Tag Archives: Relation Theory

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 →

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 →

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 →

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 →

Peirce’s 1870 “Logic of Relatives” • Comment 11.21 One more example and one more general observation and we’ll be caught up with our homework on Peirce’s “number of” function. NOF 4.3 So if men are just as apt to be … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.20 We come to the last of Peirce’s statements about the “number of” function, first quoted in Selection 11 and again with the whole set in Comment 11.2. NOF 4.1 The conception of multiplication we … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.19 Up to this point in the 1870 Logic of Relatives, Peirce has introduced the “number of” function on logical terms, such that and discussed the extent to which its use as a … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.18 An order-preserving map is a special case of a structure-preserving map and the idea of preserving structure, as used in mathematics, means preserving some but not necessarily all the structure of the … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.17 I think the reader is beginning to get an inkling of the crucial importance of the “number of” function in Peirce’s way of looking at logic.  It is one plank in the … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 11.16 We now have enough material on morphisms to go back and cast a more studied eye on what Peirce is doing with that “number of” function, whose application to a logical term is … Continue reading →