Re: [ontolog-forum] Intensional relation

[Juan de Nadie <juandenavas@xxxxxxxxx>]

Hi John. Thanks for the answer. Your e-mail have a lot of interesting information.

Considering the integer 2 as the cardinality of the set {true, false}, was another way in that I thought about this question. But, I have some troubles with this view, because was not clear for me that "the set of all n-ary (extensional) relations on D" was defined in terms of truth values. I'm confused about which are the elements of this set. The function "ρ^n" maps to sets of truth values? I don't understand wht this means.

Thanks.

Best regards.

2013/1/3 John F Sowa <sowa@xxxxxxxxxxx>

On 1/2/2013 10:50 PM, Juan de Nadie wrote:
> "/An intensional relation (or conceptual relation)//ρ^n of arity n on
> <D,W> is a total function //ρ^n : W →_2 D^n  from the set W into the set
> of all n-ary (extensional) relations on D/"
>
> I don't understand the /_2 D^n /, mainly this base 2. Why 2? I think

> that I don't understand very well the mathematical structures underlying

> this notion.

That is not your fault.  It is an example of the *worst* kind of
mathematical jargon that is used only in journals that nobody reads.

They are called "Journals of Tenure and Promotion", and their only
purpose is provide a place for academics who want to become professors
to get their "frequent flyer miles" that enable them to be upgraded.

When I was an undergraduate math major at MIT, one of the professors
told us the secret rules about how to write about mathematics:

  1. Beginning students learn calculus from very informal, non-rigorous
     textbooks that ignore all the details of the formalization.

  2. By their junior year, math majors learn how to state and prove
     theorems in an excruciatingly formal style that goes through
     every detail of every step that a computer must process.

  3. But by their graduate years, mathematicians have mastered all the
     details.  They know how each of the informal steps expands into
     a long string of formal steps.

  4. Therefore, graduate-level mathematicians are allowed to use the
     same style of talking and writing that they learned as freshmen.

  5. But people who are not professional mathematicians have never
     learned points #3 and #4.  The ones who know some mathematics are
     still at the junior level, where they feel that they must write
     in the very formal way in order to be accepted for the journals
     of tenure and promotion.

Now, to return to your question:

> I don't understand the /_2 D^n /, mainly this base 2. Why 2?

The integer 2 is the cardinality of the set {true, false}.

Whenever you have a function f from a set D to a set R, the function f
belongs to a set whose cardinality is the cardinality of the set R
raised to the power of the cardinality of the set D.

That fact is probably irrelevant to subject matter of the article
and anything you hope to learn by reading it.

Recommendations:

  1. If you are a reviewer of an article that uses such jargon, tell
     the editor that the paper should not be accepted until the author
     rewrites that jargon in a readable style.

  2. If you are a reader of an article that contains such jargon, have
     pity on the author as a struggling academic who is hoping to be
     promoted.

  3. If you are the author who wrote that, please write in the style
     that you preferred to read before you learned to write that way.

John Sowa


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