Category Archives: Geometry

Abductive Inference, Concept Formation, Hypothesis Formation • 1

In pragmatic semiotics, concept formation like hypothesis formation falls under the heading of abductive inference.  A lot has been said and there’s a lot more to say about that, but things are too much in flux right now to allow … Continue reading

Posted in Abduction, C.S. Peirce, Concept Formation, Differential Calculus, Differential Logic, Dyadic Relations, Dynamical Systems, Dynamics, Geometry, Hypothesis, Hypothesis Formation, Inference, Logic, Logic of Relatives, Mathematics, Mental Models, Peirce, Physics, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Definition and Determination : 17

Re: Ontolog Forum Discussion • Richard McCullough RM:  We clearly have some differences in the “definition” of “definition”. I suppose it all depends on the sorts of things one wants to define, something we might call the context of application.  … Continue reading

Posted in C.S. Peirce, Category Theory, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Relatives, Logical Graphs, Mathematics, Ontology, Peirce, Relation Theory, Semiotics, Sign Relations, Structure, Theorem Proving, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Definition and Determination : 15

Re: Ontolog Forum Discussion In some early math course I learned a fourfold scheme of Primitives (undefined terms), Definitions, Axioms, and Inference Rules.  But later excursions tended to run the axioms and definitions together, speaking for example of mathematical objects … Continue reading

Posted in C.S. Peirce, Category Theory, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Relatives, Logical Graphs, Mathematics, Ontology, Peirce, Relation Theory, Semiotics, Sign Relations, Structure, Theorem Proving, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Sign Relational Manifolds : 6

Semiotic Orbits, Manifolds, Arcs (SOMA) The arc of the semiotic universe is long but it bends towards universal harmony. Re: Facebook Discussion • What’s at the End of a Chain of Interpretants? Semiotic manifolds, like physical and mathematical manifolds, may … Continue reading

Posted in C.S. Peirce, Cybernetics, Differential Logic, Geometry, Logic, Manifolds, Mathematics, Peirce, Peirce List, Riemann, Semeiosis, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 4

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

The Lambda Point : 1

A note on the title.  From long ago discussions with Harvey Davis, one of my math professors at Michigan State.  I remember telling him of my interest in the place where algebra, geometry, and logic meet, and he quipped, “Ah … Continue reading

Posted in Algebra, Amphecks, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Geometry, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Peirce, Propositional Calculus | Tagged , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds : 5

Let me try to say in intuitive terms what I think is really going on here. The problem we face is as old as the problem of other minds, or intersubjectivity, or even commensurability, and it naturally involves a whole … Continue reading

Posted in C.S. Peirce, Cybernetics, Differential Logic, Geometry, Logic, Manifolds, Mathematics, Peirce, Peirce List, Riemann, Semeiosis, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds : 4

I found another set of notes on this theme that appear to get to the point more quickly, and though they read a little rough in places I think it might be worth the effort to fill out their general … Continue reading

Posted in C.S. Peirce, Cybernetics, Differential Logic, Geometry, Logic, Manifolds, Mathematics, Peirce, Peirce List, Riemann, Semeiosis, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 4 Comments

Sign Relational Manifolds : 3

I made several attempts to articulate the connections between manifold theory and semiotics in the context of numerous list discussions that interwove each other through diverse nooks of the web in the early years of the present millennium. Here is … Continue reading

Posted in C.S. Peirce, Cybernetics, Differential Logic, Geometry, Logic, Manifolds, Mathematics, Peirce, Peirce List, Riemann, Semeiosis, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds : 2

Here is a set of excerpts from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, that I used in discussing differentiable manifolds with other participants in the IEEE Standard Upper Ontology Working Group. What brought the concept of … Continue reading

Posted in C.S. Peirce, Cybernetics, Differential Logic, Geometry, Logic, Manifolds, Mathematics, Peirce, Peirce List, Riemann, Semeiosis, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment