Tag Archives: Mathematics

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

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

Triadic Relations, Intentions, Fuzzy Subsets • Discussion 3

Posted on December 9, 2012 by Jon Awbrey

Re: Peirce List Discussion • Gary Moore • Stefan Berwing I intend to get back to this subject as soon as possible but the dire political situation in my home state is once again eating up a lot of my … Continue reading →

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Probability, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment

Triadic Relations, Intentions, Fuzzy Subsets • Discussion 2

Posted on December 8, 2012 by Jon Awbrey

Re: Peirce List Discussion • Stefan Berwing Let us put fuzzy sets to one side for the moment and take up the matter of belief you raised, as I believe that connection is very apt. As it happens, there was … Continue reading →

Posted in Belief, Bertrand Russell, C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Triadic Relations, Intentions, Fuzzy Subsets : 3

Posted on December 7, 2012 by Jon Awbrey

There is at present an extensive literature on fuzzy sets and fuzzy logic.  I got another brush with the world of fuzzy in the 1990s when I returned to grad school in a systems engineering program, partly because my adviser … Continue reading →

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , | Leave a comment

Triadic Relations, Intentions, Fuzzy Subsets : 2

Posted on December 7, 2012 by Jon Awbrey

We imagine all the things we might want to talk about in a given discussion as collected together in a set X called a universe of discourse.  (In probabilistic or statistical work it might be called a sample space.) By … Continue reading →

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , | Leave a comment

Triadic Relations, Intentions, Fuzzy Subsets • Discussion 1

Posted on December 6, 2012 by Jon Awbrey

Re: Peirce List Discussion • Stefan Berwing Frequencies, histograms, and probabilities are one way to think about degrees of membership in a fuzzy subset, but there are cautions to be observed in doing that. Consider the following triadic relations: x … Continue reading →

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , | 1 Comment