In the Way of Inquiry • Recircus

Posted on January 6, 2023 by Jon Awbrey

I must lie down where all the ladders start
In the foul rag and bone shop of the heart.
— W.B. Yeats

I have in mind circling back to a point in my project on Inquiry Driven Systems, namely, the chapter addressing various Obstacles to the Project.

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Posted in Animata, C.S. Peirce, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Semiotics | Tagged , , , , , , | 4 Comments

Riffs and Rotes • Happy New Year 2023

Posted on January 1, 2023 by Jon Awbrey

\text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}.

\text{Then} ~ 2023 = 7 \cdot {17}^2 = p_{4} p_{7}^{2} = p_{{p_1}^{p_1}} p_{{p_4}}^{p_1} = p_{{p_1}^{p_1}} p_{{p_{{p_1}^{p_1}}}}^{p_1}

No information is lost by dropping the terminal 1s.  Thus we may write the following form.

2023 = p_{p^p} p_{{p_{p^p}}}^p

The article referenced below tells how forms like these correspond to a family of digraphs called riffs and a family of graphs called rotes.  The riff and rote for 2023 are shown in the next two displays.

Riff 2023

Riff 2023

Rote 2023

Rote 2023

Reference

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Zeroth Law Of Semiotics • Discussion 4

Posted on December 25, 2022 by Jon Awbrey

Re: Zeroth Law Of Semiotics • All Liar, No Paradox
Re: FB | Pattern Languages for Systemic Transformation • Esteban Trev

JA:
A statement S_0 asserts that a statement S_1 is a statement that S_1 is false.

The statement S_0 violates an axiom of logic, so it doesn’t really matter whether the ostensible statement S_1, the so-called liar, really is a statement or has a truth value.

ET:
Well the truth value can be true or false or something else — akin to 5 + 5 = 12 being a true statement, if one knows what base it involves, else it may be false.  The same for 4 + 4 = 10 being a true statement, if one knows what base it involves.

Esteban is calling attention to the fact that our place-value systems of representation for integers and other numbers are relative to the basis chosen to generate the sequence of implied place values.  The basis is, in effect, the key to the code.  We may take this as a special case of a more general fact, one I summed up as follows.

  • Reference is relative to a frame of reference.  In pragmatic semiotics, frames of reference are called sign relations.

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Posted in Animata, C.S. Peirce, Denotation, Information = Comprehension × Extension, Liar Paradox, Logic, Logical Graphs, Mathematics, Nominalism, Pragmatic Maxim, Semiositis, Semiotics, Sign Relations, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , | 6 Comments

Zeroth Law Of Semiotics • Discussion 3

Posted on December 14, 2022 by Jon Awbrey

Re: Zeroth Law Of Semiotics • All Liar, No Paradox
Re: FB | Charles S. Peirce Society • Kent Olson

KO:
The liar paradox is a self-referential paradox, yes?
I think Russell answered these.

Dear Kent,

Russell had no inkling of pragmatic semiotics so his perspective on signs and sign relations was bound to remain mired in syntacticism, in effect, a species of nominalism.  From a fully three-dimensional Peircean point of view we are able to ask, and we have to ask, what could it possibly mean for a sign to refer to itself?  Indeed, do signs refer to themselves at all, or is it only that interpreters refer signs to their objects?  The whole problem looks very different once we take that point of view.

Regards,

Jon

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Posted in Animata, C.S. Peirce, Denotation, Information = Comprehension × Extension, Liar Paradox, Logic, Logical Graphs, Mathematics, Nominalism, Pragmatic Maxim, Semiositis, Semiotics, Sign Relations, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , | 6 Comments

Survey of Differential Logic • 4

Posted on November 20, 2022 by Jon Awbrey

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account.

Elements

Blog Series

Architectonics

Applications

Blog Dialogs

Explorations

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Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • Discussion 3

Posted on November 11, 2022 by Jon Awbrey

Re: FB | Paradoxology • Alex Shkotin  

AS:
I see — “sign relation” is a special term for triadic relations of some kind (with some properties);  like this:  thing in first position and thing in second position must refer to the thing in third position.  Where “refer” is an unary partial function from one thing to another.  Am I on a right direction?

Hi Alex,

It is not uncommon in practice to find a sign s having many interpretant signs i and many referent objects o.  Generally speaking, then, we start out with a sign relation L as a subset of a cartesian product L \subseteq O \times S \times I, where O, S, I are sets called the object domain, sign domain, interpretant sign domain, respectively.  A definition of a sign relation — there are a few canonical ones we find useful in practice — will specify what sort of constraint is involved in forming that subset.

Regards,

Jon

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Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • Discussion 2

Posted on November 7, 2022 by Jon Awbrey

Re: FB | Paradoxology • Alex Shkotin  

AS:
Not on a narrow topic, but maybe you have a desire to answer.
Hypothesis.  Any material something can be a sign.
Is it possible to give an example of something material that cannot be a sign?

Hi Alex,

Sign relations are mathematical relations we can use to model processes of communication, learning, reasoning, just plain talking and thinking in general.  Anytime we can imagine a triadic relation where one thing, material or otherwise, is related to a second thing in such a way that both refer to a third thing, and that whole relationship is useful in modeling one of the above mentioned processes, then we have a candidate which may be suitable for serving the purpose of a sign relation in the pragmatic conception of the term.

Regards,

Jon

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Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • Discussion 1

Posted on November 7, 2022 by Jon Awbrey

Semiotic Orbits, Manifolds, Arcs

The arc of the semiotic universe is long but it bends towards universal harmony.

Re: FB | Semiotics, Books, Links, News • What’s at the End of a Chain of Interpretants?

Semiotic manifolds, like physical and mathematical manifolds, may be finite and bounded or infinite and unbounded but they may also be finite and unbounded, having no boundary in the topological sense.  Thus unbounded semiosis does not imply infinite semiosis.

Here are two points in previous discussions where the question of infinite semiosis came up.

Resource

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Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • 5

Posted on November 6, 2022 by Jon Awbrey

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

The problem we face is as old as the problem of other minds, or intersubjectivity, or even commensurability, and it naturally involves a whole slew of other old problems — reality and appearance, or reality and representation, not to mention the one and the many.  One way to sum up the question might be “conditions on the possibility of a mutually objective world”.

Working on what oftentimes seems like the tenuous assumption that there really is a real world causing the impressions in my mind and the impressions in yours — more generally speaking, that there really is a real world impressing itself in systematic measures on every frame of reference — we find ourselves pressed to give an account of the hypothetical unity beneath the manifest diversity — and how it is possible to discover the former in the latter.

Manifold theory proposes one type of solution to that host of problems.

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Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • 4

Posted on November 5, 2022 by Jon Awbrey

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.

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Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments