Re: Distinct linear orderings on Z

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/24/05 

Date: Thu, 24 Mar 2005 16:31:41 -0500

Jesse F. Hughes said:
> Tony Orlow (aeo6) <aeo6@cornell.edu> writes:
>
> > Jesse F. Hughes said:
> >> Tony Orlow (aeo6) <aeo6@cornell.edu> writes:
> >>
> >> > I dunno about that definition.... Soundness is in the success of the
> >> > application of results, the way I see it.
> >>
> >> That is not the technical definition of soundness.
> >>
> >> But feel free to insist that you've got it right and all the logicians
> >> are all wet. It would be par for the course.
> >>
> >>
> > tell me where I'm wrong, and when you see my point finally, speak up
> > then too.
>
> You're wrong in saying "soundness is in the success of the application
> of results", as if that has any particular meaning.
>
> A rule of inference P / Q is sound if it cannot be the case that P is
> true unless Q is true. Nothing so vague as "success in the
> application of results."
I believe you are referring to a valid argument. A false conclusion can be
logically derived either using a faulty derivation (invalid argument) or faulty
(unsound) premises. You have a contradiction in your premise when you tie the
number system in knots, and this leads to unsound conclusions.
>
> (Kolker was discussing "soundness of a system of postulates", which
> has no particular meaning to me, but Kolker often makes no particular
> sense to me.)
>
>
> 

-- 
Smiles,
Tony

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