Ali, Mitch, and Frank, (01)
AH> If you've given a definition of River, and it is inadequate
> when you encounter something as the Okavango River, ought it
> not indicate that you only need to update your definition of
> river? Isn't the whole point of defining something trying to
> abstract the generalizable qualities / properties of the
> object/entity under consideration? You can still have a
> monotonic logic, you just need smart revision policies... (02)
It's always possible to legislate a definition and to revise
the definition whenever you encounter an exception. But the
point of Waismann's notion of 'open texture' is that there is
no stopping point. If you arbitrarily choose a stopping point,
you will inevitably exclude unanticipated cases that are just
as reasonable as the ones you do include. (03)
That is a serious problem for any legal system. Any system
of laws has inevitable exceptions and borderline cases that
require a judge and jury to decide. (04)
MH> To address your Kant quote, natural language has a tendency
> to be imprecise and formal language tends towards precision,
> there is the relevance. (05)
Kant's point, Wittgenstein's point, or Waismann's point hold
equally well for a well-written definition in a natural language
or in any version of symbolic logic. We all learned algebra
and geometry from books and teachers that used natural languages. (06)
In fact, we learned logic and programming languages from books
and teachers that used NLs. But we were learning very precisely
defined mathematical concepts, and NLs are quite adequate for
teaching and expressing mathematical concepts precisely. (07)
But for continuously variable things like rivers, clouds, or
hurricanes, no notation of any kind can state precise criteria
for distinguishing borderline cases. When does a tropical
depression become a storm and then a hurricane? The weather
bureau states the criteria in terms of wind speed. But the
wind speeds vary enormously over the full extent, and they tend
to increase and decrease depending on conditions. The language
used to state those criteria is irrelevant. (08)
FK> We live in spacetime, and every existing thing (object of an
> ontology) is finally defined by its position in space and time.
> Those parameters are unique... Everything that exists has a
> date of birth and a date of death possible to forecast. (09)
Since we were talking about rivers, how would you define the
birth and death of a river? Where is the source? Some previous
stream? Which of the many smaller streams that flow into it
qualifies as the source? What happens if any of those streams
dry up and begin flowing again in different seasons? (010)
What happens to the Colorado River when the cities upstream
drain off so much water that the Colorado sometimes dries up
before it reaches the ocean? What happens to the mouth of
the river when it doesn't reach its mouth? (011)
What about the Ohio River, which is formed by the merger of the
Allegheny and the Monongahela Rivers at Pittsburgh? Precisely
which planes demarcate the boundaries between the source rivers
and the Ohio? How do you define those planes and river banks,
as the rivers rise and fall with different levels of rain?
Precisely which molecules of water are part of the river, part
of the wetlands nearby, or part of the evaporation above it? (012)
FK> On the other hand concepts (man made artefacts) are also
> products, that is objects and they also follow the same rule. (013)
Some artifacts fall into the same category as mathematical objects.
Please note the quotation by Kant: (014)
"Thus only arbitrarily made concepts can be defined synthetically.
Such definitions... could also be called declarations, since in
them one declares one's thoughts or renders account of what one
understands by a word. This is the case with mathematicians." (015)
An artifact invented by a particular person for a particular purpose
could be declared by that person as precisely as he or she desires. (016)
On the other hand, many artifacts, such as a log cabin with a dirt
floor and actual living trees at its four corners, are composed of
natural objects that have so much variation that the boundaries
of the cabin are difficult to distinguish from its surroundings. (017)
When was such a cabin born? When those four trees started to
sprout from acorns? When some person first laid another log
next to one of them? When enough logs were attached to form
four walls? When some person finally declared it to be finished?
What if it was never formally "finished", but the builder just
continued to extend it from a temporary shelter to a more
stable structure? (018)
And when did the cabin die? When the builder left it? When
it started to lose parts? When most of the walls fell down?
When the four trees at the corners died? When all traces of
the parts vanished? But there are probably molecules from the
wood still in the ground. Do they have to vanish as well? (019)
Suppose that somebody else built another log cabin next to
the first one, and other people eventually moved in to form
a village. When did the group of cabins or houses become a
village? When does a village become a town or a city? How
would you (or anyone else) define its date of birth? (020)
FK> Why is this difficult to grasp? (021)
What idea are you trying to express? That everything has
a precise birth & death? Those seem to be inherently vague
ideas. Even professional physicians and theologians cannot
agree on the exact time points for the beginning and ending
of human life. For nonliving things, those points seem to
be vague metaphors at best. (022)
I'm definitely in favor of using logic for many purposes.
But note that stating the criteria in any version of logic
(even fuzzy logic) would do *nothing* to help us resolve
any of these questions. (023)
John (024)
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