#pragmaticsemioticinformation — Public Fediverse posts

Information = Comprehension × Extension • Selection 2.3
• https://inquiryintoinquiry.com/2024/10/06/information-comprehension-x-extension-selection-2-a/

❝The third and last kind of representations are “symbols” or general representations. They connote attributes and so connote them as to determine what they denote. To this class belong all “words” and all “conceptions”. Most combinations of words are also symbols. A proposition, an argument, even a whole book may be, and should be, a single symbol.❞

(Peirce 1866, pp. 467–468)

Reference —

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Resources —

Inquiry Blog • Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

OEIS Wiki • Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

C.S. Peirce • Upon Logical Comprehension and Extension
• https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Information = Comprehension × Extension • Selection 2.2
• https://inquiryintoinquiry.com/2024/10/06/information-comprehension-x-extension-selection-2-a/

❝In the first place there are likenesses or copies — such as “statues”, “pictures”, “emblems”, “hieroglyphics”, and the like. Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters. The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less; for they stand for whatever they resemble and they resemble everything more or less.

❝The second kind of representations are such as are set up by a convention of men or a decree of God. Such are “tallies”, “proper names”, &c. The peculiarity of these “conventional signs” is that they represent no character of their objects.

❝Likenesses denote nothing in particular; “conventional signs” connote nothing in particular.❞

(Peirce 1866, pp. 467–468)

Reference —

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Information = Comprehension × Extension • Selection 2.1
• https://inquiryintoinquiry.com/2024/10/06/information-comprehension-x-extension-selection-2-a/

Re: Information = Comprehension × Extension • Selection 1
• https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-extension-selection-1-a/

Over the course of Selection 1 Peirce introduces the ideas he needs to answer stubborn questions about the validity of scientific inference. Briefly put, the validity of scientific inference depends on the ability of symbols to express “superfluous comprehension”, the measure of which Peirce calls “information”.

Selection 2 sharpens our picture of symbols as “general representations”, contrasting them with two species of representation whose characters fall short of genuine symbols.

❝For this purpose, I must call your attention to the differences there are in the manner in which different representations stand for their objects.❞

(Peirce 1866, pp. 467–468)

Reference —

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Information = Comprehension × Extension • Selection 1.2
• https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-extension-selection-1-a/

❝Thus, let us commence with the term “colour”; add to the comprehension of this term, that of “red”. “Red colour” has considerably less extension than “colour”; add to this the comprehension of “dark”; “dark red colour” has still less [extension]. Add to this the comprehension of “non‑blue” — “non‑blue dark red colour” has the same extension as “dark red colour”, so that the “non‑blue” here performs a work of supererogation; it tells us that no “dark red colour” is blue, but does none of the proper business of connotation, that of diminishing the extension at all. Thus information measures the superfluous comprehension. And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.

❝I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of “information”.❞

(Peirce 1866, p. 467)

Reference —

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Information = Comprehension × Extension • Selection 1.1
• https://inquiryintoinquiry.com/2024/10/05/information-comprehension-x-extension-selection-1-a/

Our first text comes from Peirce's Lowell Lectures of 1866, titled “The Logic of Science, or, Induction and Hypothesis”. I still remember the first time I read these words and the light that lit up the page and my mind.

❝Let us now return to the information. The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of “man”. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.❞

(Peirce 1866, p. 467)

Reference —

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Resources —

Inquiry Blog • Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

OEIS Wiki • Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

C.S. Peirce • Upon Logical Comprehension and Extension
• https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Information = Comprehension × Extension • Preamble
• https://inquiryintoinquiry.com/2024/10/04/information-comprehension-x-extension-preamble/

Eight summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manner in which different representations stand for their objects” and the way in which different inferences transform states of information. I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the cool of later reflection. Now looks to be a choice moment for taking another look.

A first pass through the variations of representation and reasoning detects the axes of iconic, indexical, and symbolic manners of representation on the one hand and the axes of abductive, inductive, and deductive modes of inference on the other. Early and often Peirce suggests a natural correspondence between the main modes of inference and the main manners of representation but his early arguments differ from his later accounts in ways deserving close examination, partly for the extra points in his line of reasoning and partly for his explanation of indices as signs constituted by convening the variant conceptions of sundry interpreters.

