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.

One God, Two Cups

If you want a headache then, so long as you are not a theist, a good destination is Craig-Land.  I was able to carry out a long meandering discussion on the nature of “objective moral values” over a period of more than three months and, while a little frustrating at times, this discussion was reasonably stable – we knew what we are talking about and we pretty much stayed on track.  Not so in another thread on the “Ontological Argument”, which took off a few weeks later.

My claim in this thread, a thread that I initiated, was that Craig continues on a cheat in the modal logic version Ontological Argument that is initially committed by Plantinga and I posed the questions: “Are there people who are seriously persuaded by this argument?  Surely some of you have worked out that something is not quite right in it?”

This claim attracted the attention of self-described logicians who wanted to prove to me that Plantinga’s BS5 is actually a logically valid argument.  Because this was not precisely what I was saying (remember I was claiming that Plantinga and Craig were cheating, not that the argument was not "a logically valid argument"), I claimed that this was a diversion and that, eventually, the argument broke down into counter claims of playing the “pea-and-cup game” - involving switches between claims of (in)validity and claims of (un)soundness.

There is some similarity between this discussion and that on “objective moral values” given that my theist opponents were trying to limit the discussion to a question of the “logical validity” of a specific theorem, namely BS5, (and they wanted to define that as meaning “internally consistent”, rather than applicable in the context in which it was being used) and were trying to avoid discussing whether the modal logic version Ontological Argument as a whole was “sound”.

I thought that I might share two things that stood out to me in these discussions, noting that these were “logicians” and thus apparently sophisticated theists.

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If I was presenting an argument about something as important as the existence of a god is to theists, I would be concerned if I could easily replace “god exists” with “my car is green” and I could logically show that my car is green when it is, in actual fact, blue.

Admittedly, in the excitement of finding an apparently brilliant argument to show that my car is green (when it's not), I might initially fail to notice that I can prove whatever the hell I wanted to prove with this argument (for example, one of the sophisticated theists used BS5 to prove that I don’t exist which, under the circumstances, I didn’t find threatening in the least).  But once it was pointed out that I could “prove” logically that I was the world’s best Morris dancer as easily as I could prove something that I actually wanted to prove, for example that spanking (as defined by my buddy, LNC) is bad, then as a rational person I would become very wary of such an argument.

Not so the sophisticated theist.  Instead, the sophisticated theist will zero in on the internal consistency of BS5 and ignore the fact that their argument (which makes use of BS5) is unsound.  This sounds like intellectual dishonesty to me, but I suppose theists are rarely accused of being intellectual.

Interestingly enough, I got challenged a couple of times on whether I was a logician, as if I wasn’t welcome to point out the fact that BS5 can be used to prove that the moon is made of green cheese when one so desires.  The reason I find it unnecessary to be a logician is that when Craig has presented this argument, he hasn’t carefully checked his audience to ensure that they are all logicians.  If he’s willing to present his argument to non-logicians, then I don’t see why non-logicians should be prevented from pointing out that an argument that relies on BS5 is bollocks (after all, the argument might work perfectly in a logician’s ivory tower and fail miserably when brought out into the real world).

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The second thing I noticed was a far more obvious case of intellectual dishonesty.  During my three weeks of discussion, the more coherent theist involved seemed to be cpdavey24.  This positive assessment of mine might be due to the halo effect given that he noted a few times that he didn’t consider Plantinga’s Ontological Argument to be particularly good.  However, the halo was tarnished somewhat by his last post.

From as early as reply #24 in our exchange, cpdavey24 began to admit that perhaps Plantinga’s and Craig’s arguments might not be good (“But look, I never said Plantinga’s or Craig’s OA was a good argument.”)  He maintained this position of strategic neutrality in replies #38, #56, #82, #117 (two mentions) and #120 (a staggering six mentions).  When I replied to #120, applauding him for effectively arguing my point, I quoted all six instances:

• If by "logic can't be used to show that it does" you mean that when "god exists" or "a maximally great being exists" is plugged in for A, the argument is unsound (though valid), then you may be right. But if by this you mean the logic itself is invalid, then this has yet to be shown

• As for for the second part of your statement, let me reiterate a fourth time that I am not arguing that God exists, nor am I arguing that Plantinga's argument is a good or "convincing" proof

• The reasoning is unsound given certain instances of A

• If by "dodgy" you mean unsound, then I agree with you; but, again, this is the case with all valid forms of reasoning

• So, again, if you want to retract your claim that Plantinga/Craig's argument is invalid, and simply hold that, like the argument above, it is a terrible and unconvincing argument (though valid), then that's fine

• First, I would never use the OA to try to save your soul, neopolitan, because it is a very complex argument and I'm not convinced it's a good argument anyway.  //  Second, I've never said the OA is the best argument one can present for the existence of God. Others on this thread might be making that claim, but I certainly am not

However, despite this, cpdavey24 had the gall to include in his reply (#130) not only further confirmation:

• First, if by “works” you mean is sound, then I’ve never said it works.

but also denial of that confirmation:

• If by “he argues my point” you mean that I have anywhere in this thread argued that Plantinga’s or Craig’s OA is unsound, then I am afraid you are simply mistaken.

His compatriot, Biep, also tried to argue that Plantinga himself wasn’t actually arguing that his Ontological Argument was sound (I’m not sure what the point of making that claim was).  When I posted Plantinga’s own words from the document in which he presented “A Victorious Modal Version”, in which Plantinga claimed that his argument was sound very clearly at least three times, Biep responded with:

• Indeed, those are not claims about the logic, but about the truth of the premises, especially the first one.

This reality realignment on the fly really makes it difficult to maintain interest in reasoned argument.  It certainly doesn’t indicate any willingness to work towards truth and understanding.

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Anyways, what I have learnt from this, yet again, is that theists are very resilient.  They will believe a ridiculous proof if it gives the answer they want, they will hide behind definitions and authority and they are more than willing to warp reality if they think it will aid their cause.  And while it just might be possible that they are not totally mad themselves, arguing with them can certainly drive a poor fellow to distraction.