Monthly Archives: May 2014

Peirce’s 1870 “Logic of Relatives” • Comment 11.19

Peirce’s 1870 “Logic of Relatives” • Comment 11.19 Up to this point in the 1870 Logic of Relatives, Peirce has introduced the “number of” function on logical terms, such that and discussed the extent to which its use as a … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 11.18

Peirce’s 1870 “Logic of Relatives” • Comment 11.18 An order-preserving map is a special case of a structure-preserving map and the idea of preserving structure, as used in mathematics, means preserving some but not necessarily all the structure of the … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 11.17

Peirce’s 1870 “Logic of Relatives” • Comment 11.17 I think the reader is beginning to get an inkling of the crucial importance of the “number of” function in Peirce’s way of looking at logic.  It is one plank in the … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 11.16

Peirce’s 1870 “Logic of Relatives” • Comment 11.16 We now have enough material on morphisms to go back and cast a more studied eye on what Peirce is doing with that “number of” function, whose application to a logical term is … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 11.15

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

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Peirce’s 1870 “Logic of Relatives” • Comment 11.14

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

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Peirce’s 1870 “Logic of Relatives” • Comment 11.13

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

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Peirce’s 1870 “Logic of Relatives” • Comment 11.12

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

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Peirce’s 1870 “Logic of Relatives” • Comment 11.11

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

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

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

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