"It is easy to be certain. One has only to be sufficiently vague."
–– Charles Sanders #Peirce
Striving for completeness may lead to posts that may feel "out of place,"
as @the_roamer has written.
#Drawing by #CharlesSandersPeirce
h/t Chris Campbell @ekaelement.bsky.social
( on #bluesky )
My inaugural lecture is now online
https://media.ed.ac.uk/media/Professor+Lauren+Hall-Lew+Inaugural+Lecture/1_upsi58yk
#sociophonetics
#sociolinguistics
#linguistics
#phonetics
#semiotics
#Peirce
#indexicality
#social
#meaning
#research
#academic
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#lecture
#Arizona
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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
Originally, I wanted to refresh my memory of the history of #pragmatism. But I quickly derailed in reading about the NOR gate, which carries also the honory name "#Peirce Operator". Because Peirce proved that NOR and NAND each are universal gates, capable of constructing any other logic gate. For example: an AA NAND and BB NAND that feed into another A'B' NAND build an OR gate.
I am a bit puzzled that I didn't realize this despite my programming excercises and vast experience with Minecraft Redstone. And, yes, a redstone torch is indeed a Peirce Gate. So you may call it Peirce Torch, if you want.
It's a beautiful sunday. #logic
https://arxiv.org/pdf/2404.18795
When Lawvere meets Peirce: an equational
presentation of boolean hyperdoctrines
by Filippo Bonchi, Alessandro Di Giorgio, Davide Trotta
Pushing algebraization of logic another step forward.
With this approach logical deductions can be made using straightforward equation manipulations.
This kind of bridge will eventually become very useful for knowledge representation!
As knowledge representation is mostly built on description logics, the community so far doesn’t appreciate the potential to enrich its toolset with algebraic methods and other existing mathematical machinery.
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/
Consider De Morgan's rules:
• ¬(A ∧ B) = ¬A ∨ ¬B
• ¬(A ∨ B) = ¬A ∧ ¬B
The common form exhibited by the two rules could be captured in a single formula by taking “o₁” and “o₂” as variable names ranging over a family of logical operators, then asking what substitutions for o₁ and o₂ would satisfy the following equation.
• ¬(A o₁ B) = ¬A o₂ ¬B
We already know two solutions to this “operator equation”, namely, (o₁, o₂) = (∧, ∨) and (o₁, o₂) = (∨, ∧). Wouldn't it be just like Peirce to ask if there are others?
Having broached the subject of “logical operator variables”, I will leave it for now in the same way Peirce himself did:
❝I shall not further enlarge upon this matter at this point, although the conception mentioned opens a wide field; because it cannot be set in its proper light without overstepping the limits of dichotomic mathematics.❞ (Peirce, CP 4.306).
Further exploration of operator variables and operator invariants treads on grounds traditionally known as second intentional logic and “opens a wide field”, as Peirce says. For now, however, I will tend to that corner of the field where our garden variety logical graphs grow, observing the ways in which operative variations and operative themes naturally develop on those grounds.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/
In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables
Deep into Jane #Addams' writings and works at the moment. Can't shake the feeling that the most fruitful reconstruction we could work on #pragmatism studies would involve raising her work to its rightful level of attention alongside the three classical "founders" of pragmatism, i.e. #Peirce, #James, #Dewey. The sheer depth of influence on Dewey from Addams' insights, resulting from her own hands-on cooperative work at Hull House, is as staggering as it is inspiring.
In the Way of Inquiry • Initial Unpleasantness
• https://inquiryintoinquiry.com/2023/01/08/in-the-way-of-inquiry-initial-unpleasantness-a/
Clouds and thunder:
The image of Difficulty at the Beginning.
Thus the superior man
Brings order out of confusion.
— I Ching ䷂ Hexagram 3
Inquiry begins in doubt, a debit of certainty and a drought of information, never a pleasant condition to acknowledge, and one of the primary obstacles to inquiry may be reckoned as owing to the onus one naturally feels on owning up to that debt. Human nature far prefers to revel in the positive features of whatever scientific knowledge it already possesses and the mind defers as long as possible the revolt it feels arising on facing the uncertainties that still persist, the “nots” and “not yets” it cannot as yet and ought not deny.
Reference —
The I Ching, or Book of Changes, R. Wilhelm and C.F. Baynes (trans.), Foreword by C.G. Jung, Bollingen Series 19, Princeton University Press, Princeton, NJ. 1st edition 1950, 2nd edition 1961, 3rd edition 1967.
Overview —
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview
Obstacles —
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_5#Obstacles
#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Semiotics #SignRelations #Semiositis #ObstaclesToInquiry
In the Way of Inquiry • Obstacles
• https://inquiryintoinquiry.com/2023/01/07/in-the-way-of-inquiry-obstacles-a/
❝Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:
❝Do not block the way of inquiry.❞
C.S. Peirce, Collected Papers, CP 1.135–136.
From an unpaginated ms. “F.R.L.”, c. 1899.
Often the biggest obstacle to learning more is the need to feel you already know. And yet there are some things you know, at least, compared to other things, and it makes sense to use what you already know well enough to learn what you need to know better. The question is, how do you know which is which? What test can tell what is known so well it can be trusted in learning what is not?
One way to test a supposed knowledge is to try and formulate it in such a way it can be taught to other people. A related test, harder in some ways but easier in others, is to try and formalize knowledge so completely that even a computer can go through the motions supposed to be definitive of its practice.
Both ways of testing a supposition of knowledge depend on putting knowledge in forms which can be communicated or transported from one medium or system of interpretation to another. Knowledge already in a concrete form takes no more than a simple reformation or transformation, otherwise it takes a more radical metamorphosis, from a wholly disorganized condition to the first inklings of a portable or sharable form.
#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Semiotics #SignRelations #Semiositis #ObstaclesToInquiry
In the Way of Inquiry • Recircus
• https://inquiryintoinquiry.com/2023/01/06/in-the-way-of-inquiry-recircus-a/
❝I must lie down where all the ladders start
In the foul rag and bone shop of the heart.❞
— W.B. Yeats
• https://web.archive.org/web/20200402124816/https://www.web-books.com/Classics/Poetry/Anthology/Yeats/Circus.htm
I have in mind circling back to a point in my project on Inquiry Driven Systems, namely, the chapter addressing various Obstacles to the Project.
Overview
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview
Obstacles
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_5#Obstacles
#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Semiotics #SignRelations #Semiositis #ObstaclesToInquiry
Sigh. I just published a Medium Essay regarding my discovery of Dewey's backsliding endorsement of Peirce's vision of scientific inquiry asymptotically approaching universal agreement: https://ironick.medium.com/deweys-bewildering-anti-melioristic-backsliding-scientific-inquiry-is-only-justified-by-a-remote-ca3573c35285
#pragmatism
#Peirce
#Dewey
#Meliorism
Calling all #Peirce scholars: what is going on with the 8th Lowell Lecture? It seems to carry at least three different titles ("How To Theorize," "Abduction," "On Selecting Hypotheses") thus rendering it pretty hard to find a copy of.
This is my first bibliographic leap into Peirce beyond his most well-known texts... is it always this complicated!? Or am I just even more tired than I think today?
#Oppenheimer quoting both William #James and Charles #Peirce in this clip on the role of analogy in science.
I'm guessing different people must draw the distinction differently. Coming from a #Peirce #Whitehead #Pragmatism + #ProcessThinking tradition, I personally view computations as processes.
For example, people of that persuasion will tend to give a process like #Inquiry equal billing with the corresponding product we all know and love as #Knowledge and maybe even consider it more fundamental.