Whether the common response to the Linda example is a fallacy or not
depends on the "normative theory" that is used as the standard of
"correct thinking".
The traditional probabilistic interpretation is purely "extensional",
in the sense that the degree of belief for "L is a C" is interpreted
as the probability for element L to fall into set C. Under this
interpretation, a larger C should correspond to a higher degree of
belief, and the normal human response is wrong.
However, if "L is a C" is interpreted "intensionally", then the degree
of belief should be determined by comparing the common PROPERTIES of L
and that of a typical C, which will usually give a higher degree of
belief to a smaller reference class C, such as "feminist bank teller".
Under this interpretation, the typical human response to the question
is correct.
The existing "heuristics and biases" research suffers from the problem
of taking one "normative theory", such as probability theory or
first-order predicate logic, as a theory that should ALWAYS be
followed, and seeing any deviation as "fallacy".
Detailed analysis:
*. on probability-related "fallacy" (such as in the work of Tversky
and Kahneman) : http://www.cogsci.indiana.edu/pub/wang.heuristic.ps
*. on logic-related "fallacy" (such as in the work of Wason) :
http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/wang.evidence.pdf
I hope my works and Mike's comment at least show that there are other
possible interpretations of the so called "human errors" --- actually
NARS behaves like a typical human in these situations, and these
behaviors are fully justifiable, as soon as the system's assumptions
differ from those of probability theory and first-order predicate
logic.
Pei
On 6/8/06, Mike Ross <[EMAIL PROTECTED]> wrote:
> Example: Linda is 31, outspoken, and very bright. She majored in
> philosophy in college. As a student, she was deeply concerned with
> discrimination and other social issues, and she participated in
> antinuclear demonstrations. Which statement is more likely to be
> true?
>
> a. Linda is a bank teller
> b. Linda is a bank teller and active in the feminist movement.
Just a nitpicky observation (which is actually totally irrelevant to
Ben's interesting point about proposition independence)
I think its actually correct to say that (b) is more likely than (a).
Humans dont get this "wrong" because they are bad at reasoning. They
get this "wrong" because of the ambiguities of natural language.
Unlike mathematical language, human speech has many statements which
are implied. I think its fair to say that in most conversational
contexts, when (b) is stated, it creates an implied second clause to
option (a):
a. Linda is a bank teller and NOT active in the feminist movement.
In this case, it is correct to say that (b) is more likely than (a).
When annoyingly logical people insist that this is wrong, they are
actually stating that the implied second argument is:
a. Linda is a bank teller and EITHER active OR not active in the
feminist movement.
This may be true on logic tests, but it aint the case in the real
world. Just something to keep in mind when talking about human
reasoning...
Mike
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