Monthly Archives: March 2014

Peirce’s 1870 “Logic Of Relatives” • Comment 10.4

From now on I will use the forms of analysis exemplified in the last set of Figures and Tables as a routine bridge between the logic of relative terms and the logic of their extended relations. For future reference, we … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Comment 10.3

We’ve been using several different styles of picture to illustrate relative terms and the relations they denote. Let us now examine the relationships that exist among the variety of visual schemes. Two examples of relative multiplication that we considered before … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Comment 10.2

To say that a relative term “imparts a relation” is to say that it conveys information about the space of tuples in a cartesian product, that is, it determines a particular subset of that space.  When we study the combinations … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Comment 10.1

What Peirce is attempting to do in CP 3.75 is absolutely amazing and I personally did not see anything on a par with it again until I began to study the application of mathematical category theory to computation and logic, back … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Selection 10

We continue with §3. Application of the Algebraic Signs to Logic. The Signs for Multiplication (cont.) The sum generally denotes no logical term.  But may be considered as denoting some two ’s. It is natural to write:     and … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Comment 9.7

From this point forward we may think of idempotents, selectives, and zero-one diagonal matrices as being roughly equivalent notions. The only reason I say roughly is that we are comparing ideas at different levels of abstraction in proposing these connections. … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment

Peirce’s 1870 “Logic Of Relatives” • Comment 9.6

By way of fixing the current array of relational concepts in our minds, let us work through a sample of products from our relational multiplication table that will serve to illustrate the application of a comma relative to an absolute … Continue reading

Posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics | Tagged , , , , , , , | 1 Comment