fritz@hpfclk.UUCP (fritz) (09/09/84)
/***** hpfclk:net.ai / sri-arpa!Laws@SRI-AI.ARPA / 10:14 am Sep 13, 1984*/
From: Ken Laws <Laws@SRI-AI.ARPA>
As an example of improper induction, consider the heap problem.
A "heap" of one speck (e.g., of flour) is definitely a small heap.
If you add one speck to a small heap, you still have a small heap.
Therefore all heaps are small heaps.
-- Ken Laws
/* ---------- */
That's a little like saying, "The girl next to me is blonde. The
girl next to her is blonde. Therefore all girls are blonde." (Or,
"3 is a prime, 5 is a prime; therefore all odd numbers are prime.")
An observation of 2 (or 3, or 20, or N) samples does *not* an inductive
proof make. In order to have an inductive proof, you must show that
the observation can be extended to ALL cases.
Mathematician's proof that all odd numbers are prime:
"3 is a prime, 5 is a prime, 7 is a prime; therefore, by INDUCTION,
all odd numbers are prime."
Physicist's proof:
"3 is a prime, 5 is a prime, 7 is a prime,... uhh, experimental error ...
11 is a prime, 13 is a prime, ...."
Electrical Engineer's proof:
"3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime..."
Computer Scientist's proof:
"3 is a prime, 5 is a prime, 7 is a prime,
7 is a prime,
7 is a prime,
7 is a prime,
7 is a prime, ..."
Gary Fritz
Hewlett Packard Co
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