ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 37
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
The uncertain inquirer continues with his re*collection
of "observations", by which he means statements that he
thinks he knows well enough to venture essaying, indeed,
to act in accord with them if their occasion also rises.
Today one is likely to treat individuals on the model of set theory,
or so one says, but that is a naive, precocious, even pre-theoretic
use of the term "set theory", for set theory at the outset does not
give any brand of absolute distinction between individuals and sets.
Depending a little on the axiomatic formalization that one opts for,
it is possible to interpret the language of sets so that all of the
entities that one can say anything sensible about will have one and
the same character, namely, that of being sets, and what the theory
handles is no kind of essential distinction between individuals and
collectives, but a purely relative subject matter, namely, a 2-adic
relation commonly represented to capture the character of belonging.
Given a suitable notion of membership one typically uses it to
construct a notion of inclusion that parallels at the level of
sets the logical relation of implication. And the distinction
between membership (x in y) and inclusion (x c y) is marked by
the fact that inclusion is transitive while membership is not.
That is, x c y and y c z implies x c z, but x in y and y in z
does not imply x in z.
At any rate, that's the way I remember it,
so I will just leave these stock ideas as
a base camp to expedite the next phase of
exploration.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o