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The Epistemic Paradigm 93

EXAMPLE 4.2: A well-known situation of general knowledge processing is
unconditional simulation producing various field realizations on the basis
of its mean and covariance. While useful in the characterization of spatio-
temporal variability, unconditional simulation is of limited value for prediction
purposes.
The informativeness of Postulate 4.1 implies information maximization at
the prior stage, which is also conditioned to the available general knowledge Q.
This stage assumes an inverse relation between information and probability:
The more informative an assessment about a mapping situation is, the less
probable it is to occur. This expresses a standard epistemic rule, namely, the
more vague and general a theory is, the more alternatives it includes (it is,
hence, more probable) and the less informative it is. Conversely, the more
alternatives a theory excludes, the more informative (less probable) it is. From
a Popperian standpoint: "The more a theory forbids, the more it tells us." So,
while the statement "Que sera sera" ("what will be, will be") is an absolutely
safe prediction model, it provides no information at all. Let us pause and
discuss another example.

EXAMPLE 4.3: A weather forecast theory A predicts that tomorrow it will
either snow, or rain, or be cloudy (but not rain), or be sunny. Another theory
B predicts that tomorrow it will either rain or it will be cloudy (but not rain).
A is a very general theory that includes several possible alternatives. Hence,
while it has a high probability (Prob^) of turning out to be true, it is not
a particularly informative theory (for it is incapable of discriminating among
alternatives). Theory B, on the other hand, includes only two alternatives and,
thus, the probability of being true is Probs < Prob^. Since, however, it is
capable of reducing the alternatives to only two, theory B is more informative
than A.
An informative scientific theory, therefore, is a prohibition: it forbids certain
things to happen. In quantitative terms, the inverse relation between infor-
r
mation and probability can be expressed as lnfo ?[x map] = {P °bg[Xma P]} •
i.e., the information about the actual mapping situation provided by § is in-
versely proportional to the probability model constructed on the basis of Q.
Given that, for technical reasons, probabilities can be very small, it is often
more convenient to work with logarithms so that information is mathematically
defined by

According to the first epistemic ideal (informativeness) of Postulate 4.1, Equa-
tion 4.2 should be maximized—in a stochastic sense—subject to the available
general knowledge Q. (In fact, this epistemic ideal may be viewed as a stochas-
tic version of a general rule of scientific reasoning, often referred to as amplia-
tive reasoning: One should use all but no more knowledge than is available.)
The detailed mathematical analysis of this ideal is presented in Chapter 5.