Monthly Archives: December 2013

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 , , , , , , , , , , , , , , , , | 5 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 , , , , , , , , , , , , , , , , | 9 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 Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Logic, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Minimal Negation Operators, Peirce, Peirce List, Physics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown, Systems Theory | Tagged , , , , , , , , , , , , , , , , , , , | 2 Comments

Icon, Likeness, Likely Story, Likelihood, Probability : 3

Posted on December 12, 2013 by Jon Awbrey

Re: Peirce List Discussion • Phyllis Chiasson A more complete excerpt and the translator’s notes are very helpful here. A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which … Continue reading →

Posted in Aristotle, C.S. Peirce, Enthymeme, Icon Index Symbol, Logic, Peirce, Peirce List, Probability, Probable Reasoning, Semiotics, Sign Relations | Tagged , , , , , , , , , , | Leave a comment

Icon, Likeness, Likely Story, Likelihood, Probability : 2

Posted on December 11, 2013 by Jon Awbrey

Re: Peirce List Discussion • Phyllis Chiasson I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some … Continue reading →

Posted in Aristotle, C.S. Peirce, Icon Index Symbol, Logic, Peirce, Peirce List, Probability, Probable Reasoning, Semiotics, Sign Relations | Tagged , , , , , , , , , | Leave a comment

Icon, Likeness, Likely Story, Likelihood, Probability : 1

Posted on December 11, 2013 by Jon Awbrey

Re: Peirce List Discussion • Benjamin Udell • Michael Shapiro Here’s a likely locus classicus for “icon” in its logical sense: A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for … Continue reading →

Posted in Aristotle, C.S. Peirce, Icon Index Symbol, Logic, Peirce, Peirce List, Probability, Probable Reasoning, Semiotics, Sign Relations | Tagged , , , , , , , , , | 1 Comment

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 Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Logic, Inquiry, Inquiry Driven Systems, Isomorphism, Laws of Form, Logic, Logical Graphs, Minimal Negation Operators, Peirce, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown, Systems Theory | Tagged , , , , , , , , , , , , , , , , , | 3 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, Cactus Graphs, Computational Complexity, Differential Logic, Inquiry, Inquiry Driven Systems, Isomorphism, Logic, Logical Graphs, Peirce, Propositional Calculus, Semiotics, Sign Relations, Systems Theory | Tagged , , , , , , , , , , , , , | 3 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, Computational Complexity, Differential Logic, Equational Inference, Fixation of Belief, General Problem Solver, Hill Climbing, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Peirce, Physics, Propositional Calculus, Scientific Inquiry, Scientific Method, Semiotics, Sisyphus, Spencer Brown, Systems Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , | 3 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, Equational Inference, Fixation of Belief, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Peirce, Peirce List, Physics, Propositional Calculus, Scientific Inquiry, Scientific Method, Semiotics, Spencer Brown, Systems Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , | 3 Comments