Tag Archives: Mathematics

Triadic Relations, Intentions, Fuzzy Subsets • 1

Posted on November 27, 2012 by Jon Awbrey

Re: Foundations Of Math Discussion • Lotfi Zadeh Way back during my first foundational crisis (1967–1972), I had been willing to consider almost any alternatives to the usual set theories, so I can remember looking at early accounts of fuzzy … Continue reading →

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , | 1 Comment

“Is it possible to advance philosophy today?”

Posted on November 25, 2012 by Jon Awbrey

Re: Stephen Rose Is it possible to advance philosophy today?  To do so, one would have to use terms that appear to have evolved in different disciplines to a point where dialog is almost impossible, even when desired. I suppose … Continue reading →

Posted in Logic, Mathematics, Peirce, Philosophy, Pragmatism, Science | Tagged , , , , , | 4 Comments

Sign Relational Manifolds • 5

Posted on November 1, 2012 by Jon Awbrey

Let me try to say in intuitive terms what I think is really going on here. The problem we face is as old as the problem of other minds, or intersubjectivity, or even commensurability, and it naturally involves a whole … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 4

Posted on October 30, 2012 by Jon Awbrey

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Sign Relational Manifolds • 3

Posted on October 23, 2012 by Jon Awbrey

I’m not sure when it was I first noticed the relationship between manifolds and semiotics but I distinctly recall the passage in Serge Lang’s Differential and Riemannian Manifolds which brought the triadic character of tangent vectors into high relief.  I … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Intentionality, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 2

Posted on October 22, 2012 by Jon Awbrey

A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 1

Posted on October 22, 2012 by Jon Awbrey

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce • Logic of Number (MS 229)

Posted on September 1, 2012 by Jon Awbrey

Selections from C.S. Peirce, [Logic of Number] (MS 229) I printed a paper on the Logic of Number in 1866, and it was not made up out of the first thoughts that came into my head about it, by any … Continue reading →

Posted in Abduction, Abstraction, C.S. Peirce, Deduction, Foundations of Mathematics, Logic, Mathematics, Peirce | Tagged , , , , , , , | 5 Comments

C.S. Peirce • New Elements (Καινὰ Στοιχεῖα) • Comment 1

Posted on August 11, 2012 by Jon Awbrey

Re: Peirce List • (1) • (2) Re: C.S. Peirce • New Elements (Καινὰ Στοιχεῖα) • 1 Interest in the reading of Peirce’s “New Elements” appears to be flagging of late, so I thought I might spice things up by … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Logic, Mathematics, Peirce, Semiotics | Tagged , , , , , | Leave a comment

C.S. Peirce • New Elements (Καινὰ Στοιχεῖα) • 1

Posted on August 9, 2012 by Jon Awbrey

Selections from C.S. Peirce, “New Elements (Καινὰ Στοιχεῖα)” Editors’ Headnote from The Essential Peirce, Volume 2 MS 517.  [First published in NEM 4:235–63.  This document was most probably written in early 1904, as a preface to an intended book on … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Logic, Mathematics, Peirce, Semiotics | Tagged , , , , , | 3 Comments