home.social

#logic-of-science — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #logic-of-science, aggregated by home.social.

fetched live
  1. Information = Comprehension × Extension • Preamble 1
    • inquiryintoinquiry.com/2026/06

    Perhaps the best perspective from which to bring the connection between the theory of signs and the theory of inquiry into its proper focus is Peirce's own Theory of Information, which he began setting forth in lectures at Harvard and the Lowell Institute in 1865 and 1866. Peirce encapsulates the elements of his theory in the following formula.

    • Information = Comprehension × Extension

    In the Resources below I link to my study of Peirce's 1865–1866 Lectures on the Logic of Science, with selections from the lectures and my commentary on them.

    Ten 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.

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

  2. Survey of Pragmatic Semiotic Information • 9

    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.

    Inference, Information, Inquiry

    Pragmatic Semiotic Information

    Semiotics, Semiosis, Sign Relations

    Sign Relations, Triadic Relations, Relation Theory

    • Blog Series • (1)

    Excursions

    Blog Dialogs

    References

    • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”.  Online.
    • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

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

    #Abduction #CSPeirce #Communication #Control #Cybernetics #Deduction #Determination #Discovery #Doubt #Epistemology #FixationOfBelief #Induction #Information #InformationComprehensionExtension #InformationTheory #Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #Interpretation #Invention #Knowledge #LearningTheory #Logic #LogicOfRelatives #LogicOfScience #Mathematics #PhilosophyOfScience #PragmaticInformation #ProbableReasoning #ProcessThinking #RelationTheory #ScientificInquiry #ScientificMethod #Semeiosis #Semiosis #SemioticInformation #Semiotics #SignRelationalManifolds #SignRelations #Surveys #TriadicRelations #Uncertainty #Visualization
  3. Information = Comprehension × Extension • Selection 2.3
    • inquiryintoinquiry.com/2024/10

    ❝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
    • inquiryintoinquiry.com/2024/03

    OEIS Wiki • Information = Comprehension × Extension
    • oeis.org/wiki/Information_%3D_

    C.S. Peirce • Upon Logical Comprehension and Extension
    • peirce.sitehost.iu.edu/writing

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

  4. Information = Comprehension × Extension • Selection 2.2
    • inquiryintoinquiry.com/2024/10

    ❝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

  5. Information = Comprehension × Extension • Selection 2.1
    • inquiryintoinquiry.com/2024/10

    Re: Information = Comprehension × Extension • Selection 1
    • inquiryintoinquiry.com/2024/10

    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

  6. Information = Comprehension × Extension • Selection 1.2
    • inquiryintoinquiry.com/2024/10

    ❝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

  7. Information = Comprehension × Extension • Selection 1.1
    • inquiryintoinquiry.com/2024/10

    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
    • inquiryintoinquiry.com/2024/03

    OEIS Wiki • Information = Comprehension × Extension
    • oeis.org/wiki/Information_%3D_

    C.S. Peirce • Upon Logical Comprehension and Extension
    • peirce.sitehost.iu.edu/writing

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

  8. Information = Comprehension × Extension • Preamble
    • inquiryintoinquiry.com/2024/10

    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
    • inquiryintoinquiry.com/2024/03

    OEIS Wiki • Information = Comprehension × Extension
    • oeis.org/wiki/Information_%3D_

    C.S. Peirce • Upon Logical Comprehension and Extension
    • peirce.sitehost.iu.edu/writing

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

  9. Pragmatic Truth • 3

    Truth Predicates

    An inquiry into the character of truth generally begins with the idea of an informative, meaningful, or significant element, the goodness of whose information, meaning, or significance may be put in question and needs to be evaluated.

    Depending on context, the element at hand may be called an ad, address, advertisement, alias, artefact, article, badge, ballot, bit, blank, blip, book, brochure, bulletin, byte, certificate, chapter, character, clause, code, colophon, command, constant, dance, dash, datum, design, diagram, digit, discussion, dissertation, document, dot, drawing, emblem, emoji, epigram, epistle, epitaph, epitext, epithet, essay, expression, fable, facsimile, figure, file, film, flag, fugue, gesture, glyph, graph, graphic, guarantee, guess, hieroglyphic, hologram, holotext, hypothesis, icon, identifier, image, impression, index, indicator, inscription, instruction, jot, khipu, label, letter, literal, logo, manual, map, mark, message, myth, note, numeral, oeuvre, opera, opinion, opus, organon, ostrakon, page, pamphlet, parable, performance, photo, phrase, picture, piece, plan, play, plot, poem, pointer, post, prescription, presentation, program, prospectus, proxy, pseudonym, query, question, quipu, recipe, replica, report, representation, representative, rune, sample, scat, schematic, scheme, score, scrawl, scribble, script, sculpture, semaphore, seme, sentence, sigil, sign, signal, signature, simulacrum, sketch, song, specimen, spell, spoor, stimulus, story, string, study, symbol, symphony, symptom, tag, tale, talk, tally, tattoo, term, text, thought, tick, ticket, title, token, trace, track, tune, typo, utterance, variable, verse, veto, video, vote, warrant, word, work, and so on.

