Monthly Archives: May 2014

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 dyadic relation — we know that the relational … Continue reading

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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 that are immanent in relative terms no matter where they locate … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 11.10

In the case of a dyadic relation that has the qualifications of a function there are a number of further differentia that arise: For example, the function depicted below is neither total nor tubular at its codomain so it can … Continue reading

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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 of can then be defined: We previously examined dyadic relations that … Continue reading

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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 if and only if the cardinality of the … Continue reading

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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 of object examples for clarifying the more abstruse … Continue reading

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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. exemplifies the quality of totality at (31) exemplifies the quality of totality at (32) exemplifies the quality of tubularity at (33) exemplifies the quality of … Continue reading

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