John - a few responses - essentially in agreement with you, but with an 
issue or two:
 
sowa@xxxxxxxxxxx writes:
I mostly 
  agree with your comments, but I just wanted to add
a few 
  clarifications:
> "Lebenswelt" is the set of mental models to which 
  I've been
> referring - and thus is distinguished from the reality in 
  the
> way I think John means.
Husserl was using the word 
  'Lebenswelt' for the perceived world,
which is based on one's percepts, 
  which could be considered part
of one's mental models.  But I'd 
  hesitate to identify them by
placing the word 'is' between 'Lebenswelt' and 
  'mental models'.
Okay - I wouldn't disagree with this, although I'm not sure whether the 
distinction is important (but maybe it is; see further discussion below). I was 
speaking somewhat loosely - perhaps it would have been better if I'd said 
"'Lebenswelt' is associated with the set of mental models ...". In any case, we 
generally act as though our perceived world is actually the reality. It 
is our perceived reality (by definition). It's only because the 
correspondence is largely rather good (true) between our perceived world 
(associated with our mental models, if not, in a sense a version of them) and 
reality that our actions work and our lives are functional. In fact, this must 
be the basis on which our capacity for such perceptions, with an adequate degree 
of truth, evolved. 
 
This reminds me of an interesting classic experiment by George Stratton in 
the 1890s, in which he wore glasses that turned the visual world upside down. 
After four days, his perceptions adjusted to "flip" the world back over, so that 
his perceived world again corresponded more directly with the existing reality, 
allowing him again more directly to relate to it. (For a description and 
references, see 
http://www.madsci.org/posts/archives/mar97/858984531.Ns.r.html ). 
I would note here that our perceptual reality shifts as we adapt to any 
situation or learn any skill. Something similar may be at work when dentists 
learn to do their work in a mirror, for example. 
 
For 
  two related German words, I'd suggest the title of an important
book by 
  Jakob Johann von Uexküll, which was published in 1909:
    
  _Umwelt und Innenwelt der Tiere_
The word 'Umwelt' is the usual German 
  word for 'environment',
but Uexküll used it in a sense that is sometimes 
  translated as
'subjective universe' of humans and animals (Tiere, in 
  German).
The word 'Innenwelt', literally 'inner world', would 
  probably
be a better equivalent for "the set of mental models".  
  That
would enable a three-way distinction:
  1. The world as it 
  actually is (i.e., reality).
  2. The world as perceived by any 
  individual of any species
     (his, her, or its Lebenswelt 
  or Umwelt).
  3. The world as modeled by any individual (the 
  Innenwelt).
I'm not familiar with the work directly, but this question occurs to me: 
Would not the "Umwelt" be the perceived outer world, and the "Innenwelt" be the 
perceived inner world of thoughts, which would typically include thoughts about 
the world, or the "Umwelt", but removed from direct perception of that world, 
and also including any other thoughts? Would "Umwelt" or "Lebenswelt" mean the 
directly perceived world, in real time? Would "Innenwelt" mean the inner 
processing of any thoughts - an inner "imagined" world - which of necessity 
involves models of the outer world and relationships in it, and variations and 
created imagined entities based on it, and additional manipulations or ideas of 
that model, all entirely in thoughts? The direct perception, as you point out, 
is a form or part of one's mental model of the world. The thoughts about it 
become another level of mental models that we manipulate in our minds, including 
what we anticipate will happen and how we remember what we perceived in the 
past. I think there is a way in which the distinction between these (direct 
perception in real time and thoughts beyond that) is not entirely clear 
(i.e. one fades into the other), but it still is probably worth making.
> 
  Rather than saying "scientifically God does not exist ...", I'd
> rather 
  say that consideration of God is outside the realm of science.
I have 
  two quibbles about that discussion:
  1. If you ask people who 
  either believe in God or don't believe
     in God how they 
  define the word 'God', you won't find any two
     who give 
  exactly the same answer -- and usually the answers
     they 
  give are so wildly different that it's almost impossible
  
     to find much, if any similarity.  (If you think the 
  discussions
     about reality are confused, they are 
  crystal clear in comparison
     to whatever definitions 
  you'll find for the word 'God'.)
I don't see how this is a quibble; it's essentially what I was saying, I 
think. Perhaps I did not make my meaning adequately clear. Consideration of God 
is outside the realm of science partly because we can't easily agree on a clear 
definition of what "God" means - and agreement on the meaning of any subject of 
scientific inquiry is one of the steps required to seek agreement about the 
reality (existence) or nature of the subject of study.
  2. Given any definition whatever, I would hesitate to say 
  that it
     is impossible to find any scientific evidence 
  for or against
     the existence of anything matching such 
  a description.  And some
     definitions are so vague 
  (e.g., Einstein's) that it's almost
     impossible to deny 
  that whatever they might refer to exists.
I would agree with this. But people who have a different definition of what 
God is than Einstein's, or than any given definition, probably couldn't even get 
to the point of agreement about the meaning or importance of testing the 
existence of the entity defined by THAT definition, when theirs is more 
important and true to them (due to their belief). Therefore, the entire 
endeavor of considering tests or proofs or evidence of whichever one we 
consider, at least as anything with the label of "God", would seem to be outside 
the realm of science. See above comment about needing to agree on what we're 
testing. 
 
Another, more commonly cited reason it's outside the realm of science is 
that many definitions of God and stipulations of what would prove God's 
existence are not subject to the rational types of tests that scientific inquiry 
uses to seek agreement of the model with reality. That is, there is no 
conceivable test that could disprove the existence under that definition or 
model, so the existence is outside the realm of an endeavor designed to test the 
accuracy or truth of models of reality. This might be considered to be because 
of the all-encompassing nature of ideas of God, which makes them unable to be 
subject to tests within that all-encompassing field, which is what science 
does.
 
Someone who wants to deny the existence of God will either a) not accept a 
definition of God that makes it impossible to deny God's existence, or b) accept 
that a God with THAT definition exists, but not one with the deniable 
definition. Existence of God is still not directly a matter of scientific 
inquiry or proof, but rather is a matter of definition (however vague) and 
acceptance (belief).