Category Archives: Logic of Relatives

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

We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 6 The application of a relation is one of the most basic operations in Peirce’s logic.  Because relation applications are so pervasive … 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. Peirce’s 1870 “Logic of Relatives” • Selection 5 The Signs for Multiplication I shall adopt for the conception of multiplication the application of a relation, in … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 4

Here is the next part of §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 4 The Signs for Addition The sign of addition is taken by Boole so that denotes everything denoted by … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 3

We move on to the next part of §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 3 The Signs of Inclusion, Equality, Etc. I shall follow Boole in taking the sign of equality … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 2

We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 2 Numbers Corresponding to Letters I propose to use the term “universe” to denote that class of individuals about which alone the … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Selection 1

We pick up the text at §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 1 Use of the Letters The letters of the alphabet will denote logical signs. Now logical terms are of … Continue reading

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Peirce’s 1870 “Logic of Relatives” • Preliminaries

In the beginning was the three-pointed star, One smile of light across the empty face; One bough of bone across the rooting air, The substance forked that marrowed the first sun; And, burning ciphers on the round of space, Heaven … Continue reading

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Precursors Of Category Theory • 3

Act only according to that maxim by which you can at the same time will that it should become a universal law. Immanuel Kant (1785) Precursors Of Category Theory Peirce Cued by Kant’s idea on the function of concepts in … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 8 Comments

Precursors Of Category Theory • 2

Thanks to art, instead of seeing one world only, our own, we see that world multiply itself and we have at our disposal as many worlds as there are original artists … ☙ Marcel Proust Precursors Of Category Theory When … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 6 Comments

Precursors Of Category Theory • 1

A few years back I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, thorough Kant and Peirce, Hilbert and Ackermann, to contemporary mathematical use.  Perhaps a few will … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 10 Comments