Category Archives: Mathematics

Systems of Interpretation • 3

Posted on March 29, 2016 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel The “triskelion” figure in the previous post shows the bare essentials of an elementary sign relation or individual triple   There’s a less skeletal figure Susan Awbrey and I used in … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 1 Comment

Systems of Interpretation • 2

Posted on March 28, 2016 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel Let’s start as simply as possible.  The following Figure is typical of many I have used to illustrate sign relations from the time I first began studying Peirce’s theory of signs. … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 2 Comments

Systems of Interpretation • 1

Posted on March 28, 2016 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel Questions have arisen about the different styles of diagrams and figures used to represent triadic sign relations in Peircean semiotics.  What do they mean?  Which style is best?  Among the most … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 1 Comment

Homunculomorphisms • 2

Posted on February 12, 2016 by Jon Awbrey

Re: John Baez • The Internal Model Principle There’s a far-ranging discussion that takes off from this point, touching on links among analogical reasoning, arrows and functors, cybernetic images, iconic versus symbolic representations, mental models, systems simulations, etc., and just … Continue reading →

Posted in Analogy, Ashby, Automata, Control Systems, Cybernetics, Homunculi, Homunculomorphisms, Iconicity, Information Theory, Inquiry, Inquiry Driven Systems, Intentionality, Internal Models, Logic, Logic of Science, Mathematics, Mental Models, Model Theory, Optimal Control, Peirce, Semiotics, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Homunculomorphisms • 1

Posted on February 11, 2016 by Jon Awbrey

Re: John Baez • The Internal Model Principle Ashby’s book was my own first introduction to cybernetics and I recently returned to his discussion of regulation games in connection with some issues in Peirce’s theory of inquiry. In that context … Continue reading →

Posted in Ashby, Automata, Category Theory, Control, Control Systems, Control Theory, Cybernetics, Homunculi, Homunculomorphisms, Information, Information Theory, Inquiry, Inquiry Driven Systems, Intentionality, Internal Models, Logic of Science, Mathematics, Mental Models, Optimal Control, Peirce, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Problems In Philosophy • 5

Posted on February 10, 2016 by Jon Awbrey

Re: Michael Harris • Are Your Colleagues Zombies? What makes a zombie a legitimate object of philosophical inquiry is its absence of consciousness.  And today’s question is whether mathematical research requires consciousness, or whether it could just as well be … Continue reading →

Posted in Aristotle, Automata, Automated Research Tools, Automation, Cognition, Computation, Consciousness, Freud, Inquiry, Inquiry Driven Systems, Intentionality, Mathematics, Mechanization, Michael Harris, Peirce, Philosophy, Philosophy of Mathematics, Philosophy of Mind, Plato, Psychology, Routinization, Socrates, Sophist, Turing Test | Tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 4

Posted on February 9, 2016 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Did Euclid Really Mean ‘Random’? These are the forms of time, which imitates eternity and revolves according to a law of number. Plato • Timaeus • 38 A Benjamin Jowett (trans.) It is … Continue reading →

Posted in Aristotle, Computation, Computer Science, Euclid, Genericity, Geometry, Iconicity, Likelihood, Likely Story, Likeness, Mathematics, Number Theory, Philosophy, Philosophy of Mathematics, Plato, Probability, Socrates | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Problems In Philosophy • 3

Posted on February 8, 2016 by Jon Awbrey

Re: R.D. Mounce Making reality our friend is necessary to survival and finding good descriptions of reality is the better part of doing that, so I don’t imagine we have any less interest in truth than the Ancients.  From what … Continue reading →

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | Leave a comment

Riffs and Rotes • 3

Posted on February 3, 2016 by Jon Awbrey

Re: R.J. Lipton • Failure Of Unique Factorization My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Relations & Their Relatives • Discussion 17

Posted on January 4, 2016 by Jon Awbrey

Re: Peirce List Discussion • HR We have been considering special properties that a dyadic relation may have, in particular, the following two symmetry properties. A dyadic relation is symmetric if being in implies that is in A dyadic relation is … Continue reading →

Posted in C.S. Peirce, Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 12 Comments