Ian,
I would certainly defend the intellectual necessity of reductionism, even to the point of describing it as a reflection of natural processes, as evidenced by some of the colloquial terms applied to it, such as distill, condense, focus, etc. As one might distill out the salient points of interest, or condense an argument to its irreducible points.
I would argue that statistics and other forms of generalization are a form of reductionism. One is simply distilling out the relationships within a larger set, rather than focusing on all the details involved. Your distinction between statistics and probability proves the point, since statistics is the set of the known, as distinct from possible consequences. A fully wholistic view would not be able to make that distinction and that is the problem with true wholism. It entails all connections and relationships, without the conceptual necessity of defining/focused sets. Much as a camera shutter left open would collect far more information, but lack clarity.
The intellect evolved out of the biological necessity of navigation by mobile organisms. Its fundamental function is to make decisions, even when the situation isn't clear. It is digital in an analog reality.
This requires reductionism of information, whether to specific details, or to generalizations. The left, linear hemisphere is better at details, while the right, instinctive side is better at generalizations. It might appear wholistic, because it deals in masses of information, but the purpose is to reduce that mass down to such binary concepts as good/bad, left/right, up/down, yes/no, 5 to 3 odds, etc.
I would also comment that the distinction you make between statistics and probabilities goes to one of the main topics usually discussed at FQXi and physics conversation in general and that would be the issue of time. Statistics only applies to what is known, ie. the past. While probabilities apply to how they might be applied, ie. predicting the future. Now consider the difference between how we acquire statistics from probabilities, vs, how we apply statistics to better understand probabilities. We acquire statistics by observing events as they happen, ie, what was future probability becomes past statistic. Now we go the other direction when we apply statistics to probabilities, we use the past to predict the future.
In my essay, the problem I point out in physics is that we only think of time in terms of how the past is used to define the future, ie. going cause and effect. Yet the physical reality is of the future becoming past. In other words, we treat time as a narrative process from past events to future ones, but the physical process is one of dynamic change that collapses probabilities into actualities. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. So rather than going from a determined(statistical) past into a probabilistic future and ending up with multiworlds, it is the collapse of probability which yields actuality. A large part of the confusion is that cause and effect isn't sequence, but energy exchange. Yesterday doesn't cause today, any more than one rung on a ladder causes the next. It is the exchange of energy, such as sunlight shining on a rotating planet, that causes the sequence of events called 'days.'
The problem is that physics goes from measurement to description and then to predictive application, without fully considering what is being measured. The same issue created the problem of epicycles and a geocentric cosmology. By measuring the action of the various heavenly bodies, ancient cosmologists developed an accurate description of their actions, such that it had predictive powers as to where those bodies might be in the future. This then created the impression that the model and its physical explanation, giant cosmic gearwheels, was true. Any anomalies were simply considered to be due to undiscovered gears and the search would be to figure out where they would be. What was overlooked was simply that the earth is also a body in motion and when Galileo placed it on orbit around the sun, everything else made more sense. Now we treat time as a series of events, because that is the foundation of our intellect, from narration to cause and effect, just as the earth is our physical foundation. But it is the process creating those events which is foundational, yet physics is more focused on the details of ever more precise measurements of events, not stepping back to see the broad picture of what causes them. So motion is ascribed to the present along the timeline, rather than the events through the present.
The present isn't some dimensionless point on a timeline, because duration doesn't exist external to the present, but is the state of the present between measured events.
One field of study that further clarifies this distinction between the determined past and the probabilistic future is Complexity theory, with order as the known and chaos as the random. Which is another example of the relationship between statistics and probability.
Regards, JM
