Re: [PEIRCE-L] Peirce's 1870 “Logic Of Relativesâ€? • Comment 11. 12

[Sungchul Ji]

Jon:

I haven't kept up with your emails, but I do have one 'burning' question. 
You wrote:

"Since functions are special cases of dyadic relations . . "  (051614-1)

Can there be functions of the type,  y = f(x), that are special cases of
"triadic relations" in the Peircena sense ?  In other words can the
following mapping be considered triadic?

                  f
             x --------> y                                    (501614-2)

With all the best.

Sung
___________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701

www.conformon.net




> Post   : Peirce's 1870 “Logic Of Relatives” • Comment 11.12
> http://inquiryintoinquiry.com/2014/05/12/peirces-1870-logic-of-relatives-%e2%80%a2-comment-11-12/
> Posted : May 12, 2014 at 2:00 pm
> Author : Jon Awbrey
>
> Peircers,
>
> Since functions are special cases of dyadic relations and since the space
> of dyadic relations is
> closed under relational composition — that is, the composition of two
> dyadic relations is again a
> dyadic relation — we know that the relational composition of two
> functions has to be a dyadic
> relation.  If the relational composition of two functions is necessarily a
> function, too, then we
> would be justified in speaking of ''functional composition'' and also in
> saying that the space of
> functions is closed under this functional form of composition.
>
> Just for novelty’s sake, let's try to prove this for relations that are
> functional on correlates.
>
> The task is this — We are given a pair of dyadic relations:
>
> • P ⊆ X × Y  and  Q ⊆ Y × Z
>
> The dyadic relations P and Q are assumed to be functional on correlates, a
> premiss that we express
> as follows:
>
> • P : X ← Y  and  Q : Y ← Z
>
> We are charged with deciding whether the relational composition P ∘ Q
> ⊆ X × Z is also functional on
> correlates, in symbols, whether P ∘ Q : X ← Z.
>
> It always helps to begin by recalling the

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