Tag Archives: Mathematics

Precursors Of Category Theory • 3

Posted on January 3, 2014 by Jon Awbrey

Act only according to that maxim by which you can at the same time will that it should become a universal law. Immanuel Kant (1785) Precursors Of Category Theory Peirce Cued by Kant’s idea on the function of concepts in … Continue reading →

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 8 Comments

Precursors Of Category Theory • 2

Posted on December 30, 2013 by Jon Awbrey

Thanks to art, instead of seeing one world only, our own, we see that world multiply itself and we have at our disposal as many worlds as there are original artists … ☙ Marcel Proust Precursors Of Category Theory When … Continue reading →

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 6 Comments

Precursors Of Category Theory • 1

Posted on December 20, 2013 by Jon Awbrey

A few years back I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, thorough Kant and Peirce, Hilbert and Ackermann, to contemporary mathematical use.  Perhaps a few will … Continue reading →

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 10 Comments

Alpha Now, Omega Later • 7

Posted on December 19, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Theorems From Physics? In a way, the relation between “physics space” and “information space” is one of the topics I address in my work on inquiry driven systems.  Here is a pertinent place in … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 4 Comments

Alpha Now, Omega Later • 6

Posted on December 6, 2013 by Jon Awbrey

Re: Alpha Now, Omega Later • Theorems From Physics? • Isomorphism Is Where It’s At In the late 1970s a number of problems in combinatorics and graph theory that I really wanted to know the answers to had driven me … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 5 Comments

Alpha Now, Omega Later • 5

Posted on December 4, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Isomorphism Is Where It’s At “Are there more good cases of isomorphism to study?” Just off the top of my head, a couple of examples come to mind. Sign Relations.  In computational settings, … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 6 Comments

Alpha Now, Omega Later • 4

Posted on December 3, 2013 by Jon Awbrey

Re: Cristopher Moore on Theorems From Physics? It is critically important to distinguish between the objective landscape, the boolean functions as mathematical objects, and the syntactic landscape, the particular formal language we are using as a propositional calculus to denote … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 6 Comments

Alpha Now, Omega Later • 3

Posted on December 2, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Theorems From Physics? Bits of Synchronicity … What kind of information process is scientific inquiry? What kinds of information process are involved in the various types of inference — abductive, deductive, inductive — … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 6 Comments

Alpha Now, Omega Later • 2

Posted on November 30, 2013 by Jon Awbrey

It’s been a while since I threaded this thread — and then there were all the delightful distractions of the holiday convergence — so let me refresh my memory as to what drew me back to these environs. I’m still … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 6 Comments

Alpha Now, Omega Later • 1

Posted on November 16, 2013 by Jon Awbrey

I am still in the middle of trying to catch up on some long put-off work but recent discussions of logical graphs and physics and the like on the Peirce List have bestirred me from my grindstone long enough to … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 8 Comments