Re: Interoperability and Vagueness
Dear Matthew,
The point I was making is that intensions are
the starting point for any notion of a concept,
function, relation, or predicate. The extension
is a derivative notion, which is very important
for many applications. But it not good practice
to identify a concept with its extension:
1. For most practical problems, the extensions
are uncomputable and unknowable. As we have
seen from recent elections, it is very hard
to guarantee an accurate count of the homo
sapiens who cast their vote for a particular
candidate, even when the stated goal is to get
as accurate a count as possible. To count the
set of homo sapiens (or any other species) even
for a single point in time is hopeless.
2. Even if there existed a well-defined set in 4D
space, we have to consider plans and hypotheses
for alternatives and estimates. Dealing only
with a definition by extension gives us no means
for dealing with possibilities. To imagine the
entire 4D set may be a useful thought experiment,
but it is not a usable definition.
The basic point is that any system of ontology must
deal with both intensions and extensions. Only small
finite sets could ever be defined by extension, and
an intensional definition by some description, axioms,
rule, operation, or procedure is the essential starting
point for any concept.
John