Back in the early 90s, when I went back to grad school
in Systems Engineering, partly in order to concentrate
on the study of intelligent systems as dynamic systems,
my advisor asked me to come up with a simple, concrete,
but nontrivial example of a sign relation, maybe even
a relatively small finite case, if that could be found
without falling into complete triviality. (01)
The ensuing exercise in Keep It Concrete And Simple (KICAS)
resulted in the following Sign Relation Primer, which some
of you have seen, but some have not  at any rate, I just
finished TeXifying it, so maybe it's worth another look in
light of our practical aims. (02)
http://mywikibiz.com/Sign_Relation_Primer_:_1
http://mywikibiz.com/Sign_Relation_Primer_:_2
http://mywikibiz.com/Sign_Relation_Primer_:_3 (03)
Jon Awbrey (04)
cc: Arisbe, Inquiry, OntoLog (05)
Jon Awbrey wrote:
> I think it might be a good idea to start a thread
> on what sign relations are good for in practice.
>
> The type of practical situation I have in mind can be described
> as follows. We find ourselves faced with a circumscribed domain
> of phenomena that interest or puzzle us, and we seek explanations
> of their more surprising aspects. So far, that's just the setting
> of science in general. If the phenomena have anything to do with
> the way we use signs to capture and convey information about any
> number of object domains, then it's likely the signtheoretic
> toolbox will come in handy.
>
> So let's go back to the basic setup that we noted already.
> I gave the following synopsis of concepts and terminology:
>
>  A ''sign relation'' is a set of elementary sign relations,
>  each of which is an ordered triple of the form (o, s, i).
>  In each triple, o is the "object", s is the "sign", and
>  i is the "interpretant sign", or "interpretant" for short.
>  Another way of saying this is that a sign relation L is
>  a subset of the cartesian product O x S x I of three sets,
>  called the "object domain" O, the "sign domain" S, and the
>  "interpretant (sign) domain" I.
> 
>  That is the basic structure of a sign relation,
>  to which may be added many other dimensions of
>  interest, for instance, determination in time
>  or relative clarity of signs and interpretants.
> 
>  As far as an "interpreter", "interpretive agent",
>  or "process of interpretation" is relevant to the
>  theory of sign relations, it may be identified with
>  the whole of some particular sign relation.
> 
>  Cf. http://planetmath.org/encyclopedia/SignRelation.html
>
> What makes any old triadic relation a sign relation
> is the fact of its satisfying a definition thereof,
> and Sean Barker has already cited one of the best,
> which is useful to quote again in fuller context:
>
>  Logic will here be defined as ''formal semiotic''.
>  A definition of a sign will be given which no more
>  refers to human thought than does the definition of
>  a line as the place which a particle occupies, part
>  by part, during a lapse of time. Namely, a sign is
>  something, ''A'', which brings something, ''B'', its
>  ''interpretant'' sign determined or created by it,
>  into the same sort of correspondence with something,
>  ''C'', its ''object'', as that in which itself stands
>  to ''C''. It is from this definition, together with a
>  definition of "formal", that I deduce mathematically
>  the principles of logic. I also make a historical
>  review of all the definitions and conceptions of logic,
>  and show, not merely that my definition is no novelty,
>  but that my nonpsychological conception of logic has
>  ''virtually'' been quite generally held, though not
>  generally recognized. (C.S. Peirce, NEM 4, 2021).
> 
>  http://www.cspeirce.com/menu/library/bycsp/l75/l75.htm
>
> Et sic deinceps ...
>
> Jon Awbrey
>
> CC: Arisbe, Inquiry (06)
 (07)
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