Category Archives: Logic

¿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

Doubt, Uncertainty, Dispersion, Entropy • 1

Posted on July 1, 2014 by Jon Awbrey

Re: Peirce List • Stephen Rose Just a note to anchor a series of recurring thoughts that come to mind in relation to a Peirce List discussion of entropy etc., but I won’t have much to say on the bio-chemico-physico-thermo-dynamic … Continue reading →

Posted in Animata, Aristotle, C.S. Peirce, Cybernetics, Differential Logic, Dispersion, Doubt, Entropy, Information, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Peirce, Semiotic Information, Semiotics, Sign Relations, Uncertainty | 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

Peirce’s 1870 “Logic of Relatives” • Comment 12.3

Posted on June 12, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 12.3 We now have two ways of computing a logical involution raising a dyadic relative term to the power of a monadic absolute term, for example, for “lover of every woman”. The first method … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 11 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 12.2

Posted on June 11, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 12.2 Let us make a few preliminary observations about the operation of logical involution which Peirce introduces in the following words. I shall take involution in such a sense that will denote everything … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 11 Comments