Monthly Archives: February 2014

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 it much more than a superficial dusting off. Let … 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. The Signs for Multiplication (cont.) Thus far, we have considered the multiplication of relative terms only. Since our conception of multiplication is the application of a relation, we can … Continue reading

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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 that he had already reached this point in his own thinking some … 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. The Signs for Multiplication (cont.) The associative principle does not hold in this counting of factors.  Because it does not hold, these subjacent numbers are frequently inconvenient in practice, … Continue reading

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

Peirce’s way of representing sets as logical sums may seem archaic, but it’s quite often used in mathematics and remains the tool of choice in many branches of algebra, combinatorics, computing, and statistics to this day. Peirce applied this genre … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Selection 6

We continue with §3. Application of the Algebraic Signs to Logic. The application of a relation is one of the most basic operations in Peirce’s logic.  Because relation applications are so pervasive and because Peirce treats them on the pattern … Continue reading

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Peirce’s 1870 “Logic Of Relatives” • Selection 5

On to the next part of §3. Application of the Algebraic Signs to Logic. The Signs for Multiplication I shall adopt for the conception of multiplication the application of a relation, in such a way that, for example, shall denote … Continue reading

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