[Inquiry] Questions Involving Categories

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

QUIC.  Note 1

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

I will use this thread to reflect on a number of passages
from Peirce's "On a New List of Categories" (1867) that
I presently have questions about, or that I think are
especially critical to understand in all of their
ramifications, to keep them in mind as I work
forward chronologically from the precursors
of that paper.

Here is a brief indicator of one critical issue:

| [Section 14]
|
| A quality may have a special determination
| which prevents its being prescinded from
| reference to a correlate.  Hence there
| are two kinds of relation.
|
| 1st.  That of relates whose reference to a ground
|       is a prescindible or internal quality.
|
| 2nd.  That of relates whose reference to a ground
|       is an unprescindible or relative quailty.
|
| C.S. Peirce, 'Chronological Edition', CE 2, 55

In trying to flesh out these bony abstractions with more sinewy examples,
I realize that one of the reasons why Peirce gives so few examples here,
aside from the fact that this whole series of American Academy papers
was addressed to experts rather than to students, may be that almost
any example you can pick is liable to be subjected, and no doubt
has been subjected, historically speaking, to endless debates.
But let us forge ahead, irregardless.

Here's a couple of contrasting examples:

1.  Regarding the quality of personhood, the reference of a relate,
    a person, to the ground of the relation involved in the matter
    may be said to be prescindible from reference to the correlate
    of another person.

2.  Regarding the quality of parenthood, the reference of a relate,
    a parent, to the ground of the relation involved in the matter
    is not prescindible from reference to the correlate of a child.

To assist my thinking about the various cases,
I will use a diagram of the following shape:

      Ground
         o
         |
         o
        / \
Relate o   o Correlate

When the reference of a relate to the ground of the relation
is prescindible from reference to a correlate, we can redraw
the figure in this fashion:

        Ground
           o
          / \
         /   \
        /     \
Relate o       o Correlate

This can be taken to indicate that relate and correlate "concur"
in a simple character that is the ground of the their relation,
in other words, the "intension" or the "comprehension" of the
relation reduces to a simple quality or a monadic predicate.

But when the reference of a relate to the ground of the relation
is imprescindible from reference to a correlate, then we leave
the figure as it is, to remind us that that the intension or
the comprehension of the relation is a quality of ordered
pairs, such as can be expressed by a dyadic predicate.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o