Category Archives: C.S. Peirce

¿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 →

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¿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 →

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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

Doubt, Uncertainty, Dispersion, Entropy • 2

Posted on July 5, 2014 by Jon Awbrey

Re: John Baez • Entropy and Information in Biological Systems To develop the concept of evolutionary games as “learning” processes in which information is gained over time. A fund of ideas toward that end can be found in the work … Continue reading →

Posted in Animata, C.S. Peirce, Cybernetics, Dispersion, Doubt, Entropy, Evolution, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Learning Theory, Uncertainty | 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 →

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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 →

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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 →

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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