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David Macy wrote: So I guess
that I'll just have to grow into the vocabulary, becoming
ever more confident with it's meaning and
use.
That's what I had to do, too. I think I've mentioned before that my father didn't speak the way he wrote? So, I had to learn the equivalent of a second vocabulary for him, once I got old enough to be interested in his work. There was a whole lotta years of "What does this mean?", "Why did you use that word to say that?", and "Why do you write like you do, Dad?" By the time I was in my early thirties, I had reached a point where we could just discuss the work, without much of that anymore, and he used to discuss each new paper as he was working on it. But there have been words that have come up in discussions here on
the list which never managed to get discussed in conversations with my father,
and I have had to do some research for those. "Holonomic" was one. In general,
I've gotten to a point where I can use the dictionary of his language (his
published work) to learn definitions of unfamiliar words. That's a
nice achievement, considering my lack of post-secondary science and math
education. You know you're pretty fluent in a language, like French, say, when
you can use a French dictionary rather than an English/French dictionary and it
gives you everything you need. If I can do it, you can do it.
DM: Perhaps it would be a lot easier just to
ask. What exactly is an impredicativity?
That's a good one! I had trouble with that word, too, and it was
one of my later acquisitions. Impredicativity has to do with an
innate, semantic self-reference, either in mathematics or in
system organization, which cannot be dispensed with. So a predicative system is
one possessing an organization which does not include any of these
kinds of essential semantic qualities and therefore all predicative systems
are reducible to syntax without loss of information. In other words; they
are computable. Impredicative systems, then, are systems with organizations
which include inherent semantic information which cannot be replaced by
syntax without loss of essential information.
In mathematics, when number theory is treated as a predicative
system and reduced to pure syntax, it causes terrible paradoxes and this was the
example my father used to show that the existence of impredicativities in
mathematics doesn't render it useless or make the use of mathematics
"unscientific" or imprecise in all usage-- it just means that there are
certain things that are inappropriate to do with it. He was
pointing out that the same is true in natural systems and the existence of
inappropriate modes of approach also exist. But he was showing
that impredicative natural systems, such as those dealt with
in biology, are not beyond the scope of science, either. They are just
beyond the scope of reductionism. He didn't feel that the two ought to be the
same; science ought not to be limited to only a reductionist
capability.
The word "impredicativity" is derived from "predicate" which
has the same Latin base roots as "predict" (dicere; to say, and prae;
before) but the connotation is different, apparently, because my
Webster's (unabridged) dictionary defines predicate as meaning "to proclaim". I
believe my father's usage is based on the fact that certain system organizations
can be reduced to formalisms and everything else about them is then "predicated"
on that information.
Judith
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