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?