    However that may be, one has the task of judging whether the bearers of information, meaning, or significance are indeed truth‑bearers or not.  That judgment is typically expressed in the form of a specific truth predicate, whose positive application to a sign, or so on, asserts the truth of the sign.

    Considered within the broadest horizon, there is little reason to imagine the process of judging a work, which leads to a predication of false or true, is necessarily amenable to formalization, and that task may always remain what is commonly called a judgment call.  But there are many well‑circumscribed domains where it is useful to consider disciplined forms of evaluation and the observation of those limits allows for the institution of what is called a method of judging truth and falsity.

    One of the first questions to be asked in this setting concerns the relationship between the significant performance and its reflective critique.  If one expresses oneself in a particular fashion, and you or someone adds “that’s true”, is there anything useful at all to be said in general terms about the relationship between those two acts?  For instance, does the critique add value to the expression criticized, does it say something significant in its own right, or is it but an insubstantial echo of the original sign?

    Resources

    cc: FB | Inquiry Driven Systems • Laws of Form • Mathstodon • Academia.edu
    cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

    #Aristotle #CSPeirce #Coherence #Concordance #Congruence #Consensus #Convergence #Correspondence #Dewey #FixationOfBelief #Information #Inquiry #JohnDewey #Kant #Logic #LogicOfScience #Method #Peirce #Philosophy #PragmaticMaxim #Pragmatism #Semiotics #SignRelations #TriadicRelations #Truth #TruthTheory #WilliamJames
  10. Survey of Pragmatic Semiotic Information • 8
    • inquiryintoinquiry.com/2024/03

    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
    • oeis.org/wiki/Information_%3D_

    { Information = Comprehension × Extension }
    • inquiryintoinquiry.com/2016/05

    { Information = Comprehension × Extension } • Revisited
    • inquiryintoinquiry.com/2019/01

    Pragmatic Semiotic Information • Ψ
    • inquiryintoinquiry.com/2023/07

    Pragmatic Semiotic Information
    • oeis.org/wiki/Pragmatic_Semiot

    Peirce's Logic Of Information
    • oeis.org/wiki/User:Jon_Awbrey/

    Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”
    • peirce.sitehost.iu.edu/writing

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

  11. Scientific Attitude • 1
    • inquiryintoinquiry.com/2015/03

    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

  12. Survey of Pragmatic Semiotic Information • 7
    • inquiryintoinquiry.com/2023/07

    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

  13. Pragmatic Semiotic Information • Ψ
    • inquiryintoinquiry.com/2023/07

    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

  14. 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

    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

  15. @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.

  16. #Definition and #Determination • #SurveyPage
    • inquiryintoinquiry.com/2020/09

    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

    3/3

  17. #Definition and #Determination • #SurveyPage
    • inquiryintoinquiry.com/2020/09

    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/

  18. The Difference That Makes A Difference That Peirce Makes • 29

    Re: Ontolog Forum • Jon Awbrey • John Sowa

    We are called to recall Peirce’s deeper meanings
    of ideas like Form (think Platonic Ideas and the
    way Aristotle compounded Form and Matter).  When
    we come to Sentiment, by any other word, Feeling,
    that is the medium of Aesthetics, which concerns
    Beauty in no merely skin-deep sense but all that
    embodies and manifests ‘the admirable in itself’,
    thus every form of life worth living.  So Peirce
    stands the normative science of Logic on grounds
    within the pale of Ethics and fixes the sight of
    Ethics on the prize Aesthetics picks to steer by.

    cc: Systems Science • Structural Modeling • Ontolog Forum • Laws of Form • Cybernetics

    #Analogy #CSPeirce #Communication #DescriptiveScience #FixationOfBelief #FormalSystems #Information #Inquiry #Logic #LogicOfRelatives #LogicOfScience #LogicalGraphs #Mathematics #NormativeScience #Paradigms #Peirce #PragmaticMaxim #Pragmatism #RelationTheory #Semiotics #SignRelations #TriadicRelations #Triadicity
  19. Icon Index Symbol • 15

    Questions Concerning Certain Faculties Claimed For Signs

    I put down the cup and turn to my mind.  It is up to my mind to find the truth.  But how?  What grave uncertainty, whenever the mind feels overtaken by itself;  when it, the seeker, is also the obscure country where it must seek and where all its baggage will be nothing to it.  Seek?  Not only that:  create.  It is face to face with something that does not yet exist and that only it can accomplish, and bring into its light.

