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

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

Scientific Attitude • 1
• https://inquiryintoinquiry.com/2015/03/10/scientific-attitude-1/

There is an outlook on the world I call the Scientific Attitude (SA). There are times when the letter “A” is better served by apperception, approach, or attunement, but attitude will do for a start.

The scientific attitude accepts appearances, as appearances, but it does not stop there — it inquires after the possible realities that would both save and solve the appearances.

Reality is what persists and the scientific attitude accepts its limitation to what persists. Thisness and thatness may come and go, but scientific knowledge rests on results that are reproducible. It is knowledge of particulars in general terms.

#Appearance #Epistemology #Generality #Haecceity #Inquiry
#InquiryIntoInquiry #Knowledge #Logic #LogicOfScience
#PhilosophyOfScience #PragmaticMaxim #Reality #Reproducibility
#Science #ScientificAttitude #ScientificMethod

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

@maxsnew

#Logic is of course classically recognized as a #NormativeScience and C.S. #Peirce wrote a lot about the #LogicOfScience, his analysis of #ScientificMethod into three types of inference — #Abduction, #Deduction, and #Induction.

#Definition and #Determination • #SurveyPage
• https://inquiryintoinquiry.com/2020/09/06/survey-of-definition-and-determination-1/

That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination. There are copies of those selections at the following sites. (See the above-linked blog page.)

#AI #AdaptiveSystems #IntelligentSystems #InquiryDrivenSystems
#Peirce #Semiotics #Semeiotics #SignRelations #LogicOfScience

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#Definition and #Determination • #SurveyPage
• https://inquiryintoinquiry.com/2020/09/06/survey-of-definition-and-determination-1/

Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as #Peirce used them in his #Logic and #Semiotics but as researchers in #ComputerScience, #Cybernetics, #Physics, and #SystemsScience found themselves forced to revisit in later years.

#AI #AdaptiveSystems #IntelligentSystems #InquiryDrivenSystems
#Semeiotics #SignRelations #LogicOfScience

2/

#Definition and #Determination • #SurveyPage
• https://inquiryintoinquiry.com/2020/09/06/survey-of-definition-and-determination-1/

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a #SystemsEngineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from #Signs and #ScientificInquiry to #Logic and #InformationTheory.

#AI #AdaptiveSystems #IntelligentSystems #InquiryDrivenSystems
#Peirce #Semiotics #Semeiotics #SignRelations #LogicOfScience

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