Re: Distinct linear orderings on Z

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 03/24/05 

Date: Thu, 24 Mar 2005 23:01:43 +0100

Tony Orlow (aeo6) <aeo6@cornell.edu> writes:

> 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.

I said soundness of a rule of inference and that's what I meant.

It is essentially the same as valid argument, but in modern logic,
"rule of inference" is the far commoner expression than the much
vaguer "argument". Also, "validity" typically applies to formulas
rather than rules, which are called "sound".

But some terminology depends on the author.

> A false conclusion can be logically derived either using a faulty
> derivation (invalid argument) or faulty (unsound) premises.

Yes, duh. Except I still do not care for this term "sound premises".

Premises are formulas. Formulas are either true or false. Soundness
adds nothing useful to the discussion.

I may have seen the terminology a long time ago --- maybe in Copi.
But it's still useless and I'm happy I don't see it more often.

> You have a contradiction in your premise when you tie the number
> system in knots, and this leads to unsound conclusions.

There is no contradiction, unless you can prove a statement of the
form A & ~A. Either give the proof of a real contradiction, or drop
the logical terminology that you don't understand.

You may not find cardinality an appropriate sense of size (oh dear!).
But the fact is that cardinality in ZFC cannot create contradictions
in the theory. It is a defined term. 

-- 
"Sorry, wakeup to the real world.  You're on your own dependent on me
as your guide. Luckily for you, I'm self-correcting to a large extent,
so if the proof were wrong, I'd tell you.  It's not wrong."
  --- James Harris confirms that his proof is correct.

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