Another categorization of this dichotomy could be the Plato universals
corresponding to Intensional definitions and the possible, vs. the
Aristotle particulars corresponding to the Extensional definitions and
the actual. The Intensional can also be associated with mathematical
descriptions and algorithmic complexity, whereas Extensional is when
something is defined by listing all of its components without assigning
any order to it or doing any information compression. I think that it
takes a person to do the Intensional, to assign order, beauty or
meaning. My belief is that we as finite persons cannot reduce that to
numbers, fully understanding it in a reductionist way. I think this is
what Stephen was getting at with Intensionality, and perhaps what is
also called simple apprehension, intuition. I guess this could be
Bruno's distinction between the inside view (G) of only the world that
is accessible to us through proof, versus being able to somehow
comprehend truth, beauty and order directly (G*).
I think there might be some confusion sometimes with what math and
numbers are about. I think that math is about Intensionality, seeing
truth, beauty and order. By definition, this is saying that we are
leaving out a lot of the particulars, we are compressing information.
Some people (particularly the reductionist view) say that math brings
us closer to understanding everything about the universe. They look at
numbers and say wow numbers are very precise, so this means we can do
the same thing with the universe. Perhaps in a way math does bring us
closer or give us a better understanding, but I think it is wrong to
believe that "closer" means that we can have a goal of actually
understanding everything. It is like Zeno's paradox, yes we are
getting closer, but what does that mean? I think that we have to
always take the humble stance that there will always be something that
we don't understand.
Tom
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Received on Wed Apr 05 2006 - 17:15:24 PDT