Luke Palmer lrpalmer at gmail.com
Tue May 6 10:36:07 EDT 2008

```On Tue, May 6, 2008 at 4:53 AM, Achim Schneider <barsoap at web.de> wrote:
> PR Stanley <prstanley at ntlworld.com> wrote:
>
>  > Hi
>  > I don't know what it is that I'm not getting where mathematical
>  > induction is concerned. This is relevant to Haskell so I wonder if
>  > any of you gents could explain in unambiguous terms the concept
>  > please. The wikipedia article offers perhaps the least obfuscated
>  > definition I've found so far but I would still like more clarity.
>  > The idea is to move onto inductive proof in Haskell. First, however,
>  > I need to understand the general mathematical concept.
>  >
>  > Top marks for clarity and explanation of technical terms.
>  >        Thanks
>  > Paul
>  >
>  Induction -> from the small picture, extrapolate the big
>  Deduction -> from the big picture, extrapolate the small

Induction has two meanings in mathematics, and I don't believe this is

See Daniel Fischer's response for the type you are asking about, and
try not to be confused by the irrelevant discussion about inductive
logic.

Luke

>  Thus, in traditional logic, if you induce "all apples are red", simple
>  observation of a single non-red apple quickly reduces your result to
>  "at least one apple is not red on one side, all others may be red",
>  i.e, you can't deduce "all apples are red" with your samples anymore.
>
>  As used in mathematical induction, deductionaly sound:
>
>  1) Let "apple" be defined as being of continuous colour.
>  2) All "apples" are of the same colour
>  3) One observed "apple" is red
>  Ergo: All "apples" are red
>
>  Q.E.D.
>
>
>  The question that is left is what the heck an "apple" is, and how it
>  differs from these things you see at a supermarket. It could, from the
>  above proof, be a symbol for "red rubberband". The samples are defined
>  by the logic.
>
>  Proposition 2 should be of course inferable from looking at one single
>  apple, or you're going to look quite silly. It only works in
>  mathematics, where you can have exact, either complete or part-wise,
>  "copies" of something. If you can think of a real-world example where
>  this works, please speak up.
>
>  That's it. Aristotlean logic sucks.
>
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