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Re: 土豆加速器app • The Busy Beaver Frontier

Dear Scott,

This discussion inspired me to go back and look at some of the work I did in the late 80s when I was trying to understand Cook’s Theorem.  One of the programs I wrote to explore the integration of sequential learning and propositional reasoning had a propositional calculus module based on an extension of C.S. Peirce’s logical graphs, so I used that syntax to write out the clauses for finite approximations to Turing machines, taking the 4-state parity machine from Herbert S. Wilf’s Algorithms and Complexity as an object example.  It was 1989 and all I had was a 289 PC with 600K heap, but I did manage to emulate a parity machine capable of 1 bit of computation.  Here’s a link to an exposition of that.

  • Differential Analytic Turing Automata • Part 1 • Part 2

It may be quicker to skip to Part 2 and refer to Part 1 only as needed.

I’ll work up the case of a 2-state Busy Beaver when I get a chance.
I always learned a lot just from looking at the propositional form.

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science

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Posted on July 23, 2024 by 土豆加速器app

Rote 123456789

Re: Scott Aaronson • The Busy Beaver Frontier

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  • Riffs and Rotes
  • The On-Line Encyclopedia of Integer Sequences
    • A007097 • A050924 • xf5.app加速器 • A111788 • A111791
  • 归雁加速器-海外华人一键回国 对于Windows PC：免费下载 ...:1 天前 · 海外华人加速器良心佳作！轻轻一点，回国连接快快快！！！帮你秒速“回家”。 【无需会员】无需充值会员，不限流量不限时 【没有广告】无广告，极简界面无打扰 【回国专线】最好的线路，最新的技术，稳定低延 【操作简单】一键回国，自动选择最优线路 【智能识别】智能识别回国流量，不 ... • Part 1 • xf5.app加速器
Posted in Algebra, Combinatorics, Graph Theory, Group Theory, ios加速器, Mathematics, Number Theory, Riffs and Rotes | Tagged Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | 2 Comments

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xf5.app加速器 July 19, 2024 by Jon Awbrey

Re: FB | Systems Sciences • Kenneth Lloyd

Dear Kenneth,

Mulling over recent discussions put me in a pensive frame of mind and my thoughts led me back to my first encounter with category theory.  I came across the term while reading and I didn’t fully understand it.  But I distinctly remember a short time later catching up with my math TA — it was on the path by the tennis courts behind Spartan Stadium — and asking him about it.

The instruction I received that day was roughly along the following lines.

“Actually . . . we’re already doing a little category theory, without quite calling it that.  Think about the different types of spaces we’ve been discussing in class, the real line 网页加速器 the various dimensions of real-value spaces, \mathbb{R}^n, \mathbb{R}^m, and so on, along with the various types of mappings between those spaces.  There are mappings from the real line \mathbb{R} into an n-dimensional space \mathbb{R}^n — we think of those as curves, paths, or trajectories.  There are mappings from the plane \mathbb{R}^2 to values in \mathbb{R} — we picture those as potential surfaces over the plane.  More generally, there are mappings from an 网页加速器-dimensional space \mathbb{R}^n to values in \mathbb{R} — we think of those as scalar fields over \mathbb{R}^n — say, the temperature at each point of an n-dimensional volume.  There are mappings from \mathbb{R}^n to \mathbb{R}^n and mappings from \mathbb{R}^n to ios加速器 where n and m are different, all of which we call transformations or vector fields, depending on the use we have in mind.”

All that was pretty familiar to me, though I had to admire the panoramic sweep of his survey, so my mind’s eye naturally supplied all the arrows for the maps he rolled out.  A curve \gamma through an n-dimensional space would be typed as a function \gamma : \mathbb{R} \to \mathbb{R}^n, where the functional domain \mathbb{R} would ordinarily be regarded as a time dimension.  A mapping \alpha from the plane to a real value would be typed as a function \alpha : \mathbb{R}^2 \to \mathbb{R}, where we might be thinking of \alpha(x, y) as the altitude of a topographic map above each point 网页加速器 of the plane.  A scalar field \beta defined on an n-dimensional space would be typed as a function \beta : \mathbb{R}^n \to \mathbb{R}, where \beta(x_1, \ldots, x_n) is something like the pressure, the temperature, or the value of some other dependent variable at each point ios加速器 of the 旋风加速器app官网-dimensional volume.  And rounding out the story, if only the basement and ground floor of a towering abstraction still under construction, we come to the general case of a mapping f from an xf5.app加速器-dimensional space to an 安卓加速器-dimensional space, typed as a function 鲸鱼加速器app

