Another Whack with the Sledgehammer

In The Sledgehammer Approach, I compared theism to believing that a test subject hit an egg with a sledgehammer while blindfolded - in the absence of actual evidence in support of that belief.

There are of course problems with the analogy.

Some theists would say that the nature of god is such that the test subject could not have missed an egg (this is equivalent to the claim that god is necessary, the theological position that it is impossible for god not to exist).  Such theists would argue that I was vague in that I said "give (the test subject) a sledgehammer" and "take some eggs" rather than specifying that the experimental protocol would require either an infinitely large sledgehammer or an infinite number of eggs, thus making it impossible for the test subject to miss.

Some atheists would say that if any eggs were put out, then that would be ignoring the fact that the god in question is logically impossible and cannot exist.  I'd probably agree if we were talking about a specific god, but strictly speaking when we are talking about theism, the god isn’t specified.

Then there is the problem of "prior probability".  If only one very small egg was put out and the sledgehammer's head was tiny (a pinhammer or needlehammer, perhaps), then the prior probability of hitting an egg would be very small.  Alternatively, if a large (but not infinite) number of eggs were put out and the sledgehammer was a monster, then it'd be highly likely that an egg would be hit.  This wasn't really what I was getting at with the article, I wasn't trying to be accurate about the likelihood of a god existing, I was only trying to explain the shading involved with being an atheist - so something like a 50-50 chance of hitting an egg was fine.  This also has the benefit of being a strong-ish version of the theist position.

The size of the sledgehammer's head, however, raises another issue.  Evidence.  The test subject would be justified in assuming a low probability to hitting an egg if the sledgehammer was light (and the head small) and a higher probability if it was heavy (and the head large).  Then there are the sounds and smells involved.  The test protocol only called for a blindfold, but an egg being smashed by a sledgehammer might make a distinguishable noise and the albumen and yolk could possibly release a scent that the test subject could pick up.  Also, the sledgehammer might have been a bit slippery after the strike, if an egg was smashed.  There are enough variations between potential test subjects with respect to their sensitivity that some might smash eggs without noticing while others would believe that they had smashed one when they hadn't.  Their beliefs, therefore, would be subjective - overdetectors would detect smashed eggs when there aren't any, underdetectors would miss a lot of smashed eggs.  (This is equivalent to "agent detection" - some atheists, like myself, reckon that theists have hyperactive agent detection.)

The point in the analogy is that there isn't any conclusive evidence, which is precisely the position that atheists take.  A theist might want to argue that there is conclusive evidence for their god, but the atheist cannot really accept that argument without becoming a theist.

The Sledgehammer Approach

First get a test subject, give her a sledgehammer and put a blindfold on her.  Then take some eggs and place them in a circle, at about sledgehammer distance from your test subject.

Spin the test subject around a bit and then tell her to swing down the sledgehammer onto the ground in front of her.  Take the sledgehammer from her, lead her carefully away from the test area, making sure she doesn't trip over any of the eggs.  Then you can remove the blindfold and give her a cup of tea and a biscuit.

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Now you ask her to explain her position regarding whether or not she hit an egg with the sledgehammer.

If I were the test subject, the first thing I'd do is check my clothes to see if I had any egg fragments on me.  Let's say there isn't, or at least she can't see any egg product on her.

Does she know that she hit an egg?  Note that she doesn't have any evidence that she did.

Does she know that she didn't hit an egg?  Note that the absence of evidence is not evidence of absence.  She could have missed it, or hit it in such a way as to not get spattered.  She doesn't have definitive evidence that she missed but she might think that she knows that she didn't hit an egg.  This would make her gnostic with respect to egg-missing.  She might, however, given the impossibility of evidence, remain agnostic on this issue.

Note here that there are three possible epistemic positions she could adopt:

She could claim to know that she hit an egg

She could claim to know that she missed all the eggs

She could state that she doesn't know whether she hit or missed

You could also ask her what she believes with respect to hitting or missing eggs and she could arrive at three similar doxic positions:

She could believe that she hit an egg

She could believe that she missed all the eggs

She could state that she doesn't believe anything with respect to whether she hit or missed

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I'm tempted to replace epistemic with gnoseic, as distinct from gnostic, but it's not a term that has taken off and there's no firm definition of the word from which I have taken it (gnoseology).  Basically I want to distinguish between that which is known (or thought to be known) and that which is believed (including that which is known to be believed and not thought to be known).  There are two Greek roots that could be used for "regarding beliefs": doxa (common belief, opinion or acceptance) and pistis (confidence, faith or trust).  There are problems with both.

Doxology means "a liturgical formula of praise to God" rather than being related to belief and pistiology means "the branch of theology which treats of the place and authority of faith" or "doctrine concerned with faith" while pisteology means "the science of faith"(!) and both of these latter terms are far too close to epistemology to avoid confusion, and replacing epistemology with gnoseology has its own problems.  Just work with me here and accept that by epistemic I mean "about knowledge" and by doxic I mean "about belief (as distinct from faith)".

