Monthly Archives: June 2014

Peirce’s 1870 “Logic of Relatives” • Intermezzo

Peirce’s 1870 “Logic of Relatives” Update • 10 April 2022 This brings me to the end of the notes on Peirce’s 1870 Logic of Relatives I began posting to the web in various discussion groups a dozen (now a score) … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 8 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 12.5

Peirce’s 1870 “Logic of Relatives” • Comment 12.5 The equation can be verified by establishing the corresponding equation in matrices. If and are two 1-dimensional matrices over the same index set then if and only if for every   Thus, a routine way … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 12.4

Peirce’s 1870 “Logic of Relatives” • Comment 12.4 Peirce next considers a pair of compound involutions, stating an equation between them analogous to a law of exponents from ordinary arithmetic, namely,  Then will denote whatever stands to every woman in … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 12.3

Peirce’s 1870 “Logic of Relatives” • Comment 12.3 We now have two ways of computing a logical involution raising a dyadic relative term to the power of a monadic absolute term, for example, for “lover of every woman”. The first method … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 12.2

Peirce’s 1870 “Logic of Relatives” • Comment 12.2 Let us make a few preliminary observations about the operation of logical involution which Peirce introduces in the following words. I shall take involution in such a sense that will denote everything … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 12.1

Peirce’s 1870 “Logic of Relatives” • Comment 12.1 To get a better sense of why Peirce’s formulas in Selection 12 mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Selection 12

On to the next part of §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 12 The Sign of Involution I shall take involution in such a sense that will denote everything which is … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 8 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 11.24

Peirce’s 1870 “Logic of Relatives” • Comment 11.24 We come to the last of Peirce’s observations about the “number of” function in CP 3.76. NOF 4.4 It is to be observed that Boole was the first to show this connection between … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 11.23

Peirce’s 1870 “Logic of Relatives” • Comment 11.23 Peirce’s description of logical conjunction and conditional probability via the logic of relatives and the mathematics of relations is critical to understanding the relationship between logic and measurement, in effect, the qualitative … Continue reading

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

Peirce’s 1870 “Logic of Relatives” • Comment 11.22

Peirce’s 1870 “Logic of Relatives” • Comment 11.22 Let’s look at that last example from a different angle. NOF 4.3 So if men are just as apt to be black as things in general, where the difference between and must … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization | Tagged , , , , , , | 6 Comments