Tag Archives: Mathematics

Relations & Their Relatives • Discussion 21

Posted on September 13, 2021 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin AS: Let me underline an important point:  first of all, we have found in nature and society one or another relation and ask how many members each example of this relation can have?  i.e. … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Riffs and Rotes • 59281

Posted on September 5, 2021 by Jon Awbrey

Re: Persiflage • 59281 Numberfile • What’s Special About 59,281? If is prime then the decimal expansion of repeats, so it makes sense to talk about the “average” of the digits of   The average can be bigger than equal … Continue reading →

Posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

On Reading Peirce • Discussion 2

Posted on September 5, 2021 by Jon Awbrey

Re: Peirce List • Jon Awbrey • Gary Richmond JA: Well, it’s true, all science is under construction. But not everything under construction is a science. GR: True.  But I’d suggest that there is no good reason to block the … Continue reading →

Posted in Anthem, C.S. Peirce, Inquiry, Inquiry Into Inquiry, Logic, Mathematics, Pragmatism, Science, Semiotics | Tagged , , , , , , , , | Leave a comment

On Reading Peirce • Discussion 1

Posted on September 4, 2021 by Jon Awbrey

Re: Peirce List • Jon Awbrey • John Sowa JFS: I detect a prebit of irony in your note. Although I respect Peirce’s ethics of terminology and observe his recommendations when they are appropriate and realistic, I also know that … Continue reading →

Posted in Anthem, C.S. Peirce, Inquiry, Inquiry Into Inquiry, Logic, Mathematics, Pragmatism, Science, Semiotics | Tagged , , , , , , , , | Leave a comment

Animated Logical Graphs • 81

Posted on August 26, 2021 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • A Negative Comment On Negations Minsky and Papert’s Perceptrons was the work that nudged me over the line from gestalt psychology, psychophysics, relational biology, etc. and made me believe AI could fly.  I later … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Relations & Their Relatives • Discussion 20

Posted on August 18, 2021 by Jon Awbrey

Re: Information = Comprehension × Extension Re: Category Theory • Morgan Rogers MR: Care to make any of this more precise? [The above] formula, for example? Yes, it will take some care to make it all more precise, and I’ve … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • Discussion 19

Posted on August 18, 2021 by Jon Awbrey

Re: Category Theory • Henry Story HS: Could one not say that Frege also had a three part relation?  I guess:  for singular terms their Sense and Reference. […] His argument could be explained very simply.  Imagine you start with … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • Discussion 18

Posted on August 17, 2021 by Jon Awbrey

Re: Relations & Their Relatives • 4 Re: Category Theory • Morgan Rogers MR: So a “sign process” would be a subset , where is a time domain? There are a couple of ways we usually see the concept of … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • 4

Posted on August 15, 2021 by Jon Awbrey

From Dyadic to Triadic to Sign Relations Peirce’s notation for elementary relatives was illustrated earlier by a dyadic relation from number theory, namely, the relation written for Cf: Relations & Their Relatives • 3 Table 1 shows the first few … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 8 Comments

Relations & Their Relatives • Comment 3

Posted on August 6, 2021 by Jon Awbrey

Here’s a couple of selections from Peirce’s 1870 Logic of Relatives bearing on the proper use of individuals in mathematics, and thus on the choice between nominal thinking and real thinking. 😸 Mathematical Demonstration & the Doctrine of Individuals • … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 9 Comments