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So, there are a limited number of workable combinations:

Believing (hit) and claiming to know

Believing (hit) and accepting a lack of knowledge

Not believing either and accepting a lack of knowledge

Believing (miss) and accepting a lack of knowledge

Believing (miss) and claiming to know

It seems unreasonable to claim to know that one hit an egg or missed all of them while also claiming to believe the opposite.  This sort of claim works only as hyperbole, an expression of surprise or shock (as in "I know I just won the lottery, but I have to keep pinching myself.  I still don't believe it!")  If you don't believe, you can't know - even if you use Plantinga's modified epistemology you are still talking about warranted true belief instead of the gold standard, justified true belief.

Similarly, it seems unreasonable to believe something and claim to know the opposite.  You might express such a contradiction as some sort of patriotic or loyal hyperbole - "I believe Moldovia is the best country in the world, although I know it isn't really" or "I believe my baby is the most beautiful ever, although I do know he looks like a miniature, bald version of the later era Elvis", but in reality you believe that Moldovia is, at best, only the second or third most liveable nation in the world and that your child is has been beaten mercilessly with the ugly stick.

Let's put this in a table to make it clear what I mean:

	Know Hit	Not Know	Know Miss
Believe Hit	YES	YES	NO
Not Believe	NO	YES	NO
Believe Miss	NO	YES	YES

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It should be pretty clear that I am talking here about pure agnosticism, weak theism/atheism and strong theism/atheism.  Theists of a certain stripe struggle understanding that not believing in a god and believing that a god does not exist is not the same position (which they label as an epistemic position rather than a doxic position).  Hopefully those theists can understand that the positions work perfectly well if we are talking about smashing (or not smashing) an egg with a sledgehammer.  Let's modify the table, so that we make the hittists theists and the missists atheists:

	Know God	Not Know	Know No God
Believe God	YES	YES	NO
Not Believe	NO	YES	NO
Believe No God	NO	YES	YES

Modifying again to ram the point home:

	Know God	Not Know	Know No God
Believe God	Strong, Hard or Gnostic Theist	Weak, Soft or Agnostic Theist	NO
Not Believe	NO	Pure or Adoxic Agnostic	NO
Believe No God	NO	Weak, Soft or Agnostic Atheist	Strong, Hard or Gnostic Atheist

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We can make another modification to the second last table to highlight a confusion that might lie behind the theists' problem with the spectrum of atheistic non-belief (and no, I am not going to try to introduce apatheism into the mix.  How much, if at all, you care about the question would introduce another axis - want god to exist (to some extent), not care, want god to not exist (to some extent)):

	Know	Not Know	Know Not
Believe	YES	YES	NO
Not Believe	NO	YES	???
Believe Not	NO	YES	YES

In informal English, it is possible to say that you know that there is no god and also say that you do not believe.  This can trip you up when you look at "Not Believe-Know Not" as a cell - it actually seems vaguely possible.  I don't think this confusion would occur in most other languages because they are structured differently and that it's the auxiliary verb (do) that leads to this confusion in modern English.  Strictly speaking, to know anything you must believe it (albeit not necessarily in the religious sense of believing).  What we also see here is an equivocation on the word "believe" - if you are working with a strong, faith-like definition of "believe" then this cell would be workable.  I, on the other hand, am using "believe" in a purely functional sense - meaning something along the lines of "hold to be true".

I am reasonably sure that a substantial proportion of people, when trying to fill the table in this last form, would at least pause for a moment when filling in the "Not Believe-Know Not" cell, some would fill it with YES and then argue that they are right.  However, I reckon that the very same people would have no problem filling the table out correctly when expressed in terms of hitting or missing an egg with a sledgehammer - because the definition of belief as approaching faith is not triggered in that example.

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Some might wonder how this construct might align with Dawkin's spectrum of belief.  That spectrum is more probabilistic and the table would look something like this:

	Know	Not Know	Know Not
100% god	YES	NO	NO
75-99% god	NO	YES	NO
51-74% god	NO	YES	NO
50% god	NO	YES	NO
25-49% god	NO	YES	NO
1-24% god	NO	YES	NO
0% god	NO	NO	YES

[I had written something here about the "0% god - Not Know" and "100% god - Not Know" cells, but it wasn't particularly important and I added confusion by misusing the term certainty.  Hopefully people can work out why those cells change to NO so I don't really need to attempt a fumbling explanation.]

Note the difference in strength between what could be called "strong atheism" and "weak atheism".  It can be as little as 1% or 0.01%.  Alternatively, you could call "1-24% (chance of) god" strong atheism, or use some other low probability range if you prefer, the higher values would then be weak atheism and the zero point zero recurring percent would be reserved for people that we call "idiots".   (Similarly anyone claiming a 100% certainty with respect to god would be an idiot, but we are generally encouraged to be more diplomatic when this sort of unrealistic certainty is expressed by a believer.)

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Hmmm.  Anyone hungry for an omelette?