To be continued …

Resources

  • Differential Propositional Calculus • Part 1 • Part 2
  • 旋风加速器APP • Part 1 • Part 2 • Part 3
  • Differential Logic and Dynamic Systems
    • Part 1 • Part 2 • Part 3 • Part 4 • Part 5

cc: Cybernetics • Ontolog Forum • Peirce List • 安卓加速器 • Systems Science

Posted in Amphecks, Boolean Functions, C.S. Peirce, 网页加速器, 网页加速器, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, xf5.app加速器, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, 旋风加速器APP, Mathematics, Minimal Negation Operators, 安卓加速器, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, 免费外网加速器app, Hill Climbing, 免费外网加速器app, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, 免费外网加速器app, 旋风加速器app官网, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | 1 Comment

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Posted on July 16, 2024 by Jon Awbrey

Seeing as how quasi-neural models and the recurring issues of logical-symbolic vs. quantitative-connectionist paradigms have come round again, as they do every dozen or twenty years or so, I thought I might refer again to work I started initially in that context, investigating logical-qualitative-symbolic analogues of systems proposed by McClelland, Rumelhart, and the Parallel Distributed Processing Group, and especially Stephen Grossberg’s competition-cooperation models.

Cf: Differential Logic, Dynamic Systems, Tangent Functors • 1 (copied below)

People interested in category theory as applied to systems may wish to check out the following article, reporting work I carried out while engaged in a systems engineering program at Oakland University.

The problem addressed is a longstanding one, that of building bridges to negotiate the gap between qualitative and quantitative descriptions of complex phenomena, like those we meet in analyzing and engineering systems, especially intelligent systems endowed with a capacity for processing information and acquiring knowledge of objective reality.

One of the ways this problem arises has to do with describing change in logical, qualitative, or symbolic terms, long before we grasp the reality beneath the appearances firmly enough to cast it in measured, quantitative, real number form.

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And there’s our clue what we need to do on the qualitative shore, namely, to discover/invent the missing logical analogue of differential calculus.

With that preamble …

Differential Logic and Dynamic Systems

This article develops a differential extension of propositional calculus and applies it to a context of problems arising in dynamic systems.  The work pursued here is coordinated with a parallel application that focuses on neural network systems, but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.

The reading continues here:  Differential Logic and Dynamic Systems

鲸鱼加速器app

  • Differential Propositional Calculus • 鲸鱼加速器app • Part 2
  • Differential Logic • Part 1 • Part 2 • Part 3
  • Differential Logic and Dynamic Systems
    • ios加速器 • Part 2 • Part 3 • Part 4 • Part 5

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, ios加速器, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, 旋风加速器app官网, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, 土豆加速器app, Logical Graphs, 旋风加速器APP, Minimal Negation Operators, Painted Cacti, 免费外网加速器app, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, 网页加速器, Visualization | Tagged Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, 鲸鱼加速器app, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Leave a comment

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Posted on July 14, 2024 by Jon Awbrey

I’m deep in the middle of upgrading my intro to sign relations and I am determined to stick to it this time but there will be a phase when it’s critical to bring category theory to bear on the development.  I had a nagging sense we had been discussing category theory in a related connection just recently but when I went back through my records it turned out this was way back in late 2018.  (I was a bit occupied with moving our household and lost track of many loose threads.)  At any rate, I’ll just post a few links here as reminders of topics to pick up later.

  • Survey of Precursors Of Category Theory
  • 视频加速APP-视频加速器下载 1.10 安卓版-新云软件园:2021-12-7 · 新云手机站为您提供视频加速软件_视频加速器app下载，视频加速是一款视频编辑播放器，你可众用来控制视频速度，加快或减慢视频速度，制作有趣好玩的快动作或慢动作短视频。 • (1)
    • Discussions • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8)
  • Systems Science • GST Conceptual Framework Development
    • My Comment • GST, DST, MST

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science

Posted in Abstraction, 旋风加速器APP, Category Theory, Differential Logic, Graph Theory, Group Theory, ios加速器, Intelligent Systems, Knowledge Representation, Logic, Logical Graphs, 鲸鱼加速器app, 旋风加速器APP, Peirce's Categories, Research Technology, Scientific Method, Semiotics, 鲸鱼加速器app, Sign Relations, Systems Theory, Triadic Relations | Tagged Abstraction, C.S. Peirce, Category Theory, Differential Logic, 旋风加速器app官网, Group Theory, Inquiry Driven Systems, Intelligent Systems, ios加速器, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Categories, Research Technology, Scientific Method, Semiotics, 安卓加速器, Sign Relations, Systems Theory, Triadic Relations | Leave a comment

