#SignRelationalManifolds • Discussion 2
https://inquiryintoinquiry.com/2022/11/07/sign-relational-manifolds-discussion-2/

Alex Shkotin asks, “Hypothesis. Any material something can be a sign. Is it possible to give an example of something material that cannot be a sign?” I reply —

Sign relations are mathematical relations able to model discourse or thought. If a relation relates 1 thing, material or not, to a 2nd thing so that both refer to a 3rd thing and the whole relation works to model discourse or thought — then it qualifies as a sign relation.

#SignRelationalManifolds • Discussion 1

• https://inquiryintoinquiry.com/2022/11/07/sign-relational-manifolds-discussion-1-2/

Torkild Thellefsen asks on #Facebook, “What's at the End of a Chain of Interpretants?”

It is a #RecurringQuestion — I answered as I often do.

#SemioticManifolds, like physical & mathematical manifolds, may be finite & bounded or infinite & unbounded but they may also be finite & unbounded, having no boundary in the topological sense. Thus #UnboundedSemiosis does not imply #InfiniteSemiosis.

#Peirce #Semiotics #Manifolds

#SignRelationalManifolds • 5

• https://inquiryintoinquiry.com/2022/11/06/sign-relational-manifolds-5-2/

Let me try to say in intuitive terms what I think is really going on here.

The problem is as old as those about #OtherMinds, #Intersubjectivity, or #Commensurability and it involves a whole slew of other old problems — #RealityVsAppearance or #RealityVsRepresentation, not to mention #TheOneAndTheMany. One way to sum up the question might be “conditions on the possibility of a #MutuallyObjectiveWorld ”.

#Peirce #Semiotics #Manifolds

#SignRelationalManifolds • 4
• http://inquiryintoinquiry.com/2022/11/05/sign-relational-manifolds-4-2/

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general line of approach.

#RepresentationInvariantOntology

• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#439

• https://web.archive.org/web/20141220180218/http://stderr.org/pipermail/inquiry/2003-April/000439.html

• https://web.archive.org/web/20141220180220/http://stderr.org/pipermail/inquiry/2003-April/000440.html

#Peirce #Semiotics #SignRelations
#Riemann #SergeLang #Manifolds
#DifferentialGeometry #DifferentialLogic

#SignRelationalManifolds • 3
• http://inquiryintoinquiry.com/2022/11/03/sign-relational-manifolds-3-2/

I'm not sure when it was I first noticed the relationship between #manifolds and #semiotics but I distinctly recall the passage in Serge Lang's Differential and Riemannian Manifolds (1995) which brought the triadic character of tangent vectors into high relief.

Excerpts from Lang's DARM

Chapter 2. Manifolds
2.1. #Atlases, #Charts, #Morphisms
• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#442
2.2. #Submanifolds, #Immersions, #Submersions
• https://web.archive.org/web/20141220174800/http://stderr.org/pipermail/inquiry/2003-May/thread.html#448

@yog

Funny I thought I replied already, must have got lost in the 0zone.

At any rate, I'm just now in the middle of reworking some old work of mine somewhat along the lines you mention.

#SignRelationalManifolds
• https://inquiryintoinquiry.com/tag/sign-relational-manifolds/

I keep getting some kind of server error ...

@yog

Funny I thought I replied already, must have got lost in the 0zone.

At any rate, I'm just now in the middle of reworking some old work of mine somewhat along the lines you mention.

#SignRelationalManifolds
• https://inquiryintoinquiry.com/tag/sign-relational-manifolds/

I keep getting some kind of server error ...

#Peirce #Kant #Riemann
#SignRelationalManifolds
https://inquiryintoinquiry.com/2022/11/01/sign-relational-manifolds-2-2/

Applications of #Manifolds are illustrated by the following excerpts from Doolin & Martin's Introduction to #DifferentialGeometry for Engineers.

https://web.archive.org/web/20110612002240/http://suo.ieee.org/ontology/thrd28.html#04056

Manifolds came up in connection with #Ontology and #Semiotics due to the issues of #Perspectivity, #OntologicalRelativity, and #Interoperability among multiple ontologies. As I see it, those are the very sorts of problems manifolds were invented to handle.

#SignRelationalManifolds
#SignRelations #Semiotics
#DifferentialManifolds
#DifferentialGeometry
#DifferentialLogic

• https://inquiryintoinquiry.com/2022/10/31/sign-relational-manifolds-1-2/

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation.

Here is a set of excerpts from Murray G. Murphey (1961), The Development of Peirce’s Philosophy, discussing Peirce’s reception of Riemann’s philosophy of geometry.

Manifolds of Signs
• https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inquiry/2003-April/thread.html#313