Much of the work I do on the C.S. Peirce/Spencer Brown approach to “mathematical hypostases underlying logic” now goes under the heading of Animated Logical Graphs. There’s a Survey of related resources I update from time to time at the following location.
cc: Cybernetics (1) (2) • Laws of Form • FB | Logical Graphs • Ontolog Forum (1) (2)
• Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) • Structural Modeling (1) (2)
• Systems Science (1) (2)
All of which inspires me to revise and extend the series of posts I shared with the old group a few years back, fixing in passing the large number of now broken links.
cc: Cybernetics • Laws of Form • Ontolog • Peirce • Structural Modeling • Systems Science
]]>Dear Cliff,
I’m still collecting my wits from the mind-numbing events of the past two weeks so I’ll copy your last remarks here and work through them step by step.
Relational systems are just the context we need. It is usual to begin at a moderate level of generality by considering a space of the following form.
(I’ll use instead of here because I want to save the letter for sign domains when we come to the special case of sign relational systems.)
We can now define a relation as a subset of a cartesian product.
There are two common ways of understanding the subset symbol in this context. Using language from computer science I’ll call them the weak typing and strong typing interpretations.
We have at this point opened two fronts of interest in cybernetics, namely, the generation of variety and the recognition of constraint. There’s more detail on this brand of relation theory in the resource article linked below. I’ll be taking the strong typing approach to relations from this point on, largely because it comports more naturally with category theory and thus enjoys ready applications to systems and their transformations.
But my eye-brain system is going fuzzy on me now, so I’ll break here and continue later …
cc: Cybernetics • Ontolog • Peirce List (1) (2) (3) • Structural Modeling • Systems Science
]]>Re: FB | Semiotics, Books, Links, News • Jon Awbrey • Dalibor Lošťák
The way I see Categories applying to Peirce’s logic and semiotics may be gleaned from the following Survey page.
The series beginning with the following post might be a good place to start.
]]>Re: Peirce List • Steven Skaggs
Re: FB | Semiotics, Books, Links, News • Muntadher Almahdawi
Another one of those recurring questions just came up in a Facebook group devoted to Semiotics and I thought it would be useful to try my hand at a fresh attempt to answer it — or at least promote further discussion.
Icon, Index, Symbol and all other classifications are ideal types abstracted from concrete signs and there are no pure types in actual existence. However, it is a consequence of triadic relation irreducibility that symbols are in a genuine sense the generic type while icons and indices are specializations or so-called degenerate cases.
]]>cc: Cybernetics • Ontolog • Peirce List • SeqFan • Structural Modeling • Systems Science
]]>Re: Previous Post
Re: Cybernetics • Cliff Joslyn
Dear Cliff,
Many thanks for your thoughtful reply. I copied a transcript to my blog to take up first thing next year. Here’s hoping we all have a better one!
Regards,
Jon
cc: Cybernetics • Ontolog • Peirce List (1) (2) • Structural Modeling • Systems Science
]]>Dear Helmut,
The distinction between “k-adic” (involving a span of k dimensions) and “k-tomic” (involving a range of k values) is one of the earliest questions I remember discussing on the Peirce List and the panoply of other lists we ranged across in those heady surfer days. It is critical not to confuse the two aspects of multiplicity. In some cases it is possible to observe what mathematicians call a projective relationship between the two aspects but that does not make them identical.
I’m adding a lightly edited excerpt from one of those earlier discussions as I think it introduces the issues about as well as I could manage today.
Arisbe List • Re: Inquiry Into Isms • k-adic versus k-tomic
Jon Awbrey • 21 Aug 2001
Here is an old note I’ve been looking for since we started on this bit about isms, as I feel I managed to express in it my point of view that the key to integrating variant perspectives is to treat their contrasting values as axes or dimensions rather than so many points on a line to be selected among, each in exclusion of all the others. To express it briefly, it is the difference between k-tomic decisions among terminal values and k-adic dimensions of extended variation.
Standard Upper Ontology List • Dyads
Jon Awbrey • 06 Dec 2000 • 08 Dec 2000
cc: Cybernetics • Ontolog • Peirce List (1) (2) • Structural Modeling • Systems Science
]]>An inquiry driven system is a system having among its state variables some representing its state of information with respect to various topics of interest, for example, its own state and the states of any potential object systems. Thus it has a component of state tracing a trajectory though an information state space.