I'm not sure that I Peirce would accept the functional notation as triadic, but
- as you say - he would prefer a a diagram/graph. Peirce draws a distinction
because the third is missing from the dyadic form. He describes this case in
several places, but most notably in a letter to Lady Welby in October 1904: (01)
"Analyze for instance the relation involved in 'A gives B to C'. Now what is
giving? It does not consist in A's putting B away from him and C's subsequently
taking B up. It is not necessary that any material transfer should take place.
It consists in A's making C the possessor according to Law. There must be some
kind of law before there can be any kind of giving — be it but the law of the
strongest. But now suppose that giving did consist merely in A's laying down
the B which C subsequently picks up. That would be a degenerate form of
Thirdness in which the thirdness is externally appended. In A's putting away B,
there is no thirdness. In C's taking B, there is no thirdness. But if you say
that these two acts constitute a single operation by virtue of the identity of
the B, you transcend the mere brute fact, you introduce a mental element. As to
my algebra of dyadic relations, Russell in his book which is superficial to
nauseating me, has some silly remarks, about my "relative addition", etc. which
are mere nonsense. He says, or Whitehead says, that the need of it seldom
occurs. The need for it never occurs if you bring in the same mode of
connection in another way. It is part of a system which does not bring in that
mode of connection in any other way. In that system, it is indispensable. But
let us leave Russell and Whitehead to work out their own salvation. The
criticism which I make on that algebra of dyadic relations, with which I am by
no means in love, though I think it is a pretty thing, is that the very triadic
relations which it does not recognize it does itself employ." (02)
Regards,
Steven (03)
On Mar 21, 2013, at 2:44 AM, sowa@xxxxxxxxxxx wrote: (04)
> Two points:
>
> 1. It is certainly true that you can map A gives B to C into a form that uses
>only dyadic relation.
>
> 2. But Peirce was trying to explain that you have simply converted one triad
>into a triad of a different form.
>
> I'll just use predicate calculus notation, since it's easy to type. But the
>point is obvious when you use a graph notation.
>
> With a triadic relation:
>
> gives(A,B,C)
>
> With three dyadic relations and a monadic relation give(x):
>
> (Ex) give(x) & agent(x,A) & theme(x,B) & recipient(x,C)
>
> In the first version, you have a triadic connection of A, B, and C to the
>relation named gives.
>
> In the second version, you have a triadic connection of A to agent to give, B
>to theme to give, and C to recipient to give.
>
> You still have a triad, but the central node is called give instead of gives.
>
> John
>
>
>
>
> (05)
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