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

To: "'ONTAC-WG General Discussion'" <ontac-forum@xxxxxxxxxxxxxx>
From: "Chris Partridge" <mail@xxxxxxxxxxxxxxxxxx>
Date: Sun, 22 Jan 2006 19:14:32 -0000
Message-id: <20060122191254.89ECA424657@xxxxxxxxxxxxxxxxxxx>
Cory,    (01)

John's note seems to me not to cover a key ontological point with respect to
intension and extension. This relates to identity.    (02)

John said:
>   1. The fundamental distinction which many of us have
>      emphasized for years is between _intension_ and
>      _extension_.  To avoid prejudging the choice of
>      technical terms, I'll use the example of Rabbit vs.
>      Peter or Thumper.  The intension of 'Rabbit' is
>      determined by some definition that is independent of
>      any actual rabbits, real or fictional.  The extension
>      of "Rabbit" at a particular point in time consists
>      of all the rabbits that happen to exist at that time.    (03)

It may help (in the long run) to get his on the table.    (04)

My perspective is that there are several metaphysical choices that have an
architectural impact on the ontology - and this is one of them.    (05)

The issue is whether the identity of intentional types/instances is
determined by their definition (rather than their extension). So if two
types have different definitions, they have different intensions and so they
are then different types.     (06)

The classical example is, I believe, equiangular triangles and equilateral
triangles - the first defined in terms of angles the second in term of
sides. Are these two types or one? One can prove mathematically that they
have the same extension.    (07)

One can have fun coming up with different definitions of the kinds of
everyday entities that appear in government systems. Are these then
different types/classes? If so, it seems to me one introduces problems in
interoperability.    (08)

However, I suspect some people would prefer to take the intensional route
(Barry, for example - and I believe he is right to say the issue should be
discussed - it will not go away because it is ignored).    (09)

I realise some people want to avoid this kind of abstract discussion, and do
REAL work. However, these choices affect the eventual ontology - and so it
makes sense to explicitly document the choice that is made. Unfortunately
this often means there has to be some discussion of the choice.    (010)

As a methodology, I prefer getting together enough relevant material in a
reasonable order before these metaphysical discussions are entered into. One
then has something more concrete to test them with. So, my preferred route
would be to postpone the discussion until we have the material. But my
experience is that it does not make sense to ignore the architectural
decisions.    (011)

Chris    (012)

PS. A small point.    (013)

CBC> * A concept for a kind/classification/type of things - rabbit    (014)

I am assuming from what you say that 'concepts' are in our mind - and that
this is the mechanism we use to deal with general things. This is a key
metaphysical choice with architectural consequences - the problem is that it
is not the only or the obvious choice.    (015)

> -----Original Message-----
> From: ontac-forum-bounces@xxxxxxxxxxxxxx [mailto:ontac-forum-
> bounces@xxxxxxxxxxxxxx] On Behalf Of Cory Casanave
> Sent: 22 January 2006 18:35
> To: 'ONTAC-WG General Discussion'
> Subject: Intension and Extension (Was RE: [ontac-forum] Type vs. Class -
> lastchance to vote. )
> Berry,
> re:
> >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.
> [[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"
> A concept <HAS> terms, definitions, sets and <AN> extent.
> 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.
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