Tag Archives: Mathematics

Frankl, My Dear • 1

Posted on September 7, 2014 by Jon Awbrey

Re: Dick Lipton and Ken Regan • (1) • (2) I need to think a little about the context Lipton and Regan have wrapped around the Frankl Conjecture, if not exactly about the problem itself.  This will be a scratch-worky … Continue reading →

Posted in Boolean Algebra, Boolean Functions, Computational Complexity, Differential Logic, Frankl Conjecture, Logic, Logical Graphs, Mathematics, Péter Frankl | Tagged , , , , , , , , | 11 Comments

C.S. Peirce • Syllabus • Selection 1

Posted on August 24, 2014 by Jon Awbrey

Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903) An Outline Classification of the Sciences 180.   This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all … Continue reading →

Posted in C.S. Peirce, Classification, Foundations of Mathematics, Logic, Mathematics, Metaphysics, Normative Science, Peirce, Phenomenology, Philosophy, Philosophy of Mathematics, Philosophy of Science, References, Science, Sources | Tagged , , , , , , , , , , , , , , | 12 Comments

¿Shifting Paradigms? • 4

Posted on August 23, 2014 by Jon Awbrey

Re: Foundational Crisis? • Harvey Friedman 2014 Aug 22 Shock and surprise are relative to a prior state of belief.  The belief that mathematics reduces to logic, and that of a purely deductive sort from given axioms, seems to be … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Inquiry, Logic, Mathematics, Model Theory, Paradigms, Peirce, Programming, Proof Theory | Tagged , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 3

Posted on August 22, 2014 by Jon Awbrey

Re: What Is Good Mathematics? • Harvey Friedman 2014 Aug 17 Speaking of mathematics in the context of “general intellectual activity” brings to mind Raymond Wilder’s take on “mathematics as a cultural system”. I would like to keep that in … Continue reading →

Posted in C.S. Peirce, Foundations of Mathematics, Inquiry, Logic, Mathematics, Model Theory, Paradigms, Peirce, Programming, Proof Theory | Tagged , , , , , , , , , | Leave a comment

Forest Primeval → Riffs & Rotes

Posted on August 17, 2014 by Jon Awbrey

Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) • (6) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions … Continue reading →

Posted in Algebra, Animata, Arithmetic, C.S. Peirce, Catalan Numbers, Combinatorics, Forest Primeval, Foundations of Mathematics, Gödel Numbers, Graph Theory, Group Theory, H.W. Gould, Integer Sequences, Logic, Martin Gardner, Mathematics, Neil Sloane, Number Theory, Paradigmata, Planted Plane Trees, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 2

Posted on August 6, 2014 by Jon Awbrey

Re: Timothy Chow • Shifting Paradigms? 2014 Jul 31 I can’t remember when I first started playing with Gödel codings of graph-theoretic structures, which arose in logical and computational settings, but I remember being egged on in that direction by … Continue reading →

Posted in Algebra, Arithmetic, Combinatorics, Foundations of Mathematics, Graph Theory, Group Theory, Inquiry, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 1

Posted on August 6, 2014 by Jon Awbrey

Re: Dana Scott • Shifting Paradigms? 2014 Jul 28 This is very interesting to me, but not all my posts make it to the list, so I will spend a few days reflecting on it and post a comment on … Continue reading →

Posted in Foundations of Mathematics, Inquiry, Logic, Mathematics, Model Theory, Paradigms, Peirce, Programming, Proof Theory | Tagged , , , , , , , , | Leave a comment

Peirce’s 1870 “Logic of Relatives” • Intermezzo

Posted on June 18, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” Update • 10 April 2022 This brings me to the end of the notes on Peirce’s 1870 Logic of Relatives I began posting to the web in various discussion groups a dozen (now a score) … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 12 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 12.5

Posted on June 15, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 12.5 The equation can be verified by establishing the corresponding equation in matrices. If and are two 1-dimensional matrices over the same index set then if and only if for every   Thus, a routine way … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 13 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 12.4

Posted on June 14, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 12.4 Peirce next considers a pair of compound involutions, stating an equation between them analogous to a law of exponents from ordinary arithmetic, namely,  Then will denote whatever stands to every woman in … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 12 Comments