reified privative, like a potful of donut holes (ignoring these sorts of donut holes) and the dark creeping into your house (along with the cold), but I am not sure that this constitutes a metaphysical impossibility, it seems to be more like a simple confusion.

So, when WLC claims that "the universe's coming into being from nothing" cannot be, because it's metaphysically impossible, he is very much begging the question.  He gets away with it because very few make the effort to dig into precisely what metaphysical impossibility is.

Maybe he's not so much of a doofus after all.  Just a big fat liar.  I nevertheless think it's broadly logically possible (and thus metaphysically possible) that he's a lying doofus.