Category Archives: Logic of Relatives

Peirce’s 1870 “Logic of Relatives” • Comment 8.6

Peirce’s 1870 “Logic of Relatives” • Comment 8.6 The foregoing has hopefully filled in enough background that we can begin to make sense of the more mysterious parts of CP 3.73. The Signs for Multiplication (cont.) Thus far, we have considered … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 8.5

Peirce’s 1870 “Logic of Relatives” • Comment 8.5 I continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating Peirce’s formalism. Since multiplication by a dyadic relative term is a logical analogue of matrix multiplication … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 8.4

Peirce’s 1870 “Logic of Relatives” • Comment 8.4 I continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating Peirce’s formalism. To familiarize ourselves with the forms of calculation available in Peirce’s notation, let us … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 8.3

Peirce’s 1870 “Logic of Relatives” • Comment 8.3 I continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating Peirce’s formalism. It is critically important to distinguish a relation from a relative term. The relation … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 8.2

Peirce’s 1870 “Logic of Relatives” • Comment 8.2 I continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating Peirce’s formalism. In the development of the story so far, we have a universe of discourse … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 8.1

Peirce’s 1870 “Logic of Relatives” • Comment 8.1 To my way of thinking, CP 3.73 is one of the most remarkable passages in the history of logic.  In this first pass over its deeper contents I won’t be able to accord … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 8

We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 8 The Signs for Multiplication (cont.) Thus far, we have considered the multiplication of relative terms only.  Since our conception of multiplication … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Proto-Graphical Syntax

Peirce’s 1870 “Logic of Relatives” • Proto-Graphical Syntax It is clear from our last Selection that Peirce is already on the verge of a graphical syntax for the logic of relative terms.  Indeed, it is likely he had already reached … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 7

We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 7 The Signs for Multiplication (cont.) The associative principle does not hold in this counting of factors.  Because it does not hold, … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Sets as Sums

Peirce’s 1870 “Logic of Relatives” • Sets as Sums Peirce’s way of representing sets as logical sums may seem arcane, but it’s quite often used in mathematics and remains the tool of choice in many branches of algebra, combinatorics, computing, … Continue reading

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