[Inquiry] Re: Peaceful Easy Feelin

[Jon Awbrey]

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PEF.  Note 9

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JA = Jon Awbrey
JP = Jim Piat

Re: PEF 8.  http://stderr.org/pipermail/inquiry/2005-April/002598.html
In: PEF.    http://stderr.org/pipermail/inquiry/2005-April/thread.html#2578

In part:

JA: Without a more general appreciation of the consequences of
    irreducibly triadic relations, the specialized disciplines
    are doomed to spin their wheels in all the old dyadic ruts.

JP responds, er, cogitates:

JP: While myself not fully understanding the nature of
    a triadic relationship -- I am at least convinced
    that something is missing in the S-R model of
    representation and oh how I wish I could my
    finger on just what it is beyond simply
    repeating to myself a triad a triad.

JP: Maybe something like this -- we as interpreters of symbols
    are the third element that mediates between symbol and object.
    That is to say that symbol and object are joined by virtue of the
    fact that our actions reflect the relationship we attribute to them.
    Two things can only stand in a representative relationship with one
    another with respect to a third thing.  IOWs two things can not stand
    for one another (in the same sense that they can be greater or less
    than one another -- ie opposed to one another) unless a third object
    is introduced.  Representation is necessarily triadic.  Perhaps
    it's as simple as that.  It's simply a matter of defining what
    representation is.  It involves three things.

JP: But how does it come about that one thing can be understood
    or interpreted as standing for another to some interpretant?
    Granted this is an irreducibly triadic affair -- but what is
    the nature of each leg of this relationship.  Without reducing
    the triad to a dyad -- what is going on?   For example the
    interpretant is not standing for the object, nor the object 
    for the interpretant or representamen.  So it seems to me
    legitimate to examine each leg of this asymmetrical triad
    and explicate (in whatever language or symbols one wants)
    just how each leg functions -- what it means or how to
    represent its logical import.

Jim,

The first thing we have to understand is that some things are just
inherently properties of whole systems, or of things only insofar
as they participate in whole systems.  So far this is an insight
that is common to both Peirce and Saussure, in their own ways.
So non-trivial examples of sign relations necessarily involve
lots of 3-tuples of the form <o, s, i> -- or <s, o, i> if
one prefers.  Thus the properties of sign relations are
properties appropriate to sets, while the combinations
and discombobulations of sign relations are of the
types appropriate to sets.  This renders it very
chancey already to speak of the "legs" of any
sign relation that does not amount to one
single 3-tuple, or what Peirce called
an "elementary sign relation".

The nearest we can get to something 2-adic that is properly derived
from a 3-adic relation is to "project" the whole 3-adic relation on
two of its domains, what we would get by deleting a column from the
corresponding relational data table, and ignoring any duplicates of
the ordered pairs that result.

One of the reasons that I selected an alternate title for this thread,
aside from trying to avoid being tangled in a literature that promises
to remain quite confused about such a symbol thing as what a simple is,
much less the pure and symbol varieties, is to allude to a personal bit
of insight from my undergraduate days, hence the *dustiness of the tune,
to wit:  Sometimes you need to quit trying to figure out how things get
connected, and think about how they got disconnected in the first place.

Jon Awbrey

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