Category Archives: Logic of Relatives

Peirce’s 1870 “Logic of Relatives” • Comment 10.11 Let us return to the point where we left off unpacking the contents of CP 3.73.  Here Peirce remarks that the comma operator can be iterated at will. In point of fact, since … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.10 The last of Peirce’s three examples involving the composition of triadic relatives with dyadic relatives is shown again in Figure 25. The hypergraph picture of the abstract composition is given in Figure 26. This … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.9 Ergo in numero quo numeramus repetitio unitatum facit pluralitatem; in rerum vero numero non facit pluralitatem unitatum repetitio, vel si de eodem dicam “gladius unus mucro unus ensis unus”. Therefore in the … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.8 Our progress through the 1870 Logic of Relatives brings us in sight of a critical transition point, one which turns on the teridentity relation. The markup for Peirce’s “giver of a horse … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.7 Here is what I get when I analyze Peirce’s “giver of a horse to a lover of a woman” example along the same lines as the dyadic compositions. We may begin with … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.6 As Peirce observes, it is not possible to work with relations in general without eventually abandoning all the more usual algebraic principles, in due time the associative law and even the distributive … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.5 We have sufficiently covered the application of the comma functor to absolute terms, so let us return to where we were in working our way through CP 3.73 and see whether we can … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.4 From now on the forms of analysis exemplified in the last set of Figures and Tables will serve as a convenient bridge between the logic of relative terms and the mathematics of … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.3 We have been using several styles of picture to illustrate relative terms and the relations they denote.  Let’s now examine the relationships which exist among the variety of visual schemes.  Two examples … Continue reading →

Peirce’s 1870 “Logic of Relatives” • Comment 10.2 To say a relative term “imparts a relation” is to say it conveys information about the space of tuples in a cartesian product, that is, it determines a particular subset of that … Continue reading →