One list I visit is perhaps the world's top list for discussing issues like fuzzy logic versus probability theory,
and how we can better understand UNCERTAINTY. A US researcher summarized a paper by Gupta, saying that
there are two general types of uncertainty, "objective" and "cognitive". (To see what he posted, go to the end.)
A researcher in Europe replied:
Dear Dr. ..,
Thanks for your clear description of the 'two broad categories' under which the 'various types of uncertainty' can be classified. However, I wonder how the two are related or can be unified. Aren't we running here into the perennial problem of the relationship between KNOWLEDGE and REALITY, a relationship on which philosophers in India, China, Japan and the West have had different views?
Here is my reply:
Many of us would see the situation as follows.
First, we would assume the existence of an Objective Reality, a larger universe or multiverse or cosmos,
whose state across state and time is determined by some kind of Underlying Physical Law. Let us call this the Objective Reality Hypothesis (ORH).
WITHIN the large set of possible Underlying Physical Laws, there is of course the traditional Einsteinian set -- laws defined over continuous
3+1-dimensional space time, expressed by stating a Lagrange function which leads to Lagrange-Euler equations, a subset of the larger set
of 3+1-dimensional partial differential equation (PDE) models.
BUT THE SET is certainly larger than that. There is no reason why it should not including stochastic PDE or mixed forwards-backwards stochastic PDE.
Any mathematically well-defined system is acceptable within ORH, so long as we can use it to make predictions.
To avoid being too pompous -- perhaps a kind of joke is in order.
One version of quantum mechanics has been stated as follows:
"First God created the universe by throwing dice many, many times, over a vast four-dimensional checkerboard. He looked out
upon his work... as you might look out upon a Christmas tree you just set up... and he said in a booming voice: 'Yuk! It is not good!'
So he gave it a good ninety degree kick and left the room never to be seen again."
Actually, many people believe that this is the closest thing we now have to a mathematically well-defined rigorous formulation of quantum field theory.
It is described in a classic book by Glimm and Jaffe. The first stage is, more precisely, simulation or implementation of a Markhov Random Field
over four-dimensional Euclidean space. The ninety degree "kick" is a Wick rotation, kicking one randomly chosen direction (original raw time)
into its analytic extension. It actually sounds like a kind of Realistic model ... if you believe that the Wick rotation has the right properties.
I tend to doubt it. What it does to certain ordinary Fourier modes...
If you go back further, to philosophers of the West like the Pythagorean Order (which I take with many grains of salt), they still support the claim that
everything we see is governed by some kind of natural law. There is a challenge in understanding what KIND of natural law. I have not seen anything in
Chinese philosophy which would contract that general sort of approach, though they would often feel in a pragmatic way that they need not be bothered with
the theory of things in general. Many in the West used to believe it can be a bit dangerous to play around too casually with things before understanding them, but
the current elections seem to reflect some other way of thinking...
In a way, this all gets back to Gupta's categorization, but tilted more towards the cognitive side. There may or may not be "uncertainties" inherent in the formulation of the
underlying Physical Law -- but within the ORH approach, these are really just options one has in trying to express what the Physical Law is.
After that... "uncertainty" is basically something we intelligent creatures experience. We experience it at "many levels," simply because our mind
works on many levels. In a sense, many of the "objective" uncertainties that Gupta talks about are essentially cognitive in nature; we use uncertainty as
an attribute of the approximate models we use to describe complex dynamical systems in the physical world. Approximation and probability are the two recurring themes here...
I tend to view "fuzziness as opposed to probability" as a hook to the approximation side of things.
Many years ago, I had a discussion about ORH with one of the leaders of one of the most powerful Sufi Orders in the world.
He basically asked: "Why do you Pythagorean types keep trying to understand how reality works in mathematical terms?
Why do you assume it is possible?"
The truly honest answer is that I do not Axiomatically commit myself at the most fundamental level to assuming that it is possible.
At the deepest level... you could say it is like what Heidegger says, or you could say I am like one of those little organisms I sketch in some slides...
simply trying to make sense of a stream of direct personal experience as best I can. That's the deepest foundation. But we have certainly learned,
over centuries and centuries, that ORH has yielded immense improvements in our ability to cope with that stream of experience, that it is very
general in what it allows (in a sense, able to encompass anything else workable as a subset), and that folks bouncing against the walls without it..
with the use of a "mirror" to connect the objective and subjective world ... do easily get lost in all kinds of crazy thrashing which goes nowhere.
Many modern philosophers say that the alternative to realism is solipsism, and the world still keeps giving us examples of people doing crazy stuff
through solipsistic thinking. We do not know the true Physical Law, and rationally should remain open-minded about a wide variety of possible theories...
(constantly updating subjective probabilities ala Raiffa for such alternatives)... but it is WAY too early to give up on understanding much
better than we now do.
But... he thrashed around a lot, went back to Pakistan after 9/11, and died. I am very sorry that I didn't work harder to improve the dialogue before it was too late.
Best of luck to us all,