Tag Archives: Relation Theory

Peirce’s 1870 “Logic of Relatives” • Comment 11.15 I’m going to elaborate a little further on the subject of arrows, morphisms, or structure-preserving mappings, as a modest amount of extra work at this point will repay ample dividends when it … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.14 Let’s now look at a concrete example of a morphism say, one of the mappings of reals into reals commonly known as logarithm functions, where you get to pick your favorite base. … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.13 As we make our way toward the foothills of Peirce’s 1870 Logic of Relatives there are several pieces of equipment we must not leave the plains without, namely, the utilities variously known … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.12 Since functions are special cases of dyadic relations and since the space of dyadic relations is closed under relational composition — that is, the composition of two dyadic relations is again a … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.11 The preceding exercises were intended to beef-up our “functional literacy” skills to the point where we can read our functional alphabets backwards and forwards and recognize the local functionalities immanent in relative … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.10 A dyadic relation which qualifies as a function may then enjoy a number of further distinctions. For example, the function shown below is neither total nor tubular at its codomain so it can … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.9 Among the variety of regularities affecting dyadic relations we pay special attention to the -regularity conditions where is equal to Let be an arbitrary dyadic relation.  The following properties can be defined. … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.8 Let’s take a closer look at the numerical incidence properties of relations, concentrating on the assorted regularity conditions defined in the article on Relation Theory. For example, has the property of being … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.7 We come now to the special cases of dyadic relations known as functions.  It will serve a dual purpose in the present exposition to take the class of functions as a source … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.6 Let’s continue working our way through the above definitions, constructing appropriate examples as we go. Relation exemplifies the quality of totality at Relation exemplifies the quality of totality at Relation exemplifies the … Continue reading →