Tag Archives: Mathematics

“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 →

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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

Higher Order Sign Relations • 1

Posted on August 1, 2012 by Jon Awbrey

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.  They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to … Continue reading →

Posted in C.S. Peirce, Higher Order Sign Relations, Inquiry, Inquiry Into Inquiry, Logic, Mathematics, Recursion, Reflection, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , | 8 Comments