Changes

===Commentary Note 11.1===

===Commentary Note 11.1===

We have reached in our reading of Peirce's text a suitable place to pause — actually, it is more like to run as fast as we can along a parallel track — where I can due quietus make of a few IOU's that I've used to pave my way.

We have reached in our reading of Peirce's text a suitable place to pause --

actually, it is more like to run as fast as we can along a parallel track --

where I can due quietus make of a few IOU's that I've used to pave my way.

The more pressing debts that come to mind are concerned with the matter

The more pressing debts that come to mind are concerned with the matter of Peirce's "number of" function, that maps a term t into a number [t], and with my justification for calling a certain style of illustration by the name of the "hypergraph" picture of relational composition. As it happens, there is a thematic relation between these topics, and so I can make my way forward by addressing them together.

of Peirce's "number of" function, that maps a term t into a number [t],

and with my justification for calling a certain style of illustration

by the name of the "hypergraph" picture of relational composition.

As it happens, there is a thematic relation between these topics,

and so I can make my way forward by addressing them together.

At this point we have two good pictures of how to compute the

At this point we have two good pictures of how to compute the relational compositions of arbitrary 2-adic relations, namely, the bigraph and the matrix representations, each of which has its differential advantages in different types of situations.

relational compositions of arbitrary 2-adic relations, namely,

the bigraph and the matrix representations, each of which has

its differential advantages in different types of situations.

But we do not have a comparable picture of how to compute the

But we do not have a comparable picture of how to compute the richer variety of relational compositions that involve 3-adic or any higher adicity relations.  As a matter of fact, we run into a non-trivial classification problem simply to enumerate the different types of compositions that arise in these cases.

richer variety of relational compositions that involve 3-adic

or any higher adicity relations.  As a matter of fact, we run

into a non-trivial classification problem simply to enumerate

the different types of compositions that arise in these cases.

Therefore, let us inaugurate a systematic study of relational composition,

Therefore, let us inaugurate a systematic study of relational composition, general enough to explicate the "generative potency" of Peirce's 1870 LOR.

general enough to explicate the "generative potency" of Peirce's 1870 LOR.

===Commentary Note 11.2===

===Commentary Note 11.2===