Re: The horse race

"Marshall Spight" <marshall.spight_at_gmail.com> wrote:

>Mark Johnson wrote:

>> But the issue is whether even theoretically, can a relation be termed
>> an ordered relation when it supposedly is defined as being unordered,
>> by definition?

>The answer is: it can't. By definition.

Exactly. By definition. Defined away.

That's what I suspected. If the building looks like it's about to go up - what fire . . wait, what building?

>> At what point does any type of sort create an ordered relation?

>When you put the relation together with the "sort" or what
>is normally called the ordering relation, you have what is
>called an ordered relation.

Well, I can understand how one would say that some ordinal attribute really is not ordering anything, but simply acts as some sort of weighting attribute. But I think at some point that becomes difficult to say. At what threshold does the weight have to be termed, a sort?

>> which makes it look more
>> like a wordplay or semantics, by the common sense of the term.

>Math is not about common sense.

But the use terms ought to be. That's the subject, not "Math".

>> I wonder if the confusion isn't over this idea of transcendence or
>> immanence and internal machine representation.

>Honestly

Because as I wrote:

>> In such confusion it
>> might lead some to insist that there is no such thing as intrinsic
>> order, when in fact what is being manipulated by a database, which is
>> really what this is all about, might become useless chaos if its
>> intrinsic order remains unaccounted.

>Sets don't have intrinsic order.

Not even a hierarchy, necessarily. Just a sorted list, nothing more. Fail to account, throw out that information, and what you have may become useless, mathematically or otherwise. The batting order? Intrinsically, the 4 spot does not hit before the 3, unless the order is changed and approved by the officials - yes? Perhaps for other purposes that set may be unordered. But there is an intrinsic order to that set. The roster of Presidents, etc. State test score rankings.

If I give you page one, with story A in column left and story B beginning over in column right, with A paragraph one following the headlines and all falling below the banner, and A paragraph three following two and preceding four, one might say the set of all paragraphs is an unordered set. But there is an intrinsic order. Received on Wed Feb 22 2006 - 20:28:17 CET