Tag Archives: Relation Theory

Peirce’s 1870 “Logic of Relatives” • Comment 9.6

Posted on March 8, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.6 By way of fixing the current array of relational concepts in our minds, let us work through a sample of products from our relational multiplication table that will serve to illustrate the … Continue reading →

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Peirce’s 1870 “Logic of Relatives” • Comment 9.5

Posted on March 4, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.5 Peirce’s comma operation, in its application to an absolute term, is tantamount to the representation of that term’s denotation as an idempotent transformation, which is commonly represented as a diagonal matrix.  Hence … Continue reading →

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

Posted on February 27, 2014 by Jon Awbrey

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

Posted on February 26, 2014 by Jon Awbrey

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 →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 11 Comments

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

Posted on February 26, 2014 by Jon Awbrey

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 →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 11 Comments

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

Posted on February 24, 2014 by Jon Awbrey

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

Posted on February 23, 2014 by Jon Awbrey

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

Posted on February 23, 2014 by Jon Awbrey

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

Posted on February 20, 2014 by Jon Awbrey

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

Posted on February 19, 2014 by Jon Awbrey

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 →

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 10 Comments