I asked you previously if it had anything new to offer compared to prior ID offerings (Dembski, Behe, even Axe's previously published works). I've read a lot of ID literature in the past and I'm not going to go out and get a book if it doesn't offer anything new and interesting.
What does it offer that prior books on ID haven't?
A development of how functional coherence (which is not mentioned in other books) as a formal concept confirms the design inference.
That's too vague a definition to be useful. What does he mean by "hierarchal arrangement"?
This is the beauty of Axes work: that the words in it are arranged in a manner as to convey the normal dictionary meaning of them, in English, to an English speaker. By doing so he makes his work accesible to the average reader who wishes to discover what he thinks on the topic that he is writing.
hierachical: of the nature of a hierarchy; arranged in order of rank.
arrangement: the action, process, or result of arranging or being arranged.
A hierachical arrangement would be an arrangement of something in a hierachical manner, having hierachical ranks.
The hierachical arrangement of a system would be a system in which parts are arranged in ranks of function so as to form the system.
Example of an hierarchical arrangement: Rank 1 (Compounds) - Rank 2 (Amino Acids) - Rank 3 (Amino Acid String) - Rank 4 (Functional protein).
How is the hierarchy determined?
According to rank of function. i.e. Compounds must first be arranged correctly in order to for amino acids to form and function in a manner for Rank 3 to be possible. Rank 1 must be correctly arranged in order to allow Rank 2 to function correctly.
What is a "high-level" function?
A function that a system carries out as a result of the coherent manner in which the hierachical arrangement permits. i.e. The pixels (Rank 1) arranged into letters (Rank 2) - words (Rank 3) - sentences (Rank 4) - paragraphs (Rank 5) in a coherent manner form the hig-level function of conveying meaning to the observer. The low level function of pixels is to form letters, but this in itself does not form the high level function, which is observed at the 5th rank.
For that matter, what is a "function" in this context? How is that defined and/or determined?
Function is the natural action of a system so arranged.
In the case of biology purpose of function is evident in that sub-systems of high level functional coherence necessarily form a part of an even more functionally coherent system that carries out such high level functions as communicating to other systems using language.
What counts as contribution and/or coordination?
Being a neccessary part of a system, without which the system does not function.
What I'm asking for is a methodological approach to actually using such a definition in a proper, reasonably objective manner.
1) Is there a methodology by which one can take an arbitrary object and apply this definition objectively?
Yes
IOW, could multiple people independently apply the methodology to the same object and get the same results?
Yes
2) Can this then be applied to biological organisms or components thereof in the same fashion?
Yes
3) Since I'm assuming this is an attempt to argue that such systems are un-evolvable, this means such an application needs to be a demonstrable barrier to evolution.
That functionally coherent sytems do not appear by a series of random mutations selected for fitness through the natural environment is perhaps a valid claim.
The test would be to make some parts available, in an environment and watch to see what happens.
The problem with science, admittedly is that the intelligence cannot be observed through the lense of MN even if it did deign to repeat it's creative action. So any results thus obtained would be subject to myopia and interpreted falsely.
However the competence of naturally occuring, intelligence free laws and forces to produce observed effects is freely observable, and given the time frame that has been available thus far, and the effects that have been produced in that time frame, the competence can be expected to be readily observable in a very short time frame.
Thousands upon thousands of new and functionally coherent systems should evolve from our experimental parts on a daily basis.
However many ways there may be of being alive, it is certain that there are vastly more ways of being dead, or rather not alive. You may throw cells together at random, over and over again for a billion years, and not once will you get a conglomeration that flies or swims or burrows or runs, or does anything, even badly, that could remotely be construed as working to keep itself alive. Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design (New York: Penguin, 1988),
This is where Behe's irreducible complexity has traditionally failed as it turns out it is not synonymous with un-evolvable.
When just so stories are regarded as synonimous with evidence then I guess we could "prove" anything, including that irreducibly complex systems can arise by NS.
Behe wrote a whole book showing the demonstrable competence of ND to produce evolution in 3 organisms over many millions of generations in the real world.