Higher Order Sign Relations

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Jon Awbrey

Dec 4, 2019, 5:00:40 PM12/4/19
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
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 )



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Jon Awbrey

Dec 23, 2019, 3:24:14 PM12/23/19
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
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 ...

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.

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.


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