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Observation by a Witness
When assessing the probability that facts alleged by a witness are true courts
explicitly, or as is more often the case, implicitly, use what the author
describes as the two Evidentiary Theorems. 
Evidentiary Theorem 1
Theorem 1 is that a witness is telling the truth, that is, the full truth and the
totally accurate truth, when three conditions are satisfied:
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Condition 1: The witness has fully observed the facts.
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Condition 2: The witness has accurately remembered the facts.
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Condition 3: The witness has truthfully recounted the facts. 
Evidentiary Theorem 2
Theorem 2 is derived from Theorem 1. Theorem 2 asserts that the probability
that a witness is telling the truth is the probability that all three conditions of
truth are satisfied. This means that Theorem 2 yields a highly useful
consequence. A court can assess the probability that evidence is true by
considering the factors that affect or determine how fully each condition is
satisfied. These factors fall within the field of cognitive science. Cognitive
science, however, is not fully explored. So, in the absence of hard science
courts need to rely on common observation and common sense. While these
may often incorporate good reason, this will not always be the case. This is
one reason that injustices can occur in making findings of fact.
Inference
Inference takes two forms. One is determining facts by references to patterns
of behaviour, which involve inductive reasoning. The other is determining facts
by causation, which involve deductive reasoning.
Patterns of Behaviour
Many things happen according to recognised patterns of behaviour. To
explain this in abstract form, assume that three facts need to be proved as part
of a case. Two facts, Fact X and Fact Z are easily proved. Assume that the
middle fact is uncertain. Assume also that a common way for things to happen
is that when Fact X occurs, Fact Y then occurs after which Fact Z also
occurs. This supports a case for proving Fact Y by inference. There is some
decent likelihood that the missing fact is Fact Y. How likely this is depends on
various factors. One is the frequency probability for Fact Y when Facts X and
Z occur. The other depends on the existence of circumstances or reasons or
explanations for Fact Y not occurring when Facts X and Y occur.
Patterns of behaviour can be deployed in two ways. First, they are deployed in
establishing a fact for which there is no direct or observational evidence. 
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