Rise of atheism: 100,000 Brits seek 'de-baptism'

[Final-Fan]

Definitions
"I’ve done my best to conform to your terminology but right when I think I’ve understood, it seems you bring a new phrase or refer to it a little differently. Like the phrase “the concept of ‘belief within belief’ versus ‘knowledge within belief’.” I already didn’t understand what you meant last time when you were dealing with the difference between knowledge, belief, and input/output."

I don't know if this is going to work, but I skimmed my posts for the parts where I thought I'd laid out things in a pretty common-sense sort of way.  Maybe having it all together (with some added commentary) will do the trick. 

But this isn't ABSOLUTE knowledge, it's knowledge within the sense data (input) of its own internal consistency with your output.  Do you deny that when you output what you perceive as "pressing Y on the keyboard" a Y appears on the screen?  Do you not expect that if you should output "pull the trigger of a loaded gun that is pointed at your body" you are going to receive input "PAIN"?

knowledge is provable/proven belief.  So we can prove, and thus know, things WITHIN our input/output data, but we can only BELIEVE that said data and knowledge is actually TRUE knowledge of a "really for real" universe.  (Or believe something else, or nothing.)

(One must) differentiate what is true/provable/possible WITHIN a belief set vs. what is true/provable/possible for ALL belief sets.  Thus knowledge is differentiated from absolute knowledge, the latter of which is what you say cannot be derived from sense data (and I don't disagree).  Here you appear to be saying that regular (i.e. non-absolute or KWIB) knowledge is not possible either, but I disagree.

For math, the math data is absolute, so it can produce absolute knowledge.  But sense data only produces relative knowledge.  To illustrate this, let me give some examples from non-self-contradicting belief sets:  within empiricism the moon is definitely rock.  The sense data proves this (under the assumption that sense data is more or less accurate).  Within the Matrix theory the moon we "see" is definitely programmed to be rock.  The sense data proves this (under the assumption that sense data is more or less accurate about telling us about things in the Matrix).  And sense data can produce this relative knowledge.  This is how it is possible for it to disprove a belief set. 

So I have been talking for some time now about knowledge that is not absolute (i.e. would not necessarily be true for any belief set) but which is certain within, or assuming, a belief set.  Within empiricism, we know the earth exists, etc.  So "knowledge within belief" means that once the initial belief set is assumed, it is certain that (whatever) is the case without needing any additional belief.  Something that is not certain without either more evidence/proof or additional belief would be what I meant by "belief within belief". 

This does not mean that KWIB is absolute knowledge ("KWOB", perhaps?), which is something that is certain without needing any initial belief at all.  For math, it may be uncertain whether the rules are there by assumption or by definition, but if it is the latter then it would be absolute knowledge.  (The last italicized quote went by that interpretation.)