Inquiry Into Inquiry

Re: Peirce List • Kirsti Määttänen

One of the chief advantages of Peirce’s systems of logical graphs, entitative and existential, is the way they escape the bounds of 1‑dimensional syntax and thus make it clear that many constraints of order imposed by the ordinary lines of linguistic text are not of the essence for logic but purely rhetorical accidents.  That does, of course, leave open the question of what constraints imposed by the 2‑dimensional medium of Peirce’s logical graphs might also be inessential to logic.

As far as visualizations of sign relations go, without worrying about their use as a calculus, there is the above 3‑dimensional example from a paper Susan Awbrey and I presented at conference in 1999 and revised for publication in 2001.

Resources

• Logical Graphs • Introduction
• Logical Graphs • Formal Development
• Logical Graphs • With Animated Proofs

References

• Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
• Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
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Re: Peirce List • Gary Fuhrman

Peirce’s existential graphs are a general calculus for expressing the same subject matter as his logic of relative terms and thus they serve to represent the structures of many‑place relations.  Cast at that level of generality, there is nothing to prevent existential graphs from being used to express the special cases of relative terms needed for a theory of triadic sign relations, for example, terms like “s stands to i for o” or “__ stands to __ for __” or any number of other forms, depending on the style one prefers.  It may give us pause that we have to use sign relations in order to mention sign relations but the fact is we do that all the time whether we are using Peirce’s semiotics or not.  Peirce’s pragmatic analysis of the process simply provides a clearer account than most other approaches do.

References

• Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
• Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
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Re: Peirce List • Jon Awbrey • John Collier

JA:

Questions about the meaning of the “central hub” in the “three‑spoked” picture of an elementary sign relation have often come up.  The central “spot”, as Peirce called it in his logical graphs, is located on a different logical plane, since it is really a place‑holder for the whole sign relation or possibly for the individual triple.  Normally I would have labeled it with a letter to indicate the whole sign relation, say or else the individual triple, say

JC:

I strongly agree, Jon.  Reading meaning into artefacts of the representation is not typically transparent.  I would say that the whole symbol represents the sign with its threefold character and that the node is not some separate signifier.  To put it on this level is, as you suggest, a category error.

Precisely.  And “artefact” is a very choice word here, with all the right connotations.  It would be unfortunate if this trivial “triskelion” figure became a caltrop to our thought, blocking the way of inquiry.

Aside from the ellipses we added to call attention to a couple of derivative dyadic relations, somewhat loosely called denotative and connotative in our paper, it is merely typical of the 3‑spoke figures in common use when I was first learning Peirce’s theory of signs, often arising to point out the differences between Saussure’s dyadic semiology and Peirce’s triadic semiotics.

The intervening decades have taught me all the ways diagrams and figures of that sort can be misinterpreted when the conventions of interpretation needed to understand them are not up and running.  It can be instructive to carry out post mortems on the various maps of misreading but if one is not up for the morbidity of that, it is probably wiser to move on to more viable representations.

References

• Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
• Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
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Re: FB | Systems Sciences • Esteban Trev

ET:

What is the difference between sign and symbol?

In Peirce’s usage, “sign” is the generic term, covering all species or types of signs.  Signs are “symbolic” to the extent they mean what they do solely by virtue of being interpreted to do so.  In Peirce’s fully triadic semiotics all signs are symbolic to some degree, even when they have the additional properties required to qualify them as “icons”, “indices”, or more specialized types.

Resources

• Semeiotic • Inquiry Blog • OEIS Wiki
• Survey of Semiotics, Semiosis, Sign Relations

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Re: Peirce List • Jerry Chandler

An elementary sign relation is an ordered triple   It is called elementary because it is one element of a sign relation where is a set of objects, is a set of signs, and is a set of interpretant signs that are collectively called the domains of the relation.

But what is the significance of that ordering?

In any presentation of subject matter we have to distinguish the natural order of things from the order of consideration or presentation in which things are taken up on a given occasion.

The natural order of things comes to light through the discovery of invariants over a variety of presentations and representations.  That type of order tends to take a considerable effort to reveal.

The order of consideration or presentation is often more arbitrary, making some aspects of the subject matter more salient than others depending on the paradigm or perspective one has chosen.

In the case of sign relations, the order in which we take up the domains or the components of a triple is wholly arbitrary so long as we maintain the same order throughout the course of discussion.

References

• Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
• Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
cc: FB | Semeiotics • Mathstodon • Laws of Form • Academia.edu

Re: Peirce List • Mike Bergman • Valentine Daniel

For its pertinence to the present discussion, here again is what Peirce wrote about the mathematical way of using individual or particular cases to make general hypotheses or suppositions:

• Mathematical Demonstration and the Doctrine of Individuals • 1

And just so we don’t forget that Peirce’s theory of individuals is not the run-of-the-mill absolute kind but makes the quality of individuality relative to the context of discussion — or the frame of reference as they say in physics — here is what he wrote about that:

• Mathematical Demonstration and the Doctrine of Individuals • 2

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