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Re: [ontolog-forum] Ontology and Category Theory

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 29 Jan 2009 14:00:43 -0500
Message-id: <4981FCDB.4060109@xxxxxxxxxxx>
Len and Pat,    (01)

As before, I agree with Pat on this point, but I'd like to
add a few more comments.    (02)

LY>> In ordinary life their are plenty of examples of 'establishing
 > identity' from simple "hello" to solving and prosecuting crime.
 > But formal meaning of identity in CT is (in my non-mathematical mind)
 > any procedure that performs identity morphism according to definition
 > of Category (cited below).    (03)

PH> We seem to be talking about two different things at the same time.
 > There is the ordinary every-day pre-formal notion of establishing
 > identity, which we do when someone calls us on the phone and we say
 > "who is this?" This means something like "figuring out who or what
 > some unknown thing or person is", where to know "what something is"
 > has never, AFAIK, been fully analyzed by linguistics and never
 > formalized, but seems to mean something like having enough
 > information about a thing to be able to mentally distinguish it
 > from other similar things, or maybe having a description of the
 > thing which is adequate for the purposes of holding a conversation,
 > or some such.    (04)

There have been many volumes written about the difficulty of verifying
identity.  They cover many different fields -- philosophy of science,
epistemology, forensics, military intelligence, security, politics,
privacy, etc.  In all these fields, the issues are extremely dependent
on the domain, the purpose, and the degree of certainty required.    (05)

In logic, these issues are masked by a simple statement, such as 'x=y'.
But that statement could be the conclusion of an arbitrarily complex
if-then rule:    (06)

   If    x satisfies the conditions...
   and   y satisfies the conditions...
   and   x and y co-occur under the conditions...
   and   further evidence...
   then  x=y.    (07)

Many philosophers talk about "identity conditions", but trying to
determine whether those conditions hold in any particular case can
be extremely difficult.    (08)

So the short answer is that it's easy to say x=y in logic, but the
practical matter of determining whether a particular observation
of x is sufficient to identify it as y may be challenging.    (09)

For these reasons, I have a skeptical attitude toward talk
about "identity conditions" as if they were a magical solution
to some very serious issues of ontology.    (010)

John    (011)

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