    — Proust • In Search of Lost Time

    Re: Peirce List (1) (2) • Tom Gollier • Jerry Rhee • John Sowa

    That passage from Proust epitomizes for me one of the most distinctive features of the inquiry process, the fact that its object is a state of information that the inquisiturus, the agent of inquiry, may never have known before.

    I have thought of inquiry and intelligence in terms of cybernetic or system-theoretic processes ever since my first encounters with the works of Arbib, Ashby, Bateson, McCulloch, Wiener, Young, and others during my undergrad years.  In the early 90s I returned to grad school in a Systems Engineering program with the idea that I might be able to string together many loose threads of unfinished business that continued to tug at my brain.  Here’s a bit I wrote at the outset of that project, that comes to mind in this context:

    Prospects for Inquiry Driven Systems • Architecture of Inquiry

    It is important to remember that knowledge is a different sort of goal from the run-of-the-mill setpoints a system might have.  The typical goal is a state that a system has actually experienced many times before, like normal body temperature for a human being.  But a particular state of knowledge an intelligent system moves toward may be a state it has never been through before.  The fundamental equivocation on this point expressed in Plato’s Meno, whether learning is functionally equivalent to remembering, was discussed above.  In spite of this quibble, it still seems necessary to regard states of knowledge as a distinctive class.  The reasons for this may lie in the fact that a useful definition of inquiry for human beings necessarily involves a whole community of inquiry.

    Resources

    cc: Peirce List (1) (2)

    #Abduction #Algorithms #Animata #ArtificialIntelligence #AutomatedResearchTools #CSPeirce #Cognition #Computation #DataStructures #Deduction #IconIndexSymbol #Induction #Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #InterpretiveFrameworks #KnowledgeRepresentation #Logic #LogicOfRelatives #LogicOfScience #LogicalGraphs #ObjectiveFrameworks #Peirce #RelationTheory #Semiotics #SignRelations #TriadicRelations #Visualization
  20. Icon Index Symbol • 14

    Questions Concerning Certain Faculties Claimed For Signs

    Re: Peirce List (1) (2) (3) • Helmut Raulien
    Re: Icon Index Symbol • (10) (11) (12) (13)

    Let me sum up the main points of the above exchange before moving on.

    Mathematics is useful in our present endeavor because it treats relations in general.  In addition — and multiplication, too — mathematics is chock full of well-studied examples of triadic relations.  When it comes to the job of analyzing sign relations and teasing out their structures we can save ourselves a lot of trouble and trial and error by examining this record of prior art and adapting its methods to handle sign relations.

    On the other hand, there are hints in Peirce’s work of how triadic relations extend across a threshold of complexity in such a way that relations of all higher adicities can be analyzed in terms of 1-adic, 2-adic, and 3-adic relations.  This is where the analogy between Peirce’s category theory and mathematical category theory both forms and breaks.  The utility of categories in mathematical theory derives from the ubiquity of functions in mathematical practice, and functions are dyadic relations.  Still, triadic relations pervade the background of mathematical category theory, being visible in the triadic composition relation and in the concept of “natural transformations”, the clarification of which is one of the original motivations for the subject.  Bringing the triadic roots of category theory into higher relief is one of my motives for bringing about an encounter with Peirce’s categories, an effort to which I have given not a few years of thought.

    That brings us to the case of sign relations proper.  These types of triadic relations form our first stepping stones and also our first stumbling blocks in the inquiry into inquiry and I gave some indications why that might be true.  I don’t know if I can do better than that at this time, but I’ll think on it further after that all-essential secondness of caffeination.

    Resources

    cc: Peirce List (1) (2) (3)

    #Abduction #Algorithms #Animata #ArtificialIntelligence #AutomatedResearchTools #CSPeirce #Cognition #Computation #DataStructures #Deduction #IconIndexSymbol #Induction #Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #InterpretiveFrameworks #KnowledgeRepresentation #Logic #LogicOfRelatives #LogicOfScience #LogicalGraphs #ObjectiveFrameworks #Peirce #RelationTheory #Semiotics #SignRelations #TriadicRelations #Visualization
Share on Mastodon

Enter the server where you have an account.