# Tag Archives: Mathematics

## 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

## Zeroth Law Of Semiotics • Discussion 2

Re: All Liar, No Paradox • Zeroth Law Of Semiotics Re: FB | Charles S. Peirce Society • Joseph Harry Paradoxes star among my first loves in logic.  So enamored was I with tricks of the mind’s eye I remember … Continue reading

## Abduction, Deduction, Induction, Analogy, Inquiry • 31

Re: Scott Aaronson • Explanation-Gödel and Plausibility-Gödel Scott Aaronson asks a question arising from Gödel’s First Incompleteness Theorem, namely, what are its consequences for the differential values of explanation, plausibility, and proof?  I add the following thoughts. A general heuristic … Continue reading

## Theme One Program • Exposition 8

Transformation Rules and Equivalence Classes The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for transforming cacti among themselves and partitioning the space of cacti into formal equivalence … Continue reading

## Theme One Program • Exposition 7

Mathematical Structure and Logical Interpretation The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. The compositional structures of cactus graphs and cactus expressions are constructed from two kinds of connective operations. … Continue reading

## Theme One Program • Exposition 6

Quickly recapping the discussion so far, we started with a data structure called an idea‑form flag and adopted it as a building block for constructing a species of graph-theoretic data structures called painted and rooted cacti.  We showed how to code … Continue reading

## Survey of Cybernetics • 2

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? Plato • … Continue reading

## Theme One Program • Jets and Sharks 3

Re: Theme One Program • Jets and Sharks • (1) • (2) Example 5. Jets and Sharks (cont.) Given a representation of the Jets and Sharks universe in computer memory, we naturally want to see if the memory serves to … Continue reading