>1. What is wrong with circular reasoning.
>In a deterministic logic model, where propositions are either true or false,
>circular reasoning can lead to flip/flops in the truth of a proposition,
>each time through the cycle, the proposition changes from true to false or
>false to true. The model is inconsistent and consequently, anything can be
>proven.
First off, circular reasoning does not cause some kind of oscillation as
you have suggested. If I assume A as a premise and conclude A, I have
used circular reasoning, but I have not caused any of the difficulties
you have described. [Perhaps you were concerned about maintaining
consistency when you assume A to prove A when ~A is already known.
However, assuming A when ~A is known is a false premise, which is a
different problem.]
The problem with circular reasoning is that it does nothing other than
restate the assumptions of the reasoner. A purely deductive argument
is, in some sense, circular since the conclusion is within the deductive
closure of the the reasoner's premises. If you accept the premises,
then the criticism of circularity is, in some sense, a matter of taste.
I'm quite surprised by the number of emails I have recieved that seem to
be interpreting my comments to be suggesting that there is some
unacceptable circularity in Bayesian reasoning. The difficulty is not
with Bayesian reasoning. The difficulty is with failure to acknowledge
the modeling assumptions that one has made.
If you are interested only in defending the validity of the inference
tools you are using, then this matter may be of little consequencde to
you. However if you are interested in actually applying these tools to
make claims such as, "The tooth fairy does (not) exist," (and hopefully,
things much more interesting than this) then things are more
complicated.
If you and I disagree about the tooth fairly we would, hopefully,
examine the modeling assumptions that we have made and if we are unable
to converge, we might be able to trace the disagreement to certain
modeling assumtpions that neither of us are able to justify and we might
simply agree to disagree until we can find a better justification for
our modeling assumptions.
Some people seem to think that this is the *only* way things can turn
out. The problem is that people are often very reluctant to admit the
modeling assumptions that they have made. In the tooth fairy example,
one might be tempted to claim that the original model assumed only that
the existence of tooth fairy would predispose people to wonder about the
tooth fairy (more so than they would otherwise wonder) and then argue,
upon the arrival of data showing wondering, that the tooth fairy is more
likely to exist. What's wrong with this? The model does not mention
other causes of wondering and, thus, implicitly encodes that *any* cause
of wondering must be the tooth fairy.
We have a situation where the tooth fairy believer is claiming an
inference from a property of the a hypothetical tooth fairy + data to
the an increased posterior on the tooth fairy. However, when we add in
the implicit modeling assumptions, we see that it is really an inference
from the assumption that the tooth fairy is the only cause of a
phenomenon + data to the existence of the tooth fairy. While the first
version purports to be making scientific evaluation about the existence
of the tooth fairy, the second demonstrates that the modeler has simply
codified his prejudices in the model and is making a rather
uninteresting claim that is primarily about his own prejudices.
Now, I suppose we can argue about whether this deception on the part of
the tooth fairy believer is circular reasoning in a strict sense. It
seems pretty clear to me that the claim, "The thing that I have defined
to be the only cause of X is more likely to exist because I have
observed X." is at best a vacuous statement. I prefer to think of this
as circular since the decision to add a parentless non-evidence node to
a bayes net corresonding to the existence of an object is a purely
ontological decision. However, if some people would prefer to use the
word vacuous, this is fine with me. In any case, it would seem that the
tooth fairy believer is either being deceptive about his assumptions, or
has assumed so much that his conclusions are vacuous and not
scientifically interesting.
BTW, I'm taking break from these arguments until Tuesday, so I won't
have anything further to say until the long weekend is over.
--
Ron Parr email: [EMAIL PROTECTED]
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Home Page: http://robotics.stanford.edu/~parr
