Category Archives: Mathematics

Frankl, My Dear • 3

Posted on September 17, 2014 by Jon Awbrey

Re: Dick Lipton & Ken Regan • (1) • (2) Here’s a few pages on differential logic, whose ideas I’ll be trying out in the present setting: Differential Logic : Introduction Differential Propositional Calculus Differential Logic and Dynamic Systems I … Continue reading →

Posted in Boolean Algebra, Boolean Functions, Computational Complexity, Differential Logic, Frankl Conjecture, Logic, Logical Graphs, Mathematics, Péter Frankl | Tagged , , , , , , , , | 10 Comments

Consequences of Triadic Relation Irreducibility • 2

Posted on September 14, 2014 by Jon Awbrey

From time to time I come to the realization that there are ways of reading Peirce that make no sense to me.  When I stop to think about the potential sources of that evident divergence from common sense, the first … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , | Leave a comment

Consequences of Triadic Relation Irreducibility • 1

Posted on September 13, 2014 by Jon Awbrey

2014 Sep 10 I will have to be out of the loop for some days, but this post will give me a peg on which I can hang a few thoughts via mobile device that have been tugging at the … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , | Leave a comment

Frankl, My Dear • 2

Posted on September 11, 2014 by Jon Awbrey

Re: Dick Lipton & Ken Regan • (1) • (2) Supplied by the cache of definitions from Post 1, I can return to the passage from (2) that seemed to jog a bit of memory and see if what I imagined … Continue reading →

Posted in Boolean Algebra, Boolean Functions, Computational Complexity, Differential Logic, Frankl Conjecture, Logic, Logical Graphs, Mathematics, Péter Frankl | Tagged , , , , , , , , | 10 Comments

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