322 13 Inductive vs. Deductive Reasoning
ology are becoming too complex for informal descriptions of the context in
which reasoning is taking place. This is especially important for combining
inferences made in different contexts.13.1 Sources and Semantics of Uncertainty
There are many sources of uncertainty. Many measurements, for example,
are intrinsically uncertain. This is apparent with sensors for which accuracy
of the measurement seems to be mainly a question of how much effort one
wishes to expend on the measurement. However, even at the level of sub-
atomic particles, there are limits to what one can measure, as stated by the
Heisenberg uncertainty principle.
A more common source of uncertainty is the fact that a stochastic model
will not include all possible variables that can affect system behavior. There
is effectively no limit on how elaborate a model can be. However, mod-
els that have too many variables become unwieldy and computationally in-
tractable. The model designer must make choices concerning which vari-
ables will be the most relevant and useful. The remaining variables are then
ignored. The cost of ignorance is nondeterminism and what appear to be
measurement errors, but what are in fact the result of unmodeled variables.
Yet another source of uncertainty is subjectivity. Probabilities are some-
times used as a means of expressing subjective assessments such as judg-
ment, belief, trust, and so on. Some philosophers take the position that prob-
ability can only be applied to events according to their relative frequencies
of occurrence, and they reject the interpretation of probability as a degree of
belief. This point of view is calledfrequentism.Most researchers and philoso-
phers today accept that probabilities can be applied both to relative frequen-
cies of occurrence as well as to other degrees of belief. This interpretation of
probability is calledBayesian analysis.
Some of the major philosophical works (specifically, Spinoza’sEthics(Spin-
oza 1998), Leibniz’sMonadology(Leibniz 1998), and Wittgenstein’sTractatus
(Wittgenstein 1922)) propound some version of logical atomism. In other
words, they conceptualize the world using objects and their attributes, and
they propose relationships identified by words that link the the mental con-
cepts of objects and attributes to the corresponding physical objects. They
also specify how more complex objects can be constructed from more ele-
mentary objects. Unfortunately, this point of view ignores issues such as
observational uncertainty, belief, judgment, and trust, all of which affect our