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Intension and Extension (Was RE: [ontac-forum] Type vs. Class - last cha

To: "'ONTAC-WG General Discussion'" <ontac-forum@xxxxxxxxxxxxxx>
From: "Cory Casanave" <cbc@xxxxxxxxxxxxxxxxxxxxxxx>
Date: Sun, 22 Jan 2006 13:35:12 -0500
Message-id: <018701c61f82$95645d30$0600a8c0@cbcpc>
>If 'rabbit' refers to a type, and if rabbit instances existed before 
>human beings, and if rabbits were able to recognize other instances
>of like type (e.g. for dating purposes) then the type rabbit existed 
>before any definition was formulated. Talk of types should thus not 
>rely too much on talk of definitions/intensions. Indeed there are 
>many types in biomedicine for which definitions have not yet been 
>supplied, and many types in all domains for which incorrect 
>definitions have been (or were for many centuries) supplied.    (01)

[[CBC] ] While a bunch of furry creatures may have existed long ago, the
concept of how these individuals are related is not part of the natural
world.  That we may decide that a set of individuals is sufficiently "more
similar" such that we classify them under a common term and concept it is a
tool WE use that is a basis for how WE think and how WE communicate.
Certainly the first classification, one common to living things is "food",
to a lion the distinction between "food" and "rabbit" may not even exist.
Some pre-human may have had a thought or grunt for "Rabbit food", and thus
was born the CONCEPT.
When we communicate such concepts we may do so by example (see, the things
in this box are the "rabbit" I was talking about) or by definition.  Both
are ways to communicate and clarify the concept that we have in OUR MINDS or
OUR logical formalisms.  Classification by example appears to be how we
learn, but isn't this discipline about being a bit more precise?
So it would seem to me there are 5 things in play;
* An actual thing - jumping across my lawn
* A concept for a kind/classification/type of things - rabbit
* A definition for the concept - Small mammal, etc.
* Sets of things - creatures in a box
* A set of individuals satisfying a concept - "extent".
* Terms for the concept - EN:"Rabbit", FR:"Lapin"    (02)

A concept <HAS> terms, definitions, sets and <AN> extent.    (03)

What was proposed but seem invalid is that we can always deduce equivalence
of concepts by equivalence of individuals.  This would not work where there
is more than one possible aspect of the same individual or where there is
change.  Perhaps there is a special kind of type where this kind of
assumption can be made.  This special kind of type would have to have
individuals completely defined by a single definition and thus not
correspond to an individual in the real world.  One example of such types is
the enumerated types found in programming languages.  "Color" may be an
example of such a type, but I am not sure yet.  I am mostly sure "Rabbit" is
NOT one of those types.  So the more general concept is the type that does
not contain this assumption.    (04)

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