I did not provided any arguments for or against God's existence. You have made an incorrect inference from my preliminary statement. The intention was to show that absolute proof is not achievable for most ideas we hold as true. Consequently, some amount of faith is necessary to accept most anything as true. This also leads into showing how probability is a more honest and realistic measurement for knowledge.
I agree that absolute proof is not achievable, but that is a red herring as it is not what is being asked. Absolute proof that a god or gods exist is not what is necessary, instead any proof or examinable evidence whatsoever would be a good start instead of mere claims.
The idea of it being possible that "there is no 'proof' that the natural world exits"
is irrelevant and does not in any way equal the possibility that there is "no 'proof' for God's existence"
I disagree in regards to faith being "necessary to accept most anything as true"
as I require ZERO faith to accept that the world I live in is real as I have no other choice but to accept that reality is reality. I require ZERO faith to accept that I am currently typing on my keyboard which is resulting in letters appearing in a message box of a Post reply form at the whywontgodhealamputees.com forums. I could choose however to have faith that I am in fact living in the matrix and Morpheous is about to call my cell phone any second to tell me to run away from computer program agents out to kill me BUT I really don't have any reason to have faith in that do I.
EDIT: One thing I do have faith in is that most people are generally good in nature and don't knowingly go out of their way to harm or trick others (granted there may be some who do, I have faith that all don't).
Perhaps you are simply implying because I have sufficient evidence that reality is reality that it is acceptable to have faith. I would have to ask how do you define 'faith'?
I myself define 'faith' as having trust that something is true without evidence. If my definition is acceptable, what happens when sufficient evidence is introduced? Is faith still applicable?
I would agree that probability is useful and realistic measurement for making a reasonable conclusion. I'm not sure about how exactly honesty or knowledge are involved. Someone could be dishonest in determining the probabilities or they could be dishonest in arriving at a conclusions based on probabilities. Additionally, knowledge is part of the data that might be used in determining the probabilities. I think your attempt at showing how probability is useful was flawed.