A very nice point, cornelis, re the constraints of logical constructs. It is, nonetheless, a stimulating exercise going on here and a pleasure to watch good minds work.
For myself, I cannot escape the belief, really a conclusion, that all of the Universe, all of reality, is a product of design and that we are exploring its modes, means and mechanics. "How?" is a fascinating question. "Why?" is more fascinating.
I agree. Diamond and general_re are very able.
Herein lies the difficulty of answering the ice cyrstal problem.
As one of my conditions stipulated, the criterion proposed by Dembski is not useful for determining that something is NOT designed. It is useful, however, for detecting design.
Thus, my answer to the ice crystal picture is this:
Putting aside the context of anthropic principle for purposes of this answer, the object in question lacks the contingency and possibly the independently given pattern necessary to positively infer design. While inorganic crystalline strucures do indeed have a certain level of complexity, they do not meet the standard of contingency required by the criterion, since the formation of ice crystals is reducible to the operation of physical/chemical laws of chemical bonding, temperature, and so on. There might be a specification pattern inherent in the six-pointed star but since the crystal is the result of physical necessity it is not neccessary to ascertain whether or not what looks like a six-pointed star constitutes an independently given pattern in this case.
So, Regis, putting aside anthropic parameters, without which ice cystrals would not be possible, the ice crystal does not exhibit the level of specified complexity that would render a secure design inference. Yes, Regis, that's my final answer to #2. If you feel my answer is not satisfactory for some reason related to the conditions of the test please let me know and I will try to be more specific.
Cordially,