Resources —

Inquiry Blog • Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

OEIS Wiki • Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

C.S. Peirce • Upon Logical Comprehension and Extension
• https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm

#Peirce #Logic #Inference #Inquiry #Abduction #Induction #Deduction #LogicOfScience
#Information #Comprehension #Extension #InformationEqualsComprehensionTimesExtension
#Semiotics #SignRelations #Icon #Index #Symbol #PragmaticSemioticInformation

Constraints and Indications • 1.2
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
• https://web.archive.org/web/20121231182129/http://comments.gmane.org/gmane.science.philosophy.peirce/9165

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems #PragmaticSemioticInformation
#Constraint #ControlSystems #Indication #Information #Inquiry #IntelligentSystems
#AdaptiveSystems #ErrorControlledRegulation #Feedback #SystemsTheory #Uncertainty
#Determination #Intentionality #Learning #Reasoning #SemioticInformation #Semiotics

Constraints and Indications • 1.2
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
• https://web.archive.org/web/20121231182129/http://comments.gmane.org/gmane.science.philosophy.peirce/9165

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems #PragmaticSemioticInformation
#Constraint #ControlSystems #Indication #Information #Inquiry #IntelligentSystems
#AdaptiveSystems #ErrorControlledRegulation #Feedback #SystemsTheory #Uncertainty
#Determination #Intentionality #Learning #Reasoning #SemioticInformation #Semiotics

Constraints and Indications • 1.2
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
• https://web.archive.org/web/20121231182129/http://comments.gmane.org/gmane.science.philosophy.peirce/9165

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems #PragmaticSemioticInformation
#Constraint #ControlSystems #Indication #Information #Inquiry #IntelligentSystems
#AdaptiveSystems #ErrorControlledRegulation #Feedback #SystemsTheory #Uncertainty
#Determination #Intentionality #Learning #Reasoning #SemioticInformation #Semiotics

Constraints and Indications • 1.2
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
• https://web.archive.org/web/20121231182129/http://comments.gmane.org/gmane.science.philosophy.peirce/9165

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems #PragmaticSemioticInformation
#Constraint #ControlSystems #Indication #Information #Inquiry #IntelligentSystems
#AdaptiveSystems #ErrorControlledRegulation #Feedback #SystemsTheory #Uncertainty
#Determination #Intentionality #Learning #Reasoning #SemioticInformation #Semiotics

Theme One Program • Motivation 1
• https://inquiryintoinquiry.com/2024/06/03/theme-one-program-motivation-1-b/

The main idea behind the Theme One program is the efficient use of graph‑theoretic data structures for the tasks of “learning” and “reasoning”.

I am thinking of “learning” in the sense of learning about an environment, in essence, gaining information about the nature of an environment and being able to apply the information acquired to a specific purpose.

Under the heading of “reasoning” I am simply lumping together all the ordinary sorts of practical activities which would probably occur to most people under that name.

There is a natural relation between the tasks. Learning the character of an environment leads to the recognition of laws which govern the environment and making full use of that recognition requires the ability to reason logically about those laws in abstract terms.

Resources —

Theme One Program • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview

Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition

Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Survey of Pragmatic Semiotic Information • 8
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas. This line of inquiry is more open‑ended than most. The question is —

• What is information and how does it impact the spectrum of activities answering to the name of inquiry?

Setting out on what would become his lifelong quest to explore and explain the “Logic of Science”, C.S. Peirce pierced the veil of historical confusions obscuring the issue and fixed on what he called the “laws of information” as the key to solving the puzzle.

The first hints of the Information Revolution in our understanding of scientific inquiry may be traced to Peirce’s lectures of 1865–1866 at Harvard University and the Lowell Institute. There Peirce took up “the puzzle of the validity of scientific inference” and claimed it was “entirely removed by a consideration of the laws of information”.

Please follow the above link for the full set of resources.
Articles and blog posts on the core ideas are linked below.

Information = Comprehension × Extension
• https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension

{ Information = Comprehension × Extension }
• https://inquiryintoinquiry.com/2016/05/18/information-comprehension-x-extension/

{ Information = Comprehension × Extension } • Revisited
• https://inquiryintoinquiry.com/2019/01/23/information-comprehension-x-extension-revisited/

Pragmatic Semiotic Information • Ψ
• https://inquiryintoinquiry.com/2023/07/22/pragmatic-semiotic-information-%cf%88-a/

Pragmatic Semiotic Information
• https://oeis.org/wiki/Pragmatic_Semiotic_Information

Peirce's Logic Of Information
• https://oeis.org/wiki/User:Jon_Awbrey/Peirce%27s_Logic_Of_Information

Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”
• https://peirce.sitehost.iu.edu/writings/v2/w2/w2_06/v2_06.htm

#Peirce #Logic #LogicOfScience #ScientificMethod #InformationTheory
#Pragmatism #Semiotics #SignRelations #PragmaticSemioticInformation

Survey of Pragmatic Semiotic Information • 7
• http://inquiryintoinquiry.com/2023/07/23/survey-of-pragmatic-semiotic-information-7/

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas. All my projects are exploratory in character but this line of inquiry is more open‑ended than most. The question is —

• What is information and how does it impact the spectrum of activities answering to the name of inquiry?

