SUO: Re: Sign Relations
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Jean-Marc Orliaguet wrote:
>
> Jon, the series of determinations does not
> make the triad less of a genuine triad, for
> the simple reason that the triad is not built
> on those determinations only. So there is no
> problem in writing that:
>
> 1) (O, S, I) is a genuine triad
> 2) then consider the mutual relations: (O,S) (S,I) (O,I) taken individually.
> 3) consider (O), (S) and (I) individually
>
> as long as you don't forget 1)
>
> "... where you have a triplet you have three pairs;
> and where you have a pair you have two units." 1.530
>
> because you can see three pairs,
> does it mean that all of a sudden
> you cannot see the triplet?
>
> JM
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Jean-Marc,
Thank you for sharing this raindrop of wit,
but the stones hereabout are whetted a bit,
as you may grok that I say in all humidity.
Having drunk ourselves deep in determination,
well, some of us, at any rate, let us return
to an elevation, and a docket of cases which
may just raise our eyes above this sea level.
Right about now, I am guessing that it is probably incumbent on me
to try and justify why an extended treatment of sign relations has
any bearing on the work of a group that is dedicated to developing
a standard upper ontology. I have already somewhat randomly given
many of my reasons before but it appears about time for a reminder.
1. We have a general interest in the ontology of objects in the world.
2. Some of these objects in the world are actually complex activities.
3. We have a general interest in the ontology of mathematical objects.
4. Objects in the world can be modeled by way of mathematical objetcs.
5. Complex activities in the world demand complex mathematical models.
Where I personally come in is at this point.
I am interested in complex agents or systems,
complex enough to be reckoned "intelligent",
whatever the heck that is, but, at any rate,
able to learn from experience and to reason
in various kinds of logical fashion. Just
about the minimal orders of relations that
are useful in modeling agents or systems
of this ilk are 3-adic relations, like
mathematical groups and sign relations.
That is just the barest bones of wit --
and it makes no sense to settle for
anything barer than this minimum --
but it already involves far more
complexity than most onlookers,
outside of C.S. Peirce, have
been willing to contemplate,
for any length of time,
up to this very day.
| Note On Notation:
|
| Especially in the discussion of schematic examples,
| I will try to be consistent about using upper case
| letters for sets, as with O, S, I for the relevant
| object, sign, interpretant domains, respectively,
| and lower case letters for elements of these sets,
| as with o, s, i for any typical instances of them.
I have to break here,
Jon Awbrey
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| On the Definition of Logic (Version 1)
|
| 1. Logic will here be defined as 'formal semiotic'.
|
| 2. 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.
|
| 3. 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'.
|
| 4. It is from this definition, together with a definition
| of "formal", that I deduce mathematically the principles
| of logic.
|
| 5. 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 non-psychological
| conception of logic has 'virtually' been quite generally
| held, though not generally recognized. (CSP, NEM 4, 20-21).
|
|
| On the Definition of Logic (Version 2)
|
| 1. Logic is 'formal semiotic'.
|
| 3. A sign is something, 'A', which brings something, 'B',
| its 'interpretant' sign, determined or created by it, into
| the same sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in which itself
| stands to 'C'.
|
| 2. This definition no more involves any reference to human thought
| than does the definition of a line as the place within which
| a particle lies during a lapse of time.
|
| 4. It is from this definition that I deduce the principles of logic
| by mathematical reasoning, and by mathematical reasoning that,
| I aver, will support criticism of Weierstrassian severity,
| and that is perfectly evident. The word "formal" in the
| definition is also defined. (CSP, NEM 4, 54).
|
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.
|
| Available at the Arisbe website:
|
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm
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I probably ought to explain a few things about my own point of view here,
the stance that I normally take as I seek to apply this or any other body
of formal ideas to the mass of computational and empirical problems with
which I have been concerned. I speak as one who appreciates and values
a formal idea, first and foremost for its beauty, but who does not stop
there, in that first place, nor allow the Hallowed Idea to rest on its
laurels atop Mount Parnassus, but goes on to treat each and every idea
that comes along as a conceptual instrument and a potential resource for
this or that particular purpose that the season may bring to bear in mind.
In my own work I am chiefly interested in bringing
sign-theoretic and system-theoretic frameworks to
bear on the study of inquiry as a dynamic activity,
and so I approach the subjects of interest, namely,
"inquiry driven systems", by stepwise refinement,
starting with bare triadic relations, adding the
notions of constraint or structure that come with
Peirce's definition of a sign relation, next adding
notions of process, sequence, or transition in time,
and finally adding the idea that inquiry is a special
type of sign process that is directed toward certain
qualities or virtues of expression, like alacrity,
aptness, clarity, or utility, in the signs that
it catalyzes, develops, evolves, or facilitates.
This is the culmination of a lifelong work,
not all of it pursued in the full light of
consciousness about what it was that was
driving me, of course, but there it is.
If I have knocked off -- now there's a choice phrase! --
one or two of the finer points, more baroque devices,
or prettier filigrees of Peirce's original notion in
the process of bending it to my work, I believe that
I have sharpened and strengthened a not too entirely
inconsiderable number of its points, edges, surfaces
in the very process of doing this work. In any case,
I fancy that Peirce would appreciate the fact that I
have not left these instrumental ideas in their case.
I will now try to give you a summary accounting of the transformations
that I have seen wrought -- by, in, and on -- this very open framework
as I have personally turned it and tuned it to my own tasks and themes.
I need to record an outline here, just in case I forget my main points:
1. Correspondence and determination as near synonyms,
perhaps no more than rhetorical variants, or else
synchronic dimension and diachronic dimension of
the information-theoretic concept of constraint.
2. Degree of determination as a measurable quantity,
explicitly related to information in Peirce 1865.
3. Information transmission as constraint or correlation.
The old saw that "information transfer does not flow".
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