>Exactly what is wrong with this argument?
The argument started only with the assumption that if the tooth fairy
existed, she would predispose people to ask questions about the tooth
fairy, i.e. their tendency to do so would be greater than the baseline
tendency. From this, and the fact that one has asked the question, we
deduce that it is more likely that the tooth fairy exists. Now think
about what you have said:
>It is a perfectly coherent set
>of beliefs (which I do not happen to share) that might plausibly be held by
>someone who places credence in the existence of the tooth fairy, and
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The whole exercise only makes sense if you start off believing in the
tooth fairy. However, the form of the argument does not require a
belief in the tooth fairy; it only requires the conditional about what a
hypothetical tooth fairy might do.
>Let F be the hypothesis that the tooth fairy exists, and W be the
>hypothesis that I wonder about her existence. What is wrong with my
>constructing the Bayes net F-->W and assigning probabilities? That's a
>perfectly fine model for me if it represents my beliefs about the tooth
>fairy.
>
>To avoid double-counting, I have to assign prior probabilities for
>existence and non-existence that do not already incorporate the evidence
>that I am wondering, which may be difficult psychologically. That I'm even
>entertaining the hypothesis and assessing a prior means I'm already
>wondering. But one could imagine asking oneself, "What would my prior
>probability be in the existence of some being I have never wondered about?"
The model does not consider other causes for the wondering. If you
construct the model knowing that you wonder, then you are constructing
the model in such way that it can do nothing other than support the
conclusion that the tooth fairy exists. This is circular. If you
construct the model before you experience an instance of wondering
(assuming that it makes sense to do this since the act of constructing
the model could be considered an act of wondering), then you are saying
that there exists a single cause of wondering and that this cause could
only be the tooth fairy. While initially appearing agnostic about the
tooth fairy, it's quite circular in regard to what the ultimate cause of
any wondering might be.
The general lesson from this is that you can't simply toss some
variables into a Bayes net without thinking about what they mean. The
variables you have chosen (as well as the ones you have not chosen) make
certain assumptions about the world. All of these assumptions
necessarily can't be modeled within the net you have constructed.
>>This is clearly bogus since I can use
>>this line of reasoning to justify anything.
>
>No! I can't justify the above argument to myself not because it's a bogus
>line of reasoning, but because I don't believe the F-->W link, and also
>because I place a miniscule prior on F being true.
Reasoning from a property of a hypothetical entity to the existence of
the entity while deluding yourself that you have not begged the question
somewhere along the way is clearly bogus.
The prior on F doesn't matter since the question here is the direction
of change in the posterior given the evidence.
>If those are your beliefs, then you have a justification for them. I
>disagree strongly with the hypothetical individual whose model we are
>discussing here, but she has the right to have her model without my calling
>it bogus and pretending there is some mathematical reason why she's not
>allowed to believe in it.
If you ignore the assumptions you made in constructing the model when
drawing a conclusion from the model, you are doing something bogus. This
is especially true of the conclusion you have drawn pertains directly to
the assumptions you have made. One has the right to *say* whatever one
wants, but circular, bogus reasoning can and should be denounced by
clear-thinking people.
> If her models are all this strange, I suspect
>her ideas will not percolate very far into the collective consciousness,
>and some shyster might be able to figure out how to make a lot of money
>from her, but let her have her ideas. (Gregory Bateson called the "New
>Age" belief system the essential element of diversity that may prevent the
>Western scientific worldview from ossifying into rigidity and
>self-destructing. We may need tooth fairy believers to keep us honest.)
Diversity and incorrect, sloppy thinking are two very different things.
We should encourage people to propose different ways of viewing things.
However, we must sharply discourage them from self-delusion about the
assumptions they are making.
>Patrick Glynn uses just this argument for the existence of God in his book
>"God: The Evidence," but his Bayes net (he doesn't write it as a Bayes
>net; he uses those "word arguments" you so dislike) has G instead of F as
Please don't confuse me with David Wolpert or Kevin Van Horn. I never
complained about the "word argument" issue.
>>The hypothesis, along with
>>the other assumptions I have made form a vicious circle.
>
>Not true. I've just argued from prior to posterior. Nothing circular.
>Our tooth fairy believer's Bayes net is a perfectly good deductive
>argument, and she may apply it to the world if she so chooses.
Nobody is afforded the luxury of hiding behind claims that they are just
reasoning with a model when the model is clearly constructed in such a
way that it begs the question.
--
Ron Parr email: [EMAIL PROTECTED]
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Home Page: http://robotics.stanford.edu/~parr