Setting out on what would become his lifelong quest to explore and explain the “Logic of Science”, C.S. Peirce pierced the veil of historical confusions obscuring the issue and fixed on what he called the “laws of information” as the key to solving the puzzle.

The first hints of the Information Revolution in our understanding of scientific inquiry may be traced to Peirce's lectures of 1865–1866 at Harvard University and the Lowell Institute. There Peirce took up “the puzzle of the validity of scientific inference” and claimed it was “entirely removed by a consideration of the laws of information”.

Fast forward to the present and I see the Big Question as follows. Having gone through the exercise of comparing and contrasting Peirce's theory of information, however much it yet remains in a rough‑hewn state, with Shannon's paradigm so pervasively informing the ongoing revolution in our understanding and use of information, I have reason to believe Peirce's idea is root and branch more general and has the potential, with due development, to resolve many mysteries still bedeviling our grasp of inference, information, and inquiry.

#Peirce #Logic #LogicOfScience #ScientificMethod #InformationTheory
#Pragmatism #Semiotics #SignRelations #PragmaticSemioticInformation

Pragmatic Semiotic Information • Ψ
• http://inquiryintoinquiry.com/2023/07/22/pragmatic-semiotic-information-%cf%88-2/

I remember it was back in ’76 when I began to notice a subtle shift of focus in the computer science journals I was reading, from discussing X to discussing “Information About X”, or \(X \to \mathrm{Info}(X)\) as I came to notate the transformation. I suppose that small arc of revolution had been building for years but it struck me as crossing a threshold to a more explicit, self‑conscious stage about that time.

#Peirce #Logic #LogicOfScience #ScientificMethod #InformationTheory
#Pragmatism #Semiotics #SignRelations #PragmaticSemioticInformation

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization

Functional Logic • Inquiry and Analogy • 5

Inquiry and Analogy • Aristotle’s “Paradigm” • Reasoning by Analogy

Aristotle examines the subject of analogical inference or “reasoning by example” under the heading of the Greek word παραδειγμα, from which comes the English word paradigm.  In its original sense the word suggests a kind of “side‑show”, or a parallel comparison of cases.

We have an Example (παραδειγμα, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

E.g., let A be “bad”, B “to make war on neighbors”, C “Athens against Thebes”, and D “Thebes against Phocis”.  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.

Aristotle, “Prior Analytics” 2.24, Hugh Tredennick (trans.)

Figure 6 shows the logical relationships involved in Aristotle’s example of analogy.

Resources

• Logic Syllabus
• Boolean Function
• Boolean-Valued Function
• Logical Conjunction
• Minimal Negation Operator
• Functional Logic • Part 1 • Part 2 • Part 3
• Cactus Language • Part 1 • Part 2 • Part 3 • References • Document History

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#Abduction #Analogy #Argument #Aristotle #CSPeirce #Constraint #Deduction #Determination #DiagrammaticReasoning #Diagrams #DifferentialLogic #FunctionalLogic #Hypothesis #Indication #Induction #Inference #Information #Inquiry #Logic #LogicOfScience #Mathematics #PragmaticSemioticInformation #ProbableReasoning #PropositionalCalculus #Propositions #Reasoning #Retroduction #Semiotics #SignRelations #Syllogism #TriadicRelations #Visualization

Theme One Program • Exposition 1.2
• https://inquiryintoinquiry.com/2022/06/15/theme-one-program-exposition-1-2/

The Idea↑Form Flag

The graph-theoretic data structures used by the program are built up from a basic data structure called an “idea-form flag”. That structure is defined as a pair of Pascal data types by means of the following specifications.

Figure 1. Type Idea = ^Form
• https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-type-idea-5eform.png

Figure 2. Code Box
• type idea = ^form;
• form = record
• sign: char;
• as, up, on, by: idea;
• code: numb
• end;

An “idea” is a pointer to a “form”.
• A “form” is a record consisting of:
• A “sign” of type “char”;
• Four pointers, “as”, “up”, “on”, “by”, of type “idea”;
• A “code” of type “numb”, that is, an integer in [0, max integer].

