Terminology quibble (was: Real value ...)

Subject: Terminology quibble (was: Real value ...)
From: Sandy Harris <sandy -at- storm -dot- ca>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Fri, 10 Nov 2000 17:26:19 -0500

Bruce Byfield wrote:

> From where I sit (in the middle, with old eggs being thrown at me
> from either side), both these positions seem to use a reductio ad
> absurdum argument. In other words, both Dan and Andrew are taking
> their arguments to ridiculous extremes.

That's not what "reductio ad absurdum" means.
It actually means a specific method of proof.

Assume that what you want to prove is false.
Using the assumption, prove a contradiction or absurdity.
Since the result is obviously wrong, one of the premises must be.
Therefore your assumption is false.
Therefore what you wanted to prove is true.

For example, to prove no even number except two is prime.

Assume such a number exists.
Since it is even, it is by definition divisible by two.
Since it is prime, it is by definition divisible only by itself and one.
Since it is not two by our assumption, this is a contradiction.
Hence no number satisfying our assumption exists.

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