Monthly Archives: February 2014

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

Boole rationalized the properties of what we now call boolean multiplication, roughly equivalent to logical conjunction, in terms of the laws that apply to selective operations. Peirce, in his turn, taking a very significant step of analysis that has seldom … Continue reading

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

An idempotent element in an algebraic system is one that obeys the idempotent law, that is, it satisfies the equation Under most circumstances it is usual to write this as If the algebraic system in question falls under the additional … Continue reading

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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 or idea.  To what faculties of the mind … Continue reading

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

Let us backtrack a few years and consider how George Boole explained his twin conceptions of selective operations and selective symbols. Let us then suppose that the universe of our discourse is the actual universe, so that words are to … 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. The Signs for Multiplication (cont.) It is obvious that multiplication into a multiplicand indicated by a comma is commutative,1 that is, This multiplication is effectively the same as that … Continue reading

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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 the multiplication of relative terms only. Since our … Continue reading

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

Since multiplication by a dyadic relative term is a logical analogue of matrix multiplication in linear algebra, all of the products that we computed above can be represented in terms of logical matrices, that is, arrays of boolean coordinate values. … Continue reading

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

To familiarize ourselves with the forms of calculation that are available in Peirce’s notation, let us compute a few of the simplest products that we find at hand in the Othello universe. Here are the absolute terms: Here are the … Continue reading

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

It is critically important to distinguish a relation from a relative term. The relation is an object of thought that may be regarded in extension as a set of ordered tuples that are known as its elementary relations. The relative … Continue reading

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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 characterized by the following equations: This much forms … Continue reading

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