Monthly Archives: May 2014

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 and discussed the extent to which its use as a measure, such that satisfies the relevant measure-theoretic principles, for starters, these … Continue reading

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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 of the structure of the source domain in the transition to the … Continue reading

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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. Among other things it is one of the planks in the bridge from logic … Continue reading

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

We have enough material on morphisms now 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 indicated by writing the term in square brackets, … Continue reading

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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 maps, as a modest amount of extra work at this point will repay ample dividends when it comes time to revisit Peirce’s “number of” function … Continue reading

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

Let’s now look at a more homely 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. In this case we have and and … Continue reading

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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 that we must not leave the plains without, namely, the utilities variously known as arrows, morphisms, homomorphisms, structure-preserving maps, among … Continue reading

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