2/3/2006 9:12 AM
Discussion
Communication
from John Sowa
Dick,
The equation in your diagram relates the probability of knowing every option to the probability of recognizing the situation correctly.
However, there is one more factor to be considered: the fact that any given situation can be perceived "correctly" in an open-ended number of ways (perhaps infinite) for any number of different purposes.
Every view or description of a view (in any notation, language, formalism, or picture) leaves out far more detail than it can possibly describe. And there is no way to know whether the details critical for a given purpose (i.e., problem about which some decision is to be made) have been captured by the description -- unless the purpose is recognized as an essential criterion for an adequate description.
Richard Ballard said:
Mathematics must become
probabilistic rather than truth conditional and it must become conservative and
cost aware to claim any relevance to
reality.
There is a mathematical theory of probability: it is called "theory of probability", of which there are many different variants. Every statement of probability is a metalevel statement about some other proposition P. It has the form
Probability(P)=x, where x is some number between 0 and 1.
If you want a probabilistic theory of probability, you can add another metalevel:
Probability(Probability(P))=y.
The point about cost awareness is the distinction between science and engineering. The standard definition is
Engineering is the application of science for the purpose of solving a given problem within the limits of available resources, which include budgets, deadlines, personnel, tools, material, etc.
Note the word "purpose". That is where the positivists failed. They ignored purpose -- not by accident, they were passionately dedicated to the idea that all discussion of purpose had to be eliminated. That was why their theories ended up as irrelevant to any application whatever.
John Sowa