Category Archives: Philosophy

Triadic Relations • Examples from Mathematics For the sake of topics to be taken up later, it is useful to examine a pair of triadic relations in tandem.  We will construct two triadic relations, and each of which is a … Continue reading →

Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them;  and for the present purpose such an enumeration would be worse than superfluous:  it would be a great inconvenience. … Continue reading →

Relation Theory • Species of Dyadic Relations Returning to 2‑adic relations, it is useful to describe several familiar classes of objects in terms of their local and numerical incidence properties.  Let be an arbitrary 2‑adic relation.  The following properties of … Continue reading →

Relation Theory Two further classes of incidence properties will prove to be of great utility. Regional Incidence Properties The definition of a local flag can be broadened from a point to a subset of a relational domain, arriving at the … Continue reading →

Relation Theory • Local Incidence Properties The next few definitions of local incidence properties of relations are given at a moderate level of generality in order to show how they apply to -place relations.  In the sequel we’ll see what … Continue reading →

Relation Theory • Definition It is convenient to begin with the definition of a -place relation, where is a positive integer. Definition.  A -place relation over the nonempty sets is a -tuple where is a subset of the cartesian product Several … Continue reading →

Relation Theory • Preliminaries Two definitions of the relation concept are common in the literature.  Although it is usually clear in context which definition is being used at a given time, it tends to become less clear as contexts collide, … Continue reading →

Here’s an introduction to Relation Theory geared to applications and taking a moderately general view at least as far as finite numbers of relational domains are concerned (-adic or -ary relations). Relation Theory This article treats relations from the perspective … Continue reading →