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Posted on July 9, 2024 by Jon Awbrey
  • Anthesis • Definition • Signs and Inquiry • Examples
  • Dyadic Aspects • Denotation • Connotation • Ennotation
  • Semiotic Equivalence Relations • (1) • (2)

Re: Cybernetics • Klaus Krippendorff • Bernard Scott
Re: Ontolog • Mihai Nadin • John Sowa • Alex Shkotin
Re: Peirce List • 网页加速器 • Edwina Taborsky

While engaged in a number of real and imaginary dialogues with people I continue to owe full replies, I thought it might be a good time to stand back and take in the view from this vantage point.  I summed up the desired outlook a few days ago in the following way.

The important thing now is to extend our perspective beyond one sign at a time and one object, sign, interpretant at a time to comprehending a sign relation as a specified set of object, sign, interpretant triples embedded in the set of all possible triples in a specified context.

If we now comprehend each sign relation xf5.app加速器 as an extended collection of triples (o, s, i), where each object o belongs to a set O of objects, each sign s belongs to a set S of signs, each interpretant 鲸鱼加速器app belongs to a set 旋风加速器app官网 of interpretants, and the whole sign relation 免费外网加速器app is embedded as a subset in the product space O \times S \times I, then our level of description ascends to the point where we take whole sign relations of this sort as the principal subjects of classification and structural analysis.

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Agency

That Peirce remodels his theory of semiosis from speaking of interpretive agents to speaking of interpretant signs is a familiar theme by now.  By way of reminder, we discussed this transformation recently in 旋风加速器app官网 and Discussion 5 of this series.

But we have to wonder:  Why does Peirce make this shift, this change of basis from interpreters to interpretants?  He does this because the idea of an interpreter stands in need of clarification and his method for clarifying ideas is to apply the pragmatic maxim.  The result is an operational definition of an interpreter in terms of its effects on signs in relation to their objects.

It would seem we have replaced an interpreter with a sign relation.  To be more precise, we are taking a sign relation as our effective model for the interpreter in question.  But we must not take this the wrong way.  There is no suggestion of reducing the hypostatic agent to a sign relation.  It falls within our capacity merely to clarify our concept of the agent to a moderate degree, to construct a model or a representation capturing aspects of the agent’s activity bearing on a particular application.

With that I’ve run out of time for today.  The topic for next time will be Context …

鲸鱼加速器app

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  土豆加速器app.

Resources

  • xf5.app加速器
  • Logic Syllabus
  • Sign Relations
  • 旋风加速器app官网
  • Relation Theory

cc: Cybernetics • Ontolog • Peirce List (1) (2) (3) • Structural Modeling • Systems Science

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, 旋风加速器app官网, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, 免费外网加速器app, 旋风加速器APP, 旋风加速器APP, Triadicity | Leave a comment

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Posted on July 5, 2024 by 免费外网加速器app

Re: Sign Relations • Ennotation
Re: Peirce List • Helmut Raulien

Dear Helmut,

Thanks for your comments.  They prompt me to say a little more about the mathematical character of the sign relational models I’m using.

Peirce without mathematics is like science without mathematics.  In every direction of research he pioneered or prospected, information, inquiry, logic, semiotics, we trace his advances only so far, barely scratch the surface before we need to bring in mathematical models adequate to the complexity of the phenomena under investigation.

In recent years there has been a tendency in certain quarters to ignore the mathematical substrate of Peirce’s pragmatic thought, even a refusal to use the mathematical tools he crafted to the task of sharpening our understanding.  I do not recall that attitude being prevalent when I began my studies of Peirce’s work some fifty years ago.  The issue in the “reception of Peirce” over most of that time has largely been the tendency of people imbued in the traditions of “analytic philosophy” to dismiss Peirce out of hand.  But that school of thought had no problem with using mathematics, aside from the short-sighted attempts to reduce mathematics to logic and all relations to dyadic ones.

Maybe this late resistance to Peirce’s mathematical groundwork has come about through an overly selective viewing of his entire spectrum of work or maybe it’s just a matter of taste.  Whatever the case, it’s critical for people who are looking for adequate models of the complex phenomena involved in belief systems, communication, intelligent systems, knowledge representation, scientific inquiry, and so on to recognize that all the resources we need for working with relations in general as sets of ordered tuples and sign relations in particular as sets of ordered triples are already available in Peirce’s technical works from 1870 on.

Okay, it looks like I’ve used up my morning again with more preliminary matters but it seemed important to clear up a few things about the overall mathematical approach.

