Re: what are keys and surrogates?

From: Keith H Duggar <duggar_at_alum.mit.edu>
Date: Sun, 20 Jan 2008 09:18:03 -0800 (PST)

Jan Hidders wrote:
> Keith H Duggar wrote:
> > David BL wrote:
> > > Jan Hidders wrote:
> > > > Keith H Duggar wrote:
> > > > > Jan Hidders wrote:
> > > > > > David is making a valid and correct point.
>
> > > > > No he wasn't. Perhaps you forgot too quickly that his original
> > > > > point (which he repeated in various ways) was:
>
> > > > > "it [is] more precise to say that the
> > > > > graph of a function is a relation"
>
> > > > > not that there are different definitions of "function".
>
> > > > > > There are many possible valid definitions of the notion of
> > > > > > function, even within mathematics, and it is not always the
> > > > > > case that functions are identified with their graphs.
>
> > > > > The only one to thus far claim that functions are associated
> > > > > with their graphs was David! Let's draw a simplified picture
> > > > > of the formalisms discussed and the various combinations one
> > > > > might choose
>
> > > > > F1 = function is {(x,y)}
> > > > > F2 = function is (D,C,G={(x,y)})
> > > > > R1 = binary relation is {(x,y)}
> > > > > R2 = binary relation is (D1,D2,G={(x,y)})
>
> > > > > possible combinations
>
> > > > > (F1 R1) (F1 R2)
> > > > > (F2 R1) (F2 R2)
>
> > > > > You yourself have pointed out under both (F1 R1) and (F2 R2)
> > > > > "a function is a relation". Furthermore, you also claim your
> > > > > experience indicates mathematicians choose either (F1 R1) or
> > > > > (F2 R2) not (F1 R2) nor (F2 R1) ie the one David holds high.
>
> > > > > Finally, who can know what David meant by "more precise" but
> > > > > I would choose (F2 R2) as more precise than his pet (F2 R1).
>
> > > They are formalisms; all are valid.
>
> > > > > Based on the above (mostly your own claims here simplified),
> > > > > would you not agree that "a function is a relation" is both
> > > > > more common and more precise than "the graph of a function
> > > > > is a relation"?
>
> > > > Before I answer that let me first agree that your simplified picture
> > > > is correct. But as far as I understand him I don't think that David
> > > > actually disagrees with that picture.
>
> > > Agreed.
>
> > > > Do I think that the "a function is a relation" definition is both more
> > > > common? Yes, I do. Do I think that it is more precise? The statement
> > > > "the graph of a function is a relation" has the benefit of being true
> > > > for several definitions of the notion of function. As such it might be
> > > > preferable in the context of the c.d.t glossary where it is important
> > > > to make clear what the different definitions are. Of course it is not
> > > > really a definition but just the description of a certain property and
> > > > in that sense less precise. But also here, I doubt that David would
> > > > actually disagree with that.
>
> > > Agreed.
>
> > > I should have make the implicit assumptions in my original statement
> > > explicit, so it would be...
>
> > > "If we assume F2, R1 then it is more precise
> > > to say that the graph of a function is a relation".
>
> > Why not simply
>
> > "Or If we assume F2 and R1 then the
> > graph of a function is a relation." ?
>
> > Why would you still want to qualify it as "more precise"?
> > By doing so you would continue to maintain a precise-boy
> > facade ie one who claims their language is "more precise"
> > solely to demonstrate "knowledge" and "correct" others.
>
> So you actually agree with him, but you don't like the way he said it?

Perhaps you should read the origin of this sub-thread again. No, Jan, I do not agree with his /originating/ statement

"it [is] more precise to say that the
graph of a function is a relation".

I thought that should be crystal clear at this point so I am unable to understand your confusion on this point. It should also be clear that "more precise" is key to my disagreement. Furthermore, it should be obvious, based on his exact words, that David would still claim it to be "more precise" were he to make the claim today. And, no, "more precise" is not part of "the way he said it" it is material to his claim.

No, not even close. I think DBL sounded ignorant and foolish as one who has only a superficial grasp of the concepts they wrongly believe they have mastered. I would have thought you could have deduced that from the quote Mark Twain I included in my original reply.

You and David have both classified my posts as "aggressive" and now you classify me as "worked up". That fascinates me.

I would not have classified someone who responds at their leisure (up to two days) as "worked up". I would not have classified someone who responds to David elsewhere thusly

Keith H Duggar wrote:
> David BL wrote:
> > Keith H Duggar wrote:
> > > There was once another poster that trolled around always
> > > or that poster.
> > Depending on how one reads that, it could be seen as
> > implying Reinier is trolling. Was that your intention?
>
> No, that was not my intention. I should have been more
> precise.
>
> > IMO he is not.
>
> I agree. I do not believe rpost is trolling. Thanks
> for pointing out this ambiguous language.

as "aggressive". I would not classify succinct, clear, and logical arguments as aggressive. I would not even classify core-aimed psychological barbs such as "precise-boy" (that still makes me chuckle) as aggressive anymore than some of the previous barbs I've invented such as "wikipeducation". I would not classify someone playfully aligning paragraphs to certain fixed width columns as "worked up".

No. If anything I would have classified myself as cold and calculating and my posts re DBL as inexorable pursuance.

As I wrote above neither did I.

> Remember that it is very easy on usenet to read more into
> words than what was actually intended.

I agree. I believe you and David have read certain emotion into my posts and motivations into me that are absent.

KHD.F6 Received on Sun Jan 20 2008 - 18:18:03 CET

Original text of this message