Illustration 2: Collins Case
In People v
Collins
an elderly lady in Los Angeles was knocked down and
robbed.
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Bystanders said the assailants were a caucasian female with blond
hair tied in a ponytail and black male with a beard and moustache. They
escaped in a yellow motor car. The two defendants in the case fell within these
broad
descriptions. However, the victim
but could not conclusively identify
them as the assailants. In an attempt to prove their guilt, the prosecutor used a
mathematics professor to estimate
the probability that this couple could or
could not be the guilty party. At first instance both defendants were convicted.
On appeal, the conviction was overturned. The court criticised the way in
which probability had been used, because it failed to take into account the
probable dependencies between the characteristics, for example, bearded men
commonly sport moustaches. Other criticism by academics was that it was an
example of the prosecutor's fallacy.
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However, there has also been some
academic support for the decision.
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Common Errors
Two common errors with induction consist of hasty generalisation and biased
sample. These need to be explained. In practice both can be, and often will be,
avoided by repeated observations made in varieties of circumstances.
Hasty Generalisation
Hasty generalisation
is known by a variety of other labels -
fallacy of
insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact,
the law of small numbers,
hasty induction, and secundum quid.
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Hasty
generalisation constitutes the logical fallacy
of reaching an inductive
generalisation based on too little evidence. This error is capture in the proverb
formlated by Aristotle (384 BC - 322 BC) and cited in earlier discussion: “One
___________________
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People v Collins, 438 P2d 33 (Cal 1968)
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Finkelstein and Fairley (1970), Kreith (1976)
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Tribe (1971)
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The expression secundum quid is Latin for "according to something" It is an
abbreviation for the maxim in which it is used "a dicto simpliciter ad dictum
secundum quid". Litteraly this means “from a saying [taken too] simply to a saying
according to what [it really is]” that is, according to its truth as holding only under
special provisos. In plainer language, one simple observation becomes a
universal truth. This fallacy occurs when a general proposition is used as the
premise for an argument without conceding the restrictions and qualifications that
govern it; the point is that these restrictions and qualification potentially
invalidate the argument.
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