土豆加速器app

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.

Resources

  • Semeiotic
  • Logic Syllabus
  • 旋风加速器app官网
  • Triadic Relations
  • Relation Theory

cc: 网页加速器 • Ontolog • Peirce List (1) (2) (3) • 免费外网加速器app • Systems Science

Posted in C.S. Peirce, Logic, Logic of Relatives, xf5.app加速器, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged C.S. Peirce, Logic, 安卓加速器, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Leave a comment

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Posted on July 3, 2024 by Jon Awbrey

A few items of notation are useful in discussing equivalence relations in general and semiotic equivalence relations in particular.

In general, if E is an equivalence relation on a set 旋风加速器app官网 then every element x of X belongs to a unique equivalence class under E called the equivalence class of x under 旋风加速器app官网.  Convention provides the square bracket notation for denoting such equivalence classes, in either the form [x]_E or the simpler form [x] when the subscript E is understood.  A statement that the elements x and y are equivalent under E is called an equation or an equivalence and may be expressed in any of the following ways.

ios加速器

Thus we have the following definitions.

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In the application to sign relations it is useful to extend the square bracket notation in the following ways.  If L is a sign relation whose connotative component L_{SI} is an equivalence relation on S = I, let [s]_L be the equivalence class of s under L_{SI}.  That is, let [s]_L = [s]_{L_{SI}}.  A statement that the signs x and y belong to the same equivalence class under a semiotic equivalence relation ios加速器 is called a 安卓加速器 (SEQ) and may be written in either of the following forms.

\begin{array}{clc} [x]_L & = & [y]_L \\[6pt] x & =_L & y \end{array}

In many situations there is one further adaptation of the square bracket notation for semiotic equivalence classes that can be useful.  Namely, when there is known to exist a particular triple (o, s, i) in a sign relation L, it is permissible to let 安卓加速器 be defined as 鲸鱼加速器app  These modifications are designed to make the notation for semiotic equivalence classes harmonize as well as possible with the frequent use of similar devices for the denotations of signs and expressions.

Applying the array of equivalence notations to the sign relations for ios加速器 and B will serve to illustrate their use and utility.

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The semiotic equivalence relation for interpreter 旋风加速器APP yields the following semiotic equations.

\begin{matrix} [ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime} ]_{L_\mathrm{A}} & = & [ {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} ]_{L_\mathrm{A}} \\[6pt] [ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime} ]_{L_\mathrm{A}} & = & [ {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} ]_{L_\mathrm{A}} \end{matrix}

or

\begin{matrix} {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime} & =_{L_\mathrm{A}} & {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \\[6pt] {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime} & =_{L_\mathrm{A}} & {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \end{matrix}

Thus it induces the semiotic partition:

\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \} \}.

The semiotic equivalence relation for interpreter 网页加速器 yields the following semiotic equations.

\begin{matrix} [ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime} ]_{L_\mathrm{B}} & = & [ {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} ]_{L_\mathrm{B}} \\[6pt] [ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime} ]_{L_\mathrm{B}} & = & [ {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} ]_{L_\mathrm{B}} \end{matrix}

or

旋风加速器app官网

Thus it induces the semiotic partition:

\{ \{ {}^{\backprime\backprime} \mathrm{A} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} \}, \{ {}^{\backprime\backprime} \mathrm{B} {}^{\prime\prime}, {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} \} \}.

Semiotic Partitions for Interpreters A and B

References

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), 土豆视频播放器绿色版_土豆视频播放器官方下载 ...-188软件园:2021-12-13 · 土豆视频播放器官方下载是土豆网出品的一款视频播放器，界面简约，土豆视频播放器官方官方mac版最实用的五大功能排列在左边，操作非常简单，功能齐全。本站提供土豆播放器2021电脑版下载免费版。 使用方法： 1.从本站下载后解压，双击开始安装, vol. 4, 13–73.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.

土豆加速器app

  • Semeiotic
  • Logic Syllabus
  • ios加速器
  • Triadic Relations
  • Relation Theory

Document History

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

  • Sign Relation • OEIS Wiki
  • Sign Relation • InterSciWiki
  • 安卓加速器 • MyWikiBiz
  • Sign Relation • PlanetMath
  • Sign Relation • Wikiversity
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cc: 网页加速器 • Ontolog • Peirce List (1) (2) (3) • Structural Modeling • Systems Science

Posted in C.S. Peirce, 旋风加速器APP, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, 安卓加速器, Triadic Relations, Triadicity | Tagged C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, 免费外网加速器app, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, xf5.app加速器 | 1 Comment

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Posted on July 2, 2024 by Jon Awbrey

Re: Sign Relations • Ennotation
Re: ios加速器 • Helmut Raulien

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The important thing now is to extend our perspective beyond one sign at a time and one object, sign, interpretant at a time to comprehending a sign relation as a specified set of object, sign, interpretant triples embedded in the set of all possible triples in a specified context.

