Tag Archives: Logic

Propositions As Types Analogy • 1

Posted on January 29, 2013 by Jon Awbrey

Re: R.J. Lipton • Mathematical Tricks One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a … Continue reading →

Posted in Animata, C.S. Peirce, Combinator Calculus, Combinatory Logic, Curry–Howard Isomorphism, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, Proof Theory, Propositions As Types Analogy, Type Theory | Tagged , , , , , , , , , , , , | 3 Comments

Riffs and Rotes • 1

Posted on January 28, 2013 by Jon Awbrey

Re: Richard J. Lipton • Making Primes More Random There’s a study called generalized primes which investigates in a more general way the relationship between arbitrary elements called primes and the composites which can be formed from them according to … Continue reading →

Posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | 2 Comments

Triadic Relation Irreducibility • 2

Posted on January 18, 2013 by Jon Awbrey

Re: Peirce List • Matt Faunce • Jon Awbrey • Jon Awbrey Though my present object has more to do with the logical and mathematical aspects of triadic relations than it does with their psychological embodiments, the following exchange on … Continue reading →

Posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 1 Comment

Triadic Relation Irreducibility • 1

Posted on January 17, 2013 by Jon Awbrey

The core insight of Peirce’s conceptual system is the recognition that triadic relations are sui generis, constituting a class by themselves.  Understanding the properties of triadic relations and the consequences of their irreducibility is critical to understanding Peirce’s thought and work.  … Continue reading →

Posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 11 Comments

Tenacity, Authority, Plausibility, Inquiry

Posted on January 15, 2013 by Jon Awbrey

Re: Peter Cameron • Mathematics and Logic My favorite polymathematician, Charles Sanders Peirce, gave a fourfold classification of what he called “methods of fixing belief”, or “settling opinion”, most notably and seminally in his paper, “The Fixation of Belief” (1877).  … Continue reading →

Posted in Authority, Belief, Belief Fixation, C.S. Peirce, Fixation of Belief, Inquiry, Logic, Method, Philosophy of Science, Plausibility, Science, Scientific Inquiry, Scientific Method, Tenacity, Uncertainty | Tagged , , , , , , , , , , , , , , | 4 Comments

Theme One • A Program Of Inquiry 3

Posted on December 31, 2012 by Jon Awbrey

Re: Peirce List • Gary Richmond The program I wrote for my M.A. in Psych was barely a prototype, a “test of concept”, as they say, but I continued to develop and apply the underlying collection of ideas to a number … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 2

Posted on December 21, 2012 by Jon Awbrey

Re: Peirce List • Jerry Chandler I think I was probably the first person in that particular psychology department to submit a program as a master’s thesis, at any rate they didn’t have regular procedures set up for that kind … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 1

Posted on December 20, 2012 by Jon Awbrey

Re: Peirce List • Jerry Chandler • Jon Awbrey • Gary Richmond • Christophe Menant I view psychology, throughout its many branches, as a fascinating and compelling collection of subjects, so much so I spent one of my parallel lives … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Semiotics, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Constants, Inconstants, and Higher Order Propositions

Posted on December 20, 2012 by Jon Awbrey

A question arising on the Foundations Of Math List gives me an opportunity to introduce the subject of higher order propositions, which I think afford a better way to handle the situations of confusion, doubt, obscurity, uncertainty, and vagueness often … Continue reading →

Posted in Foundations of Mathematics, Higher Order Propositions, Irving Anellis, Logic, Mathematics | Tagged , , , , | Leave a comment

Demonstrative And Otherwise

Posted on December 17, 2012 by Jon Awbrey

I am constantly encountering what I perceive as echoes of Peircean themes in places where acquaintance with or interest in Peirce’s work is slight at best, and that leaves me with a lot of pent up thoughts that I’ve learned through … Continue reading →

Posted in Abduction, Artificial Intelligence, C.S. Peirce, Computation, Computational Complexity, Cybernetics, Deduction, Induction, Inquiry, Inquiry Driven Systems, Intelligent Systems, Logic, Peirce, Programming, Semiotics | Tagged , , , , , , , , , , , , , , | 2 Comments