#triadicrelations — Public Fediverse posts

Pragmatic Semiotic Information • Comment 3
• https://inquiryintoinquiry.com/2024/03/22/pragmatic-semiotic-information-comment-3/

Memories are coming back to me more through the association of ideas than ordered by time or place. I can sense, almost touch a tangle of thoughts interlaced with each other — the “information first” approach to ontology, the “arrows only”, element‑free angle on category theory, Peirce's relativity of generals and individuals dispatching nominalism once and for all — but there is at core a hard knot of ideas so tightly wound it makes it difficult to articulate the links or see the untying if there is one to make.

#Peirce #Logic #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #PragmaticSemioticInformation

Pragmatic Semiotic Information • Comment 2
• https://inquiryintoinquiry.com/2024/03/20/pragmatic-semiotic-information-comment-2/

I was at the time working as a “scanner” in the High Energy Physics Lab at Michigan State, sitting in a darkened room measuring tracks of particle interactions projected on a lighted scanning table from reels and reels of bubble chamber photographs gathered at CERN in a massive mad dash accelerator experiment some years before. For my part it was a menial job, 4pm to midnight every worklong day, but even a minion can imagine himself sharing in a hunt for the Ω⁻ particle, or whatever the Grail or Questying Beastie was at the time.

Meanwhile, in another part of the grove, I was spending my daylight hours checking off the final boxes for my Bachelor's degree, the main thing being to get my paper on Peirce, “Complications of the Simplest Mathematics”, approved as a substitute for a field study requirement. That had taken me two years' work in MSU's media library, poring through the microfilm reels of Peirce's Nachlass in search of enlightenment about a single puzzling paragraph I tripped over in his Collected Papers.

#Peirce #Logic #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #PragmaticSemioticInformation

Pragmatic Semiotic Information • Comment 1
• https://inquiryintoinquiry.com/2024/03/18/pragmatic-semiotic-information-comment-1/

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”, a transformation I noted mentally as \( X \to \mathrm{Info}(X) \) whenever I ran across it. 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 #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #PragmaticSemioticInformation

Pragmatic Semiotic Information • 2.1
• https://inquiryintoinquiry.com/2024/03/04/pragmatic-semiotic-information-2/

What is information that a sign may bear it?

Three more questions arise at this juncture.

• How is a sign empowered to contain information?
• What is the practical context of communication?
• Why do we care about these bits of information?

A very rough answer to these questions might begin as follows.

Human beings are initially concerned solely with their own lives but then a world obtrudes on their subjective existence and so they find themselves forced to take an interest in the objective realities of its nature.

In pragmatic terms our initial aim, concern, interest, object, or “pragma” is expressed by the verbal infinitive “to live”, but the infinitive is soon reified into the derivative substantial forms of “nature”, “reality”, “the world”, and so on. Against that backdrop we find ourselves cast as the protagonists on a “scene of uncertainty”.

The situation may be pictured as a juncture from which a manifold of options fan out before us. It may be an issue of “truth”, “duty”, or “hope”, the last codifying a special type of uncertainty as to “what regulative principle has any chance of success”, but the chief uncertainty is that we are called on to make a choice and all too often we have very little clue which of the options is most fit to pick.

#Peirce #Logic #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #PragmaticSemioticInformation

Pragmatic Semiotic Information • 1.2
• http://inquiryintoinquiry.com/2024/03/03/pragmatic-semiotic-information-1/

A question of what's true is a “descriptive question” and there exist what are called “descriptive sciences” devoted to answering descriptive questions about any domain of phenomena one might care to name.

A question of what's to do, in other words, what must be done by way of achieving a given aim, is a “normative question” and there exist what are called “normative sciences” devoted to answering normative questions about any domain of problems one might care to address.

Since information plays its role on a stage set by uncertainty, a big part of saying what information is will necessarily involve saying what uncertainty is. There is little chance the vagaries of a word like “uncertainty”, given the nuances of its ordinary, poetic, and technical uses, can be corralled by a single pen, but there do exist established models and formal theories which manage to address definable aspects of uncertainty and these do have enough uses to make them worth looking into.

#Peirce #Logic #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #PragmaticSemioticInformation

Pragmatic Semiotic Information • 1.1
• http://inquiryintoinquiry.com/2024/03/03/pragmatic-semiotic-information-1/

Information • What's it good for?

The good of information is its use in reducing our uncertainty about an issue which comes before us. But uncertainty comes in many flavors and so the information which serves to reduce uncertainty can be applied in several ways. The situations of uncertainty human agents commonly find themselves facing have been investigated under many headings, literally for ages, and the categories subtle thinkers arrived at long before the dawn of modern information theory still have their uses in setting the stage of an introduction.

Picking an example of a subtle thinker almost at random, the philosopher‑scientist Immanuel Kant surveyed the questions of human existence within the span of the following three axes.

• What's true?
• What's to do?
• What's to hope?

The third question is a bit too subtle for the present frame of discussion but the first and second are easily recognizable as staking out the two main axes of information theory, namely, the dual dimensions of “information” and “control”. Roughly the same space of concerns is elsewhere spanned by the dual axes of competence and performance, specification and optimization, or just plain knowledge and skill.

#Peirce #Logic #Inquiry #Information #Uncertainty #ScientificMethod
#Semiotics #Semiosis #RelationTheory #SignRelations #TriadicRelations
#InformationEqualsComprehensionTimesExtension #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