Doug and Ed, (01)
I'm glad that you agree with each other, because I agree with both
of you. Following is my response to Ed's note in the other forum. (02)
John (03)
-------- Original Message --------
Subject: Re: [architecture-strategy] Relationship between types, classes
and sets
Date: Thu, 20 Jan 2011 14:51:59 -0500
From: John F. Sowa
To: architecture-strategy@xxxxxxxxxxxxxxx (04)
On 1/20/2011 12:57 PM, Ed Barkmeyer wrote:
> No mathematical object can change types, because whatever predicates it
> satisfies, it will always satisfy, and whatever predicates it does not
> satisfy, it will never satisfy. (05)
That depends on how you use mathematics. Note that math can represent
and simulate any kinds of change in the weather, human societies, or
nuclear physics. (06)
> But when we assign 'types' to objects in a dynamic world, like people
> or vehicles or vacation plans, the objects have 'state' and can change
> 'state'. Predicates that are associated with 'states' can therefore
> become true or become false at different times. (07)
That's true. (08)
This raises the question about what kind of ontology (or family of
ontologies) might be appropriate to an application. Aristotle's
suggestion (which is still widely used) is to distinguish substance
(or essence) from accident: Some predicates that describe the
essence of an object don't change, but others that describe the
accidents can change. (09)
> Ship of Theseus paradox: This is the Ship of Theseus, but over
> time every timber has been replaced. (010)
The US Army edicted a good solution to that problem for rifles:
any soldier can request a replacement for any part of a broken
rifle, but you don't want soldiers to "hoard" rifles by building
new ones piece by piece. (011)
So they declared that the stock of a rifle had a unique serial no.
Any part other than the stock was replaceable, but if the stock
broke, the soldier had to turn it in and be assigned a new rifle. (012)
In effect, the army declared that the substance or essence of the
rifle resides in its stock. People often make decisions that have
ontological implications, whether or not they ever heard the O-word. (013)
I would argue that this issue does not raise any problem in math
or logic, but in ontology. If you adopt a suitable ontology for
the application, the other issues fall into place more readily. (014)
(And by the way, I have nothing against using OWL when appropriate,
but just using OWL notation does not automagically give you ontology.) (015)
John (016)
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