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in changing grain size? If we start with a large-grained structure and resolve
it, will our computational complexity burdens be reduced?
3 Defining Causality
Coming to a precise description of what is meant by causality and causal rea-
soning is di
cult. There are multiple and sometimes conflicting definitions.
Zadeh [34] suggested that a precise, formal definition might not be possible.
Pearl [21] replied: “For me, the adequacy of a definition lies not in abstract ar-
gumentation but in whether the definition leads to useful ways of solving con-
crete problems.” Regardless of arguments regarding the specificity of causality,
people have a commonsense belief that there are causal relationships. Satis-
factorily and explicitly specifying them is di
cult, as is the description of the
associated impreciseness.
Friedman [3] argues that any cause that we isolate is never the whole cause
and that every direct cause itself has its own direct causes, so that networks of
causation spread synchronically across the economy and diachronically back
into the mists of time. If this is true, granules must necessarily be imprecise
as separation trough truncation from a network would be required.
Granger [6] defined causality depends on one-way, time ordered concep-
tion of causality. In contrast, Simon [27, 28] provides an analysis of causality
that does not rely on time order. Some believe [7, p 1] that causal relations
are mostly indicated by asymmetric relationships. An abbreviated list of the
relationships that Hausman's [7] elements of causal relationships is:
•
Time-order:
Effects do not come before causes - This corresponds with
commonsense understanding. Unfortunately, it is at variance with Ein-
steinium space-time. This raises the question: If there is a commitment to
commonsense reasoning, what should be done when commonsense reason-
ing differs from scientific understanding?
•
Probabilistic Independence
•
Agency
or
manipulability:
Causes can be used to manipulate their effects,
but effects cannot be used to manipulate their causes. Effects of a common
cause cannot be used to manipulate one another.
•
Counterfactual dependence:
Effects counterfactually depend on their
causes, while causes do not counterfactually depend on their effects
•
Overdetermination:
Effects over determine their causes, while causes rarely
overdetermine their effects
•
Invariance:
Dependent variables in an equation are effects of the indepen-
dent variables
•
Screening-off:
Causes screen off their effects
•
Robustness:
The relationship between cause and effect is invariant with
respect to the frequency of the cause
