Mauro > By "incommensurable" I mean the "residual" that's always present in every calculation, measurement, modeling or simulation of a physical process.
Okay - I am with you there. What you seem to be describing is the difference between true randomness and a stochastic process - which itself is a loaded term (and Wiki totally blew it, IMHO in defining 'stochastic'). In my estimation a stochastic process is NEVER a totally random process, due to what you are calling a "residual" - and insofar as "random" is the true counterpart to a deterministic process. Instead, a stochastic process means there is usually indeterminacy in its precise outcome or future evolutionary state, but probability distributions will indicate in hindsight that some outcomes can be influenced by an unknown input, possibly non-physical or inter-dimensional... unlike a random process where there is nothing but chance, and no favored distribution curve. There is a thin line there. Actually not that thin, but ... if there is something valid in nature such as what may be called the "meme" of Rupert Sheldrake, or a self-perpetuating "information field"; and personally I am certain that there is such an abstraction - then it can explain things in evolution that seem "non-random" but not precisely predictable either... ... like "convergent evolution" for instance ... which describes the acquisition of the same biological trait in totally unrelated lineages (the sabre-tooth marsupial "tiger" and other marsupials being strikingly identical to mammalian, except for a couple of radical hidden differences, and 20 million years of elapsed time where true randomness was NOT evident in hindsight). In terms of "free will" this means that when the initial condition (or starting point) is known, even if there is an infinite range of possibilities where a process of change (evolutionary process) might proceed, some paths are far more probable (in retrospect) and other paths are far less probable (randomness be damned). And this can be due to a "residual" influence going beyond so-called "survival of the fittest". This influence may in many cases also be called an "information field" ... especially if one's aesthetics and other sensibilities are of a certain slant. ... and even if - it should be added, such a rationalization permits the theist enough room to scientifically justify I.D. to some large degree ! They are after all, most likely correct - if they are moderate in the scope of claims and dispense with "revealed" dogma stuff. All of which brings us full-circle in the ongoing Galileo (or Darwin) vs. the establishment struggle of "wills". Jones