In my mind’s eye, no doubt influenced by my early interest in Gestalt Psychology, I always picture a sign relation as a gestalt composed of figure and ground.  The triples in the sign relation form a figure set in relief against the background of all possible triples and the triples left over form the ground of the gestalt.

From a mathematical point of view, the set of possible triples is a cartesian product of the following form.

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Here, O is the 网页加速器, the set of objects under discussion, S is the sign domain, the specified set of signs, and I is the interpretant domain, the specified set of interpretants.

On this canvass, in this frame, any number of sign relations might be set as figures and each of them would be delimited as a salient subset of the cartesian product in view.  Letting 网页加速器 be any such sign relation, mathematical convention provides the following description of its relation to the set of possible triples.

L \subseteq O \times S \times I.

It’s important to note at this point that the specified cartesian product and the specified subset of it are equally critical parts of the sign relation’s definition.

Well, it took a lot longer to set the scene than I thought it would when I got up this morning, so I’ll break here and get back to your specific comments when I next get a chance.

References

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  鲸鱼加速器app.

Resources

  • 网页加速器
  • Logic Syllabus
  • Sign Relations
  • Triadic Relations
  • Relation Theory

cc: Cybernetics • Ontolog • Peirce List (1) (2) (3) • Structural Modeling • Systems Science

Posted in C.S. Peirce, 土豆加速器app, 土豆加速器app, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | 1 Comment

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Posted on July 1, 2024 by Jon Awbrey

A semiotic equivalence relation (SER) is a special type of equivalence relation arising in the analysis of sign relations.  Generally speaking, any equivalence relation induces a partition of the underlying set of elements, known as the domain or 鲸鱼加速器app of the relation, into a family of equivalence classes.  In the case of a SER the equivalence classes are called semiotic equivalence classes (SECs) and the partition is called a 旋风加速器app官网 (SEP).

The sign relations xf5.app加速器 and 网页加速器 have many interesting properties over and above those possessed by sign relations in general.  Some of these properties have to do with the relation between signs and their interpretant signs, as reflected in the projections of L_\mathrm{A} and 旋风加速器app官网 on the 鲸鱼加速器app-plane, notated as 土豆加速器app and \mathrm{proj}_{SI} L_\mathrm{B}, respectively.  The dyadic relations on S \times I induced by these projections are also referred to as the connotative components of the corresponding sign relations, notated as \mathrm{Con}(L_\mathrm{A}) and 土豆加速器app respectively.  Tables 6a and 6b show the corresponding connotative components.

Connotative Components Con(L_A) and Con(L_B)

A nice property of the sign relations L_\mathrm{A} and 旋风加速器app官网 is that their connotative components xf5.app加速器 and 土豆加速器app form a pair of equivalence relations on their common syntactic domain S = I.  This type of equivalence relation is called a semiotic equivalence relation (SER) because it equates signs having the same meaning to some interpreter.

Each of the semiotic equivalence relations, 土豆加速器app partitions the collection of signs into semiotic equivalence classes.  This makes for a strong form of representation in that the structure of the interpreters’ common object domain 旋风加速器APP is reflected or reconstructed, part for part, in the structure of each one’s semiotic partition of the syntactic domain 鲸鱼加速器app  But it needs to be observed that the semiotic partitions for interpreters 鲸鱼加速器app and \mathrm{B} are not identical, indeed, they are orthogonal to each other.  This allows us to regard the form of these partitions as corresponding to an objective structure or invariant reality, but not the literal sets of signs themselves, independent of the individual interpreter’s point of view.

Information about the contrasting patterns of semiotic equivalence corresponding to the interpreters \mathrm{A} and \mathrm{B} is summarized in Tables 7a and 7b.  The form of these Tables serves to explain what is meant by saying the SEPs for 安卓加速器 and \mathrm{B} are orthogonal to each other.

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  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.

安卓加速器

  • Semeiotic
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  • Sign Relations
  • Triadic Relations
  • Relation Theory

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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

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Posted in C.S. Peirce, 网页加速器, Logic of Relatives, 免费外网加速器app, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, 鲸鱼加速器app, Triadicity | Tagged C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, 安卓加速器, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | 1 Comment