Re: What Is Information That A Sign May Bear It? -- Discussion

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WIS Discussion.  Note 8

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FK = Frances Catherine Kelly

FK: You asked what is meant by my saying that "any group of signs
    that is identified (or teridentified?) as a relation must be
    a dyadic duality in structure with two poles".

FK: It is my understanding that if the information in a sign is
    reduced logically to only two parts as opposed to three parts,
    whether those two parts are the sign-object and the sign-vehicle,
    or the sign-vehicle and the sign-effect, then a relation has been
    identified and any relation must have only two parts that act as
    poles in the relation.  Any relation is thus dyadic in structure.

FK: The problem here is that any sign or sign-situation of semiosis
    must be 3-adic and trichotic.  In any event, if the dual relation
    of poles is merely identified, which every relation must be to be
    a relation, then a third entity has already been introduced into
    the relation by virtue of this identity.  My curiosity therefore
    is how a relation of raw syntaxic information can be made dyadic
    when it must be trichotic to be identified as a realtion at all.

FK: (Incidentally, the topic of "relations" recently debated
    by you and others on the Peirce List has been consulted
    by me in its archives for some added background.)

Frances,

What did I say to make you think that "the information in a sign
is reduced logically to only two parts as opposed to three parts"?

I cannot figure out what you are saying in the rest of the message,
but when you say that "Any relation is thus dyadic in structure",
that sounds most certainly wrong to me.  Can you explain that?

Peirce's definition of a sign, any one of them, defines a sign
as something that exists in a certain sort of 3-adic relation.
A 3-adic relation, regarded in extension, is a set of 3-tuples.
Thus, it is a subset of a 3-fold cartesian product X x Y x Z.
We must not confuse the relation L c X x Y x Z with any one
of its 3-tuples, nor must we confuse the "arity", "adicity",
or "valency" of the relation with the number of values in
its any one of its domains.  Very often in logic we have
to think about domains that have only 2 values, as with
the boolean domain B = {0, 1} = {false, true}, but that
is an entirely different issue from the arity of the
relations that we are considering.  For instance,
there are non-degenerate 3-adic relations that
are subsets of B x B x B.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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