# Category Archives: Geometry

## Definition and Determination • 16

Re: Ontolog Forum • Richard McCullough RM:  What is your view of definitions? A recurring question, always worth some thought, so I added my earlier comment to a long-running series on my blog concerned with Definition and Determination. Survey of Definition … Continue reading

## Definition and Determination • 15

Re: Ontolog Forum • Richard McCullough 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 … Continue reading

## Sign Relational Manifolds • Discussion 1

Semiotic Orbits, Manifolds, Arcs The arc of the semiotic universe is long but it bends towards universal harmony. Re: FB | Semiotics, Books, Links, News • What’s at the End of a Chain of Interpretants? Semiotic manifolds, like physical and … Continue reading

## 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

## 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

## 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

## Sign Relational Manifolds • 4

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general … Continue reading

## Sign Relational Manifolds • 3

I’m not sure when it was I first noticed the relationship between manifolds and semiotics but I distinctly recall the passage in Serge Lang’s Differential and Riemannian Manifolds which brought the triadic character of tangent vectors into high relief.  I … Continue reading

## Sign Relational Manifolds • 2

A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants … Continue reading

## Sign Relational Manifolds • 1

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop … Continue reading