ONT Re: Apposite Purposes Of Logical Languages Objectified (APOLLO)
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Many years ago, a teacher asked what I thought mathematics was.
It was a question that I had already spent a while thinking on,
and so I answered, without hesitation, "The form of experience,
and the experience of form". There was this eternal moment of
astonished silence ... and then my teacher changed the subject.
The reason that I am telling you this story at this time is because
of what it leaves unsaid, a theme that the story leaves understated,
all the while invoking and turning on it, and that is the motive of
reflection that it takes to transform the 'form of experience' into
the 'experience of form'.
We have spent enough time with the Babel of languages
that issue forth from the logical strata at the level
of ZOL(2) to get a sense of their common objects, and
even to see how terribly fascinating such a miniature
cosmos can be for a susceptible sort of combinatorial
mentality, but Lot(16) and its like are awfully small
potatoes as far as your average universe of discourse
goes, and we must recall that we have a larger object
in recreating ourselves pushing such small fry around.
But the process that we have put ourselves through during this exercise,
half-reflectively, half-routinely, does manage to exemplify the forms
of conduct that I am lumping together under the name of "reflection".
To see this, we need only reflect on how we started and how we ended,
and to consider the difference in perspective on ZOL and its object
that we achieved in the intervening process. We began by thinking
of logic as an active form of conduct, the conduct of our thought
in which we elect to experience ourselves acting, and we ended,
or at least paused for the moment, at the point where we had
examined this conduct from so may different angles and sides
and had expressed its insights in so many different styles
of syntax that we had managed to objectify a component of
this activity in the precipitate form of a faceted body,
a jewel-like solid that can be turned over in the mind
as though it were meant all along to give a strangely
literal meaning to the idea of an "object language".
Anyway, that's kind of how I see it.
Jon Awbrey
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