Represented in terms of “digraphs”, or directed graphs, the combination of an idea pointer and a form record is most easily pictured as an “arc”, or directed edge, leading to a node labeled with the other data, in this case, a letter and a number.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Exposition 1.1
• https://inquiryintoinquiry.com/2024/06/09/theme-one-program-exposition-1-b/

Theme One is a program for constructing and transforming a particular species of graph‑theoretic data structures, forms designed to support a variety of fundamental learning and reasoning tasks.

The program evolved over the course of an exploration into the integration of contrasting types of activities involved in learning and reasoning, especially the types of algorithms and data structures capable of supporting all sorts of inquiry processes, from everyday problem solving to scientific investigation. In its current state, Theme One integrates over a common data structure fundamental algorithms for one type of inductive learning and one type of deductive reasoning.

We begin by describing the class of graph-theoretic data structures used by the program, as determined by their local and global features. It will be the usual practice to shift around and view these graphs at many different levels of detail, from their abstract definition to their concrete implementation, and many points in between.

The main work of the Theme One program is achieved by building and transforming a single species of graph-theoretic data structures. In their abstract form these structures are closely related to the graphs called cacti and conifers in graph theory, so we’ll generally refer to them under those names.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 6
• https://inquiryintoinquiry.com/2022/08/20/theme-one-program-motivation-6-2/

Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here.

In one of the projects I submitted toward a Master’s in psychology I used the Theme One program to analyze samples of data from my advisor’s funded research study on family dynamics. In one phase of the study observers viewed video-taped sessions of family members (parent and child) interacting in various modes (“play” or “work”) and coded qualitative features of each moment’s activity over a period of time.

The following page describes the application in more detail and reflects on its implications for the conduct of scientific inquiry in general.

Exploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data

In this application a “phrase” or “string” is a fixed-length sequence of qualitative features and a “clause” or “strand” is a sequence of such phrases delimited by what the observer judges to be a significant pause in the action.

In the qualitative research phases of the study one is simply attempting to discern any significant or recurring patterns in the data one possibly can.

In this case the observers are tokenizing the observations according to a codebook that has passed enough intercoder reliability studies to afford them all a measure of confidence it captures meaningful aspects of whatever reality is passing before their eyes and ears.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 5
• https://inquiryintoinquiry.com/2022/08/20/theme-one-program-motivation-5-2/

Since I’m working from decades-old memories of first inklings I thought I might peruse the web for current information about Zipf’s Law. I see there is now something called the Zipf–Mandelbrot (and sometimes –Pareto) Law and that was interesting because my wife Susan Awbrey made use of Mandelbrot’s ideas about self-similarity in her dissertation and communicated with him about it. So there’s more to read up on.

Just off-hand, though, I think my Learner is dealing with a different problem. It has more to do with the savings in effort a learner gets by anticipating future experiences based on its record of past experiences than the savings it gets by minimizing bits of storage as far as mechanically possible. There is still a type of compression involved but it’s more like Korzybski’s “time-binding” than space-savings proper. Speaking of old memories …

The other difference I see is that Zipf’s Law applies to an established and preferably large corpus of linguistic material, while my Learner has to start from scratch, accumulating experience over time, making the best of whatever data it has at the outset and every moment thereafter.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 4
• https://inquiryintoinquiry.com/2022/08/19/theme-one-program-motivation-4-2/

From Zipf’s Law and the category of “things that vary inversely with frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient codes.

In its first application the environment the Learner has to learn is the usage behavior of its user, as given by finite sequences of characters from a finite alphabet, which sequences of characters might as well be called “words”, together with finite sequences of those words which might as well be called “phrases” or “sentences”. In other words, Job One for the Learner is the job of constructing a “user model”.

In that frame of mind we are not seeking anything so grand as a Universal Induction Algorithm but simply looking for any approach to give us a leg up, complexity wise, in Interactive Real Time.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 3
• https://inquiryintoinquiry.com/2022/08/18/theme-one-program-motivation-3-2/

Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s. Along with its research program the lab did a lot of work on augmentative communication technology for limited mobility users and the observations I made there prompted the first inklings of my Learner program.

Early in that period I visited John’s course in mathematical linguistics, which featured Laws of Form among its readings, along with the more standard fare of Wall, Chomsky, Jackendoff, and the Unified Science volume by Charles Morris which credited Peirce with pioneering the pragmatic theory of signs. I learned about Zipf’s Law relating the lengths of codes to their usage frequencies and I named the earliest avatar of my Learner program XyPh, partly after Zipf and playing on the xylem and phloem of its tree data structures.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 2.2
• https://inquiryintoinquiry.com/2022/08/17/theme-one-program-motivation-2-2/

As I mentioned, work on those two projects proceeded in a parallel series of fits and starts through interwoven summers for a number of years, until one day it dawned on me how the Learner, one of whose aliases was Index, could be put to work helping with sundry substitution tasks the Modeler needed to carry out.

