Richard Wein wrote:
> From: Ivar Ylvisaker <ylvisaki@erols.com>
>
> >Second, Dembski specifically disavows that this is what he means by a
> >design inference. He writes a little later in the reference cited
> >above:
> >
> >"Thus, we shall never see a design hypothesis D pitted against a
> >chance hypothesis H so that E confirms D better than H just in case
> >P(D|E) is greater than P(H|E). This may constitute a "Bayesian
> >design inference," but it is not the design inference stemming from
> >the Explanatory Filter."
>
> >He seems to waver a bit about this conviction in his "Intelligent
> >Design" though the book still contains a description of the filter.
> >See "abduction" in the index.
>
> I haven't got "Intelligent Design". Perhaps you could quote me the relevant
> passage, if it's not too long.
"Abduction" and an "inference to the best explanation" are similar
concepts. Finding a relevant passage using the latter term is easier.
On page 274 of Intelligent Design, Dembski quotes Sober ("Philosophy
of Biology," page 33):
[Start Sober's quote; Dembski added the material in []]
"[Paley's] argument involves comparing two different arguments -- the
first about a watch, the second about living things. We can represent
the statements involved in the watch argument as follows:
A: The watch is intricate and well suited to the task of timekeeping.
W1: The watch is the product of intelligent design.
W2: The watch is the product of random physical processes.
"Paley claims that P(A|W1) >> P(A|W2) [i.e., the probability of A
given that W1 is the case is much bigger than the probability of A
given that W2 is the case]. He then says that the same pattern of
analysis applies to the following triplet of statements:
B: Living things are intricate and well-suited to the task of
surviving and reproducing.
L1: Living things are the product of intelligent design.
L2: Living things are the product of random physical processes.
"Paley argues that if you agree with him about the watch, you also
should agree that P(B|L1) >> P(B|L2). Although the subject matters of
the two arguments are different, their logic is the same. Both are
inferences to the best explanation in which the Likelihood Principle
[a statistical principle which says that for a set of competing
hypotheses, the hypothesis that confers maximum probability on the
data is the best explanation] is used to determine which hypothesis
is better supported by the observations."
[End Sober quote]
[Ivar: In mathematics, a vertical bar "|" is equivalent to the words
"given or given that," e.g., P(B|L1) means the probability of B
given that L1. The notation ">>" means "much greater than."]
Dembski continues on the next page:
"Inference to the best explanation is inherently competitive (cf.
section 7.4). Best explanations are not best across all times and
circumstances. Rather they are best relative to the hypotheses
currently available and the background information we have to
evaluate those hypotheses. Sober therefore has to leave the door open
to design even though he doesn't think it very likely that design
will ever pose a serious threat to Darwinism. He concedes, "Perhaps
one day, [design] will be formulated in such a way that the auxiliary
assumptions it adopts are independently supported. My claim is that
no [design theorist] has succeeded in doing this yet." [snip ref.]
The burden of this book has been to show that design remains a live
issue and can once again be formulated as the best explanation for
the origin and development of life."
The thesis of Dembski's "The Design Inference" (TDI) is not an
inference to the best explanation. In Sober's notation, TDI asserts
that if one can show that P(L2) is essentially zero, then P(L1) must
be very nearly one. An inference to the best explanation asserts
that design is a better explanation than random processes if
P(B|L1) >> P(B|L2).
Using the same notation, here is Bayes's rule:
P(L1|B) = ( P(B|L1)P(L1) ) / ( P(B|L1)P(L1) + P(B|L2)P(L2) )
where P(L1) and P(L2) are the probabilities of L1 and L2 before using
the observation B. Bayes's rule is mathematically correct. However,
Bayes's rule remains controversial because of the problems of
assigning values to P(L1) and P(L2).
It is the value on the left side of Bayes's rule that people really
care about. However, if P(L1) is about equal to P(L2), then
P(B|L1) >> P(B|L2) leads to the same conclusion, i.e., the inference
to the best explanation points to the same answer.
Note that if Dembski can show that P(L2) is essentially zero, then
Bayes's rule says that P(L1|B) is essentially one, i.e., intelligent
design is true.
On the other hand, if assigning a persuasive value to P(L2) proves
difficult, then the inference to the best explanation is a plausible
fallback position. Nevertheless, it is a different and much less
ambitious argument.
Ivar
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