[Haskell-cafe] Re: Induction (help!)

[Achim Schneider]

"Luke Palmer" <lrpalmer at gmail.com> wrote:

> 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
> the type of induction the OP was asking about.
> 
> 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.
> 
I was referring to traditional logic in the aristotlean sense, I should
have been more explicit there. The key difference is really whether you
define (or proof) the big picture by the small picture, or try to make
deductions about some already-existant big thing by the small picture
you already have.

The method is the same, but the intent and awareness of the model
characteristic of your reasoning differ, thus leading to results that
are either valid or invalid.

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