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From: robison@eosp1.UUCP (Tobias D. Robison)
Newsgroups: net.ai
Subject: Re: Now and Then
Message-ID: <1106@eosp1.UUCP>
Date: Tue, 11-Sep-84 12:27:15 EDT
Article-I.D.: eosp1.1106
Posted: Tue Sep 11 12:27:15 1984
Date-Received: Fri, 14-Sep-84 20:59:36 EDT
Organization: Exxon Office Systems, Princeton, NJ
Lines: 42

References:

Mark Chilenskas discussion of inductive proof is not correct for
mathematics, and greatly understates the strength of
mathematical inductive proofs.  These work as follows:

Given a hypothesis;

- Prove that it is true for at least one case.
- Then prove that IF IT IS TRUE FOR A GENERIC CASE,
  IT MUST BE TRUE FOR THE NEXT GENERIC CASE.

Fore example, in a hypothesis about an expression with regard
to all natural numbers, we might show that it is true if "n=1".
We then show that IF it is true for "n", it is true for "n+1".

By induction we have shown that the hypothesis is absolutely true
for every natural number.  Since true: n=1 => true for n=2,
				 true: n=2 => true for n=3, etc.

It is the responsibility of the prover to prove that induction
through all generic cases is proper; when it is not, additional
specific cases must be proved, or induction may not apply at all.

Such an inductive proof is absolutely true for the logical system it
is defined in, and just as correct as any deductive proof.
When our perception of the natural laws change, etc., the proof
remains true, but its usefulness may become nil if we perceive
that no system in the real world could possibly correspond to the proof.

In non-mathematical systems, it is possible that both deductive
and inductive proofs will be seriously flawed, and I doubt one
can try to prefer "approximate proofs" of one type over the other.
If a system is not well-enough defined to permit accurate logical
reasoning, then the chances are that an ingenious person can
prove anything (see net.flame and net.religion for examples, also
the congressional record).

	- Toby Robison (not Robinson!)
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