Monthly Archives: February 2014

Peirce’s 1870 “Logic of Relatives” • Comment 9.4

Peirce’s 1870 “Logic of Relatives” • Comment 9.4 Boole rationalizes the properties of what we now call boolean multiplication, roughly equivalent to logical conjunction, by means of his concept of selective operations.  Peirce, in his turn, taking a radical step … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 9.3

Peirce’s 1870 “Logic of Relatives” • Comment 9.3 An idempotent element in an algebraic system is one which obeys the idempotent law, that is, it satisfies the equation   Under most circumstances it is usual to write this as If … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 9.2

Peirce’s 1870 “Logic of Relatives” • Comment 9.2 In setting up his discussion of selective operations and their corresponding selective symbols, Boole writes the following. The operation which we really perform is one of selection according to a prescribed principle … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Comment 9.1

Peirce’s 1870 “Logic of Relatives” • Comment 9.1 Perspective on Peirce’s use of the comma operator at CP 3.73 and CP 3.74 can be gained by dropping back a few years and seeing how George Boole explained his twin conceptions of selective … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 9

We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 9 The Signs for Multiplication (cont.) It is obvious that multiplication into a multiplicand indicated by a comma is commutative,1 that is, … Continue reading

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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

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 5 Comments