Monthly Archives: June 2014

Peirce’s 1870 “Logic Of Relatives” • Intermezzo

This brings me to the end of the notes on Peirce’s 1870 Logic of Relatives that I began posting to the web in various online discussion groups a dozen years ago. Apart from that there are only the scattered notes … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 12.5

The equation can be verified by establishing the corresponding equation in matrices: If and are two 1-dimensional matrices over the same index set then if and only if for every   Thus, a routine way to check the validity of is to check … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 12.4

Peirce next considers a pair of compound involutions, stating an equation between them that is analogous to a law of exponents in ordinary arithmetic, namely, Then will denote whatever stands to every woman in the relation of servant of every … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 12.3

We now have two ways of computing a logical involution that raises a dyadic relative term to the power of a monadic absolute term, for example, for “lover of every woman”. The first method operates in the medium of set … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 12.2

Let us make a few preliminary observations about the operation of logical involution, as Peirce introduces it here: I shall take involution in such a sense that will denote everything which is an for every individual of   Thus will … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Comment 12.1

To get a better sense of why the above formulas mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials and definitions: is a set singled out … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Selection 12

On to the next part of §3. Application of the Algebraic Signs to Logic. The Sign of Involution I shall take involution in such a sense that will denote everything which is an for every individual of   Thus will … Continue reading

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