Tag Archives: Logic

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

Abduction, Deduction, Induction, Analogy, Inquiry • 1

Posted on August 16, 2012 by Jon Awbrey

Here are several excursions I made into the subjects of Abduction, Deduction, Induction, and Analogy, comparing Peirce’s first formulations with those in Aristotle and focusing on the ways those patterns of inference fit into the Cycle of Inquiry.  Much of … Continue reading →

Posted in Abduction, Analogy, Aristotle, Artificial Intelligence, C.S. Peirce, Deduction, Induction, Inquiry, Inquiry Driven Systems, Intelligent Systems Engineering, Logic, Mental Models, Peirce, Scientific Method, Semiotics, Systems | Tagged , , , , , , , , , , , , , , , | 6 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

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