post edit is down on the bottom of your posts, left corner... but thanks to an update, the original topic creating post cannot be edited by us peons

• Premises:
  
  1. There are far too many definitions for "god" (and more being born every minute) to refute them all properly.
  2. We are not yet in possession of a complete understanding of the universe, leaving a small space for the potential of one of those many possible "gods".
  3. The evidence so far does not leave a great deal of room for god, however, and things are looking worse for god every day. The chances of there being a god, even given the amorphous definitions, are so slim as to not be much worth worrying about.
• Conclusion:
  
  • I am therefore an "agnostic atheist".

I probably know more about this than the other people here, so I will give it a shot. I think your problem is in P1 and P2. The phrase "is to claim" is very vague, but that's okay because there are only two ways to translate the argument:

Possibility One

1. K <=> C

2. B <=> C

Possibility Two

1. K => C

2. B => C

Both interpretations fail. Possibility One fails because it implies that knowledge and belief are identical, which is false. Possibility Two doesn't fail right away but still ruins your argument because it leaves you with:

1. K => C

3. Therefore, ~K => ~C

Which is fallacious.

Also, as an aside, you should as an atheist deny P3 anyway. I claim God exists, so I know God exists by the following deduction:

1. ~K => ~C (Your P3)

2. C

3. Therefore, K

 Dante,

It's an interesting attempt.  What you are using is called sentential logic (almost) and that's not a very good system for what you are trying to say, I would recommend predicate logic.  That way you avoid playing word games as evidenced in a prior comment.

You're use of 'believe' and 'know' implies an identity between them (only because in this instance they can be said to have the same exact qualities and none different).  That is reason enough to reject the argument outright, since there are plenty of claims where knowledge and belief can be at odds without being internally contradictory, assuming that knowledge entails certainty.  (e.g. the existence of me as a entity.  You believe I exist, but do not know).  

(∀x)[Ax > Bx]  For every claim, if knowledge is claimed, belief is implied

(∃x)[Bx & ~Ax] There is a claim for which there is belief without knowledge

Not really sure where to go from there.  That’s just a simple statement of fact, but at least you have a starting place.

Thank you all for the comments. Obviously I will have to take a hard look at my argument. Shows how important it is to use logical notation instead of natural language. Have not gotten there yet.

By the way what would be your suggestions for an introduction to logic book? One that is really thorough and a novice can learn from.

"Knowledge" is still ultimately "belief", just with very strong justification, at least from the that person's point of view.

Shouldn't really use the term "knowledge" in a rigorous argument, because calling something "knowledge" is just begging the question of whether it is a 'justified' belief, which is a matter of opinion. All we have are beliefs, held with varying degrees of strength, as well as differing degrees of general acceptance and external solid evidence, Beliefs that would be very hard to deny, like that I am sitting in front of my computer at the moment, we feel we can safely call knowledge, even thow there is a finite chance I could be imagining it.

So we have to have ways of assigning very broad relative probabilities to propositions that we have little or no hard evidence for or against. Otherwise Russell's famous orbitting teapot is just as 'possible' as any other idea that is not logically imposssible, which is clearly wrong in every practical sense.

This is where ideas like Occam's Razor and, more technically, Bayesian analysis, are useful, to allow us to assign likelihoods to propositions on the basis of assessing the relative probability of various aspects of the proposition. These tools really only help us put propositions on a scale from almost certainly true to extremely unlikely, but particularly with Bayesian ideas, helps us sort them in consistent way. For example, if one idea involves some aspect, say "omnipotence" which we find of very low plausibility, then any other proposition incorporating that idea should be discounted to the same degree, and so on for any other detail of a proposition.

Note that these are the sorts of tools we need to apply to such arguments, where simple true/ false logic fails to capture the subtleties of the discusssion.

Logic is essential, but massively insufficient, for understanding reality.