Changes

===Commentary Note 11.5===

===Commentary Note 11.5===

It always helps me to draw lots of pictures of stuff, so let's extract the somewhat overly compressed bits of the "Relations In General" thread that we'll need right away for the applications to Peirce's 1870 LOR, and draw what icons we can within the frame of Ascii.

The right form of diagram can be a great aid in rendering complex matters comprehensible, so let's extract the overly compressed bits of the "Relations In General" thread that we need to illuminate Peirce's 1870 "Logic Of Relatives" and draw what icons we can within the current frame.

For the immediate present, we may start with 2-adic relations and describe the customary species of relations and functions in terms of their local and numerical incidence properties.

For the immediate present, we may start with 2-adic relations and describe the customary species of relations and functions in terms of their local and numerical incidence properties.

Let ''P'' ⊆ ''X'' × ''Y'' be an arbitrary 2-adic relation.  The following properties of P can be defined:

Let <math>P \subseteq X \times Y</math> be an arbitrary 2-adic relation.  The following properties of <math>~P~</math> can be defined:

:{| cellpadding="6"

{| align="center" cellspacing="6" width="90%"

| ''P'' is "total" at ''X''

|

| iff

| ''P'' is (&ge;1)-regular at ''X''.

P ~\text{is total at}~ X

& \iff &

| ''P'' is "total" at ''Y''

P ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ X.

| iff

| ''P'' is (&ge;1)-regular at ''Y''.

P ~\text{is total at}~ Y

& \iff &

| ''P'' is "tubular" at ''X''

P ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ Y.

| iff

| ''P'' is (&le;1)-regular at ''X''.

P ~\text{is tubular at}~ X

& \iff &

| ''P'' is "tubular" at ''Y''

P ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ X.

| iff

| ''P'' is (&le;1)-regular at ''Y''.

P ~\text{is tubular at}~ Y

& \iff &

P ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ Y.

|}

|}