ONT Re: Inquiry Driven Systems
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the figure:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| s^1 |
| · |
| · |
| · |
| · |
| p · · · · s^2 |
| · · |
| · · |
| · · |
| · · |
| q · · · · s^3 |
| · |
| · |
| · |
| · |
| s^4 |
| |
o-----------------------------------------------------------o
the legend:
| relation P:
|
| <p, s^1, s^1>
| <p, s^1, s^2>
| <p, s^2, s^1>
| <p, s^2, s^2>
|
| <q, s^4, s^4>
| <q, s^4, s^3>
| <q, s^3, s^4>
| <q, s^3, s^3>
| relation Q:
|
| <p, s^1, s^1>
| <p, s^1, s^3>
| <p, s^3, s^1>
| <p, s^3, s^3>
|
| <q, s^4, s^4>
| <q, s^4, s^2>
| <q, s^2, s^4>
| <q, s^2, s^2>
now i know that this looks like a contrived example, but i can tell you
that the larger part and the greater art of the contrivance was to find
what is nigh unto a minimal example of the phenomena of interest, being
one that contains many of the most critically realistic features of far
more complex cases. one of the 'critical features' that i have in mind
trying to illustrate can be explained in the following way. many times
we find ourselves faced with just such a 'muddle' as the one with which
we set out here, where the muddling aspect presents itself, among other
things, in the predicament that we lack a fixed association of signs to
objects, in the way that would be required of their absolute properties.
the critical moment, the turning point of the whole inquiry, comes when,
instead of throwing up our hands in despair, even though we may do some
of that at first, but rather than giving up all hope then and there, we
move on to consider relative properties, in this case, looking at pairs
and triples and higher tuples of objects and signs, to see if there are
relations among them that may be invariant or preserved in some fashion.
in our more casual idioms, we frequently find ourselves expressing such
a relation in the figure of a "proportion". as an aid to the intuition,
i have made some attempt to collect a variety of these figures, like so:
1. from the standpoint of L,
v is to w in regard to u as
y is to z in regard to x.
2. there is a manner L in which
v is to w in regard to u as
y is to z in regard to x.
3. there is a perspective L in which the turning
of the segment <v, u> into the segment <w, u>
appears to form the same angle as the turning
of the segment <y, x> into the segment <z, x>.
4. there is a point of view L from which the turning of v into w about u
appears to describe the same angle as the turning of y into z about x.
5. there is a relation L such that <u, v, w> and <x, y, z> are both in L.
6. there is a relation L that includes the elements <u, v, w>, <x, y, z>.
jon awbrey
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