Even when the "continuum" actually consists of a large number of small "steps", and is thus in reality "quantized" (as in the individual generations of a long evolutionary sequence), it's still a continuum in the long view.
Remember that there's an issue of scale here. What is "grainy" under a microscope may be extremely "smooth" when viewed as a whole.
Even my grayscale "continuum of gray" photo example actually used 256 discrete values of luminosity. But it still provides for "smooth" contours in the photo, and my points about it still stand.
So let's not get bogged down losing the forest for the trees (which is rather an apt metaphor here).
The point, in a nutshell, is that some processes, data, phenomena, etc. etc. manifest as "smooth" gradients on the "big picture" scale (whether or not they may be discrete under the "microscope" is beside the point), and to (mis)model them as just a few (or in the worst case, only two) discrete "states" which "jump" from one category to another is quite simply a fallacy in every sense of the word:
fal-la-cy (fal'uh see) n. pl. <-cies>
1. a deceptive, misleading, or false notion,
belief, etc.; misconception.
2. a misleading or unsound argument.
3. deceptive, misleading, or false nature;
erroneousness.
4. any of various types of erroneous
reasoning that render arguments
logically unsound.
And your example of fossils being "quanta" of evolution is irrelevant to that. Yes, evolution is "quantized" into generations, and yes, life is "quantized" into individuals. There's no fallacy in that, nor does that contradict the fact that evolution proceeds by "smooth" transitions when viewed across hundreds of generations or more, and makes a continuum of living forms.
[In short: Is the "either alive or dead" paradigm missing the boat by breaking up the reality into too few too-broad categories?]
We were investigating abiogenesis!
Yes. Exactly.
The grey-scaling would have been the domain of the investigation.
If by that you mean that you were examining the nature of the transition between completely "nonliving" and "life as we know it today", *and* were aware that the transitions in between would likely be a "gray area" of things which were "not fully nonliving but not fully living as we now know it", then fine -- but is that actually the case? Because your next statement gives me cause for concern:
We had a solid, elegant mathematical definition of life v. non-life/death [Shannon]. The "fallacy" was raised as an objection to that definition.
And rightly so, if your "solid, elegant mathematical definition of life" gave a "binary" result -- i.e., "if it meets this definition it is 'living', if it doesn't then it is 'non-living'"... That would be quantizing the range of possibilities of "life" into living/nonliving, yes/no, black/white.
If you were trying to devise a "yes/no" test for "life", then you were indeed "quantizing" what may well be a "continuum", without first establishing that it *is* a binary condition (is/isn't) as opposed to a continuum ("degrees of life").
In a darkness to light example, all the grey-scales in the world will not cancel the definition of "black" and "white".
I never said that they would. The point, however, is that a "is this white or not" test would be grossly misleading, because a "no" result would imply "black" to the person applying the test, even though a "very almost white but just not *quite*" level of gray would also qualify as "not white" -- even though most people would consider it more "white" than "not-white".
In short, recognizing black and white should not become a mental trap against seeing the gray.
Further, the grey scales should not be an objection to investigating how a scene got from "black" to "white" when they are in fact, the whole point of such an investigation.
Correct, but that wasn't Tortoise's concern. He was concerned that a binary "living or not" test would be unable to distinguish the details of such a transition, and would instead engender a mindset (or worse, may be the result of a mindset) which doesn't recognize the gray parts.
I tend to agree -- even today, apart from abiogenesis, I think it's a big mistake to try to define "life" in a way that draws any kind of sharp line between "living" and "nonliving". I think the reality is more complex than that, there is no such clean dividing line.
You have proposed some "Shannon information" test, but I haven't seen the details (if you could point me to a post which lays it all out, I'd appreciate it). But that approach in general seems doomed to failure to me, since many things we definitely do not consider alive *also* exchange Shannon information (computers, simple natural objects such as crystals, etc.), plus many things we consider alive often exchange no Shannon information whatsoever for long periods of time (e.g. quiescent anthrax spores).
To answer your last question first because it requires no discussion, here are primary links where you can read up on information theory and molecular biology and Shannon's mathematical theory of communications:
Returning to the "quantizing the continuum" discussion....
In order to know we had a successful theory we needed a starting point and an ending point - what is non-life and what is life. The theory itself would address all the grey scales in between.
That is where the fallacy of quantizing the continuum killed the investigation - and, as far as I'm concerned, all such investigations. Thus I now consider all theories of abiogenesis trash - there can be no such theory if science refuses to accept a clear definition of life, non-life and death.
The corrolary is this: to whatever extent the correspondents apply the fallacy to abiogenesis, it must also be applied to all other theory including evolution. And as you know the entire theory of evolution is a construct of a continuum of life based on a quantization of another continuum, the geologic record.
It is a poison pill - not to Intelligent Design but to Evolution theory as well as abiogenesis, where it is most obvious.