ONT Re: Intension & Extension
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John, Robert, Seth, ...
Here are some of the problems that I see with
a whole class of "concept analysis" proposals
that attempt to treat concepts as elements in
some sort of ordered set.
I will arrange the various elements that come into play
within the sort of dual framework that I have been using
to explain ontologies from a sign relational perspective.
The next Figure is supposed to suggest the kind of picture
that I usually have in mind, illustrating a local fragment
of the typical setup:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| s_n |
| p ... q · · |
| \ / · · · |
| ^ ^ · · · · |
| \ / · · · · · |
| o< · · · · · · · · · · · · · · s_m |
| / \ · · · · · |
| ^ ^ · · · · |
| / \ · · · |
| i ... j · · |
| s_1 |
| |
o-----------------------------------------------------------o
The order structure, as a mathematical object, goes into
the "objective framework" (OF) half of the picture, while
all of the sensory, signal, syntactic material, including
experiential data and intellectual concepts of every kind,
is constellated within the "interpretive framework" (IF)
half of it, where I have sought to adumbrate the vast
nebulosity of signs s_1, ..., s_m, ..., s_n that
will typically envelop a given object o.
Do not worry too much about the particular order structure here.
I tend to use heterogeneous collections of different orderings,
organized into what I call "objective genres and motifs". And
so you may feel free to think of anything on the order of an
object o, its properties p and q, and its instances i and j.
The thing that I was objecting to under the title of "an objectifying discourse"
is a type of error that is also known as "illegitimate reification", and this
can be recognized as a particular way of "confusing maps with territories".
In this case, it amounts to confusing a concept, an
intellectual symbol, with an object of that concept.
Mathematical thinkers are very prone to this sort of
thing, probably for the reason that they are inclined
to dismiss the practical work of computation and what
they are disposed and trained to call "mere notation".
So their imaginations race ahead to the canonical
concept or the normal sign s_1 that constitutes
the most conventional choice for denoting its
object, and since they thereby wish away the
actual work of computing this normal form
from the much more likely obscure sign
with which the thinking process began,
they are susceptible to committing
a specious identification of the
concept reducing the manifold
with the objectified product
of that very reduction.
Or something like that ...
Jon Awbrey
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