ONT Re: Relations And Their Divisitudes
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
RATD. Note 5
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Is There A "Calculus Of Semiotic Abstraction For Ordinary Language" (COSAFOL)?
Better to be unwashed than brainwashed, I always say.
Speaking of which, I find myself forced by years of sadistical brainwashing
to call these so-called "events", like GIVINGEVENT001, GIVINGEVENT002, etc.,
by the more proper name of "episodes", "occurrences", "outcomes", or maybe
"event-instances" is the best I can do by way of a compromise-formulation.
At any rate, I think that you are right to be suspicious of calling these
event-instances by the name of hypostatic abstractions, since the utility
of a hypostatic abstraction -- to compromise once again and to use a form
of words that is popular hereabouts -- is to remove a structure from its
embedding in space and time, so to speak, rather than to fix it in same.
On the other hand, it may be possible to interpret these token "events"
another way, perhaps as pseudonyms for the relevant tuples themselves,
that is, "GIVINGEVENT001", when shorn of its irrelevancies, is really
just another name for the 3-tuple x = <A, B, C>, whereby the 2-adic
relations that are notated as "giver", "gift", "givee", since they
are in fact the sorts of 2-adic relations that all, well, most of
the world calls by the name of "functions", may be recognized as
the familiar projections that have long been part and parcel of
the definition of k-tuples and k-fold cartesian products, since
the days of Descartes at least.
Still, you are right to be suspicious of thinking that this move,
however it may be construed, adds anything to the understanding
of the 3-adic relations, that is to say, the sets of 3-tuples
themselves, since this brand of "analytic" reconstruction is
all just a bit of a shell game, or maybe 3-card monte, and
quite beside the point.
That is because the relations that we are concerned with here
are formal relations, whose extensions are k-tuples of things,
and considerations of space and time eventuality do not enter
into their definitions at this level of formal abstraction.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o