Richard Wein wrote:
WRE>This does not mean that we actually believe it to be due to
WRE>chance, or that we consider the chance hypothesis sufficient
WRE>to the task. But like other forms of statistical inference,
WRE>chance gives us a null hypothesis to perhaps reject.
RW>But you can't just calculate the probability of an event "as
RW>if it were due to chance". You need to assume a chance
RW>hypothesis. For example, the probability of rolling a 6 with a
RW>die takes a different value if I assume the die is fair than
RW>if I assume the die is biased in a particular way.
In the case of testing a die for fairness, the relevant chance
hypothesis is that each possible outcome is equiprobable.
This is exactly how we do go about testing the fairness of
die, by detecting whether actual rolls of the die
significantly differ from our expectations of equiprobability.
IIRC, where Dembski does give examples of chance hypotheses in
TDI, they clearly are premised upon equiprobability of
outcomes.
I just noticed something that looks like an inconsistency in
terminology in TDI and Dembski's other essays.
[Quote]
For J to be constructible by means of logical connectives from
the same items of information out of which I is constructed is
what we mean by saying I <i>generates</i> J, or equivalently, J is
<i>generated</i> by I.
[End Quote - WA Dembski, TDI, p. 149]
In "Design as a theory of information" and in later discussion
of evolutionary computation, Dembski specifically denies the use
of "generated" or "generation" to cover the concept that a logical
transformation of prior information results in a different
arrangement of information afterwards.
Wesley
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