Logical Principles of a Topological Explanation

We aim to demonstrate the applicability of Peirce’s iconic logic in the context of current topological explanations in the philosophy of science. We hold that the logical system of Existential Graphs is similar to contemporary topological approaches, thereby recognizing Peirce’s iconic logic (Beta Graphs) as a valid method of scientific representation. We base our thesis on the nexus between iconic logic and the so-called NonReduction Theorem. We illustrate our assumptions with examples derived from biology (protein folding).

On the higher singularities of plane algebraic curves

1. During the last sixty years the principal questions presented by the higher singularities of plane algebraic curves have been completely solved, and definite results obtained. The two most successful lines of research have been by expansions and quadratic transformation. By each method it has been shown that a higher singularity may be looked upon as containing concealed or “latent” multiple points or lines in addition to those immediately recognized; and from each, with the help of small quantities, has been constructed a topological explanation of these latent multiple elements, which are accounted for as situated in the immediate vicinity of the point and line base of the singularity. Further, by each method it has been proved that as regards the numerical relations known as Plvicker's equations a singularity produces the same effect as a definite number of nodes, cusps, bitangents, and stationary tangents.