Higher Order Sign Relations

[Jon Awbrey]

Cf: Higher Order Sign Relations : 2
At: http://inquiryintoinquiry.com/2019/12/04/higher-order-sign-relations-%e2%80%a2-2/

Re: FB | Charles S. Peirce Society ( https://www.facebook.com/groups/peircesociety/ )
Re: John Corcoran ( https://www.facebook.com/groups/peircesociety/permalink/1768975423238442/ )

Questions about use and mention came up recently on Facebook. In pragmatic semiotics the trade-off between
signs-of-objects and signs-as-objects opens up the wider space of "higher order sign relations". Here is how I
introduced the subject in an earlier writing:

When interpreters reflect on their own use of signs they require an appropriate technical language in which to pursue
those reflections. For this they need signs referring to sign relations, signs referring to elements and components of
sign relations, and signs referring to properties and classes of sign relations. The orders of signs developing as
reflection evolves can be placed under the description of "higher order signs" and the extended sign relations involving
them can be referred to as "higher order sign relations".

* Continue Reading at "Higher Order Sign Relations"
( https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/
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[joseph simpson]

Jon:

This is a very interesting insight:

"The subject matters of relations, types, and functions enjoy a form of recursive involvement with one another that makes it difficult to know where to get on and where to get off the circle of explanation. As I currently understand their relationship, it can be approached in the following order:

Relations have types.

Types are functions.

Functions are relations.

In this setting, a type is a function from the places of a relation, that is, from the index set of its components, to a collection of sets that are called the domains of the relation."

We have also tied in the definition of a system as:

"A system is a relationship associated with a collection of objects."

or 

"A system is a relation mapped over a set of objects."

The connection between and among the concepts of function, relation, type and system are very powerful and interesting.

We further expand the application of system by making a distinction between a natural language "relationship" and a mathematical "relation."  

The mapping of a natural language relationship to a mathematical relation has many useful and valuable attributes in the assessment of generic design processes and generic ontology structures.

I will review our work in this area when I get time and post a more detailed statement.

Bottom line, this is a key, fundamental area of integration.

Take care, be good to yourself and have fun,

Joe

 

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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

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[joseph simpson]

Len:

Are you able to provide a reference or references to your tool?

Is the software tool available for use now?

Is your software tool open source?

Can you provide a bit more information about your specific tool?

I believe we have addressed some of these issues in the past, but we may now be in a better position to make more progress.

Take care and have fun,

Joe

On Mon, Dec 9, 2019 at 9:55 AM Lenard Troncale <lrtro...@cpp.edu> wrote:

Joe, and others,

Usually I am a silent member of this group. But I keep the records perhaps for later study. And I widely advertise and recommend the work of this hard working group with many delicious products.

However, this particular comment hooked me so I enter the fray. In the Systems Processes Theory (SP3T) we have Linkage Propositions developed from the sciences that are not the logical map relations (complete from logic; seemingly all possible relations)  that you are developing for an extension of Warfield Systems Thinking tools, but rather experimentally determined and evidenced influences between systems mechanisms (as isomorphies) found in natural systems. We have encountered the exact same problem I think you cite here. Often the same “edge” between isomorphies as nodes in the systems network can have several simultaneous meanings. “A partial cause of” is also an influence. So is a “a partial result of.” How does one distinguish these from simple feedbacks?  Also there may be taxonomic or subsumption relations simultaneously between the same two isomorphies. Should they be expressed multiply and redundantly as separate relations or clustered into one?

If you guys solve this for your application or tool, you will probably solve it for mine. Please let me know. We are all working on the same general system model so to speak.

Len Troncale

Dr. Len Troncale
Professor Emeritus and Past Chair
Dept. of Biological Sciences,
Founding Director Emeritus, Inst. for Advanced Systems Studies,

College of Science
Currently Lecturer, Masters in Systems Engineering

IME Dept., College of Engineering,
California State Polytechnic University
3801 W. Temple Ave.
Pomona, California 91768
Claremont Office:

General Systems Research, Development, and Consulting (GSRDC)

232 Harrison, Suite B: 909-541-5095

Cell: 909-374-6115
Email: lrtro...@cpp.edu

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[joseph simpson]

Ken:

You said:

"Furthermore, there are several dimensions in the location of the “system of interest” within the contexts. As this locus changes within those metric spaces, the dynamics involved are useful and informative.  In other words, the structure one is modeling is not static, but dynamic."

This is an excellent advertisement for the General System Cube, which has a range of methods and techniques to address any system.  Each specific facet of a system may be mapped onto or into the General System Cube, which provides an interface between formal and informal methods and languages.

Take care and have fun,

Joe

On Mon, Dec 9, 2019 at 4:23 PM <kall...@gmail.com> wrote:

All,

 

Words represent a category of concepts whose structures, therefore meanings, differ in different contexts. The combinatorics of concepts and contexts boggle the mind (at the level of lint). The problem may be assuming that the relations are isomorphies – and particularly binary isomorphisms. At best, they represent homomorphisms, but even that is not assured. By focusing on one isomorphism, which may not hold true, you often miss other, perhaps more correct, morphisms whose workings provide interesting information as to their development of meaning.

 

Furthermore, there are several dimensions in the location of the “system of interest” within the contexts. As this locus changes within those metric spaces, the dynamics involved are useful and informative.  In other words, the structure one is modeling is not static, but dynamic.

 

“In times of change, learners inherit the earth, while the learned find themselves beautifully equipped to deal with a world that no longer exists.” – Eric Hoffer.

 

Ken Lloyd

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[Jon Awbrey]

Cf: Higher Order Sign Relations : 3
At: http://inquiryintoinquiry.com/2019/12/23/higher-order-sign-relations-%e2%80%a2-3/

Re: Higher Order Sign Relations
At: https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Re: Ontolog Forum ( https://groups.google.com/d/topic/ontolog-forum/B9HpfImt3aQ/overview )
::: Joseph Simpson ( https://groups.google.com/d/msg/ontolog-forum/B9HpfImt3aQ/R7shee_3BAAJ )

Travel delayed ... so I have a little time ...

<QUOTE> JA:
The subject matters of relations, types, and functions enjoy a form of recursive involvement with one another which

makes it difficult to know where to get on and where to get off the circle of explanation. As I currently understand
their relationship, it can be approached in the following order:

* Relations have types.
* Types are functions.
* Functions are relations.

In this setting, a "type" is a function from the "places" of a relation, that is, from the index set of its

"components", to a collection of sets known as the "domains" of the relation.
</QUOTE>

My 3-basket mantra recited above harks back to the mid 1980s when I took a course on Applications of Lambda Calculus
from John Gray at Illinois. It was all about categories, combinators, and computation, focusing especially on cartesian
closed categories, one of the hot topics of the day. We had a packet of readings from the classic sources and used J.
Lambek and P.J. Scott's Introduction to Higher Order Categorical Logic as our main text. I followed that up with a
supervised independent study where I explored various themes of my own.

The directions I pursued, and continue to continue, all have to do with mutating category theory just far enough to
encompass Peirce's 3-eyed vision in a more natural fashion.

I'll make that more explicit when I next get a chance.

Regards,

Jon