Tag Archives: Logical Graphs

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 →

Peirce’s 1870 “Logic of Relatives” • Comment 11.5 Everyone knows the right sort of diagram can be a great aid in rendering complex matters comprehensible.  With that in mind, let’s extract what we need from the Relation Theory article to … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.4 The task before us is to clarify the relationships among relative terms, relations, and the special cases of relations given by equivalence relations, functions, and so on. The first obstacle to get … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.3 Before I can discuss Peirce’s “number of” function in greater detail I will need to deal with an expositional difficulty I have been carefully dancing around all this time, but one which … Continue reading →