Tag Archives: Mathematics

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

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

Notes on the Foundations of Mathematics • 2

Posted on July 5, 2012 by Jon Awbrey

Selections from R.L. Wilder, Introduction to the Foundations of Mathematics I.   The Axiomatic Method Since the axiomatic method as it is now understood and practiced by mathematicians is the result of a long evolution in human thought, we shall … Continue reading →

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

Notes on the Foundations of Mathematics • 1

Posted on July 5, 2012 by Jon Awbrey

Re: Peirce List Discussions 2012 • (1) • (2) • (3) • (4) Cf: Previous Discussions 2005–2006 • (A) • (B) • (C) I will have to be off and on the internet for the next month or so, and … Continue reading →

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

Approaching Peirce

Posted on June 30, 2012 by Jon Awbrey

I gradually grow accustomed to the distinct possibility that there will always be different readings, and even divergent interpretations of Peirce’s writings. Some of that appears to be a two- or three-cultures issue — the readings that befit aesthetic, cultural, … Continue reading →

Posted in Anthem, Inquiry, Logic, Mathematics, Peirce, Science, Semiotics | Tagged , , , , , , | 2 Comments

C.S. Peirce • Of Triadic Being

Posted on June 14, 2012 by Jon Awbrey

Selection from C.S. Peirce, “Some Amazing Mazes, Fourth Curiosity” (c. 1909) Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them; and for the present purpose such an enumeration would … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, References, Relation Theory, Semiotics, Sources | Tagged , , , , , , , | 3 Comments