So I began integrating the functions of the Learner and the Modeler, at first still working on the two component modules in an alternating manner, but devoting a portion of effort to amalgamating their principal data structures, bringing them into convergence with each other, and unifying them over a common basis.

Another round of seasons and many changes of mind and programming style, I arrived at a unified graph-theoretic data structure, strung like a wire through the far‑flung pearls of my programmed wit. But the pearls I polished in alternate years maintained their shine along axes of polarization whose grains remained skew in regard to each other. To put it more plainly, the strategies I imagined were the smartest tricks to pull from the standpoint of optimizing the program’s performance on the Learning task I found the next year were the dumbest moves to pull from the standpoint of its performance on the Reasoning task. I gradually came to appreciate that trade-off as a discovery.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 2.1
• https://inquiryintoinquiry.com/2022/08/17/theme-one-program-motivation-2-2/

A side-effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding each other, even when those two styles of thinking inhabit the very same soul.

The way it came about was this. The code from which the program is currently assembled initially came from two distinct programs, ones I developed in alternate years, at first only during the summers.

In the Learner program I sought to implement a Humean empiricist style of learning algorithm for the adaptive uptake of coded sequences of occurrences in the environment, say, as codified in a formal language. I knew all the theorems from formal language theory telling how limited any such strategy must ultimately be in terms of its generative capacity, but I wanted to explore the boundaries of that capacity in concrete computational terms.

In the Modeler program I aimed to implement a variant of Peirce’s graphical syntax for propositional logic, making use of graph-theoretic extensions I had developed over the previous decade.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

Theme One Program • Motivation 1
• https://inquiryintoinquiry.com/2022/08/16/theme-one-program-motivation-1-2/

The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”.

I am thinking of learning in the sense of learning about an environment, in essence, gaining information about the nature of an environment and being able to apply the information acquired to a specific purpose.

Under the heading of reasoning I am simply lumping together all the ordinary sorts of practical activities which would probably occur to most people under that name.

There is a natural relation between the tasks. Learning the character of an environment leads to the recognition of laws which govern the environment and making full use of that recognition requires the ability to reason logically about those laws in abstract terms.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism

#ThemeOneProgram • #SurveyPage
• https://inquiryintoinquiry.com/2022/06/12/survey-of-theme-one-program-4/

A program I worked on all through the 80s aimed to develop #Algorithms and #DataStructures for integrating #EmpiricalLearning and #LogicalReasoning. I had earlier developed programs for #Learning #TwoLevelFormalLanguages and for #PropositionalLogic #ConstraintSatisfaction based on C.S. #Peirce's #LogicalGraphs. Getting those 2 faculties to work together meant integrating the ways of #Empiricism and #Rationalism.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism
#ModelTheory #ProofTheory #Semiotics
#ParallelDistributedProcessing #PDP
#Grossberg #McClelland #Rumelhart

#ThemeOneProgram • #SurveyPage
• https://inquiryintoinquiry.com/2022/06/12/survey-of-theme-one-program-4/

A program I worked on all through the 80s aimed to develop #Algorithms and #DataStructures for integrating #EmpiricalLearning and #LogicalReasoning. I had earlier developed programs for #Learning #TwoLevelFormalLanguages and for #PropositionalLogic #ConstraintSatisfaction based on C.S. #Peirce's #LogicalGraphs. Getting those 2 faculties to work together meant integrating the ways of #Empiricism and #Rationalism.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism
#ModelTheory #ProofTheory #Semiotics
#ParallelDistributedProcessing #PDP
#Grossberg #McClelland #Rumelhart

#ThemeOneProgram • #SurveyPage
• https://inquiryintoinquiry.com/2022/06/12/survey-of-theme-one-program-4/

A program I worked on all through the 80s aimed to develop #Algorithms and #DataStructures for integrating #EmpiricalLearning and #LogicalReasoning. I had earlier developed programs for #Learning #TwoLevelFormalLanguages and for #PropositionalLogic #ConstraintSatisfaction based on C.S. #Peirce's #LogicalGraphs. Getting those 2 faculties to work together meant integrating the ways of #Empiricism and #Rationalism.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism
#ModelTheory #ProofTheory #Semiotics
#ParallelDistributedProcessing #PDP
#Grossberg #McClelland #Rumelhart