On Tue, July 17, 2012 17:25, Chris Partridge wrote: (01)
> So a Sowa-class can change extension "at different times, places, and
> possible (or actual) worlds." (02)
That's a basic property of a class. (03)
> But some Sowa-classes do not change extension and some do - agreed? (04)
Sure. Some classes are timeless, such as the class of all integers. (05)
> For example the singleton set {John Sowa} does not change extension;
> but maybe it is not a Sowa-class? (06)
Sets are not classes; one reason being that their membership is necessarily
fixed. If you mean a set, then it is not a class. (07)
The class of all persons named "John Sowa" has different instances at
different times and in different possible worlds. Whitepages.com gives 56
listings for instances of this class in the US alone (i did not check to see
which of these may be duplicate listings). (08)
If by "the singleton set {John Sowa}" you mean the set whose only
member is the 4D worm that is the computer scientist we all know
and love, then its single member would be way off in the future at
the time of the formation of the solar system and would be an
unhypothesized fictitious being in Middle Earth. (09)
If, on the other hand, you mean all persons who meet a certain
criteria, and select the criteria so as to uniquely select our John
Sowa, then in other contexts, there would be no (or possibly several)
instances of the class. Whether a class is a singleton, is context-
related. (010)
> So we have some fixed extension Sowa-classes and some variable
> extension Sowa-classes.
> Sowa-classes that change extension can be indexed by the ways in which
> they change extensions, fixing them modulo variables. (011)
Since there are an infinite number of possible extensions,
i am confused as to what such an indexing method would be. (012)
> Sowa-classes that don't change extension don't need to be indexed. (013)
Then how can a reasoner find them? (014)
> It sounds as if you are agreeing with me. (015)
[it seems like a change of author here.] (016)
> Sowa-classes sound awfully like what a lot of people call concepts/terms.
> They certainly aren't like sets. (017)
Agreed. (018)
> I guess, if we want to have something that does not change extension,
> these concepts/terms aren't up to the job. (019)
One rarely reasons over all possible contexts. Classes are certainly up
to handling reasoning within a single context or limited set of contexts.
In a single context, a class would have a fixed extension. (020)
>> In either case, there is no "instance" of a meter. The length of
>> something is always determined by a relation (some procedure
>> that carries out some kind of comparison). (021)
> Better to say, the length of something is always determined by a relation
> (that *can* be evaluated some *possible* procedure that carries out some
> kind of comparison). Otherwise unmeasured metres are not a metre -
> an odd claim. (022)
>> In either case, there is no "instance" of a meter
>
> Either way I can easily work out the instances. It is the actual (or if
> you take on board the amendment above - the possible) evaluations. (023)
It depends on whether one defines a metre as a distance -- in which case
it is an individual, not a class -- or as two points that are a metre apart.
Cyc treats Meter as a function and "a meter" or (Meter 1.0) as a individual
distance. (024)
I'm not sure of the utility of defining a class of all things (e.g., pairs of
points) that are a meter apart. Of course, such a class can be defined.
It might have some issues near small black holes, but that's another
matter. (025)
-- doug foxvog (026)
> For more see e.g. this excellent book
> http://www.amazon.co.uk/Basic-Concepts-Measurement-Brian-Ellis/dp/0521095565/
>
> Best regards,
> Chris
>
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
>> Sent: 17 July 2012 22:00
>> To: ontolog-forum@xxxxxxxxxxxxxxxx
>> Subject: Re: [ontolog-forum] The concepts can change?
>>
>> On 7/17/2012 3:35 PM, Chris Partridge wrote:
>> > It looks to me as if one can distinguish between (a) terms/classes
>> > whose definitions (membership conditions) change over time but whose
>> > extension remains the same across time and (b) terms whose extensions
>> > change over time, so are probably not classes in any set-theoretic
> sense.
>>
>> For each class, the defining relation is fundamental. The set of
> instances can
>> change at different times, places, and possible (or actual) worlds.
>>
>> > for a standards body at any particular time there is an official
>> > definition of a metre and so the extension of the class metre at any
>> > particular time is fixed by the official definition at that time.
>>
>> The old standard was the distance between two marks on a bar made of a
>> platinum-iridium alloy when measured at the melting point of ice.
>>
>> The current standard is equal to 1,650,763.73 wavelengths of the
> orange-red
>> emission line in the spectrum of a krypton-86 atom in a vacuum.
>>
>> In either case, there is no "instance" of a meter. The length of
> something is
>> always determined by a relation (some procedure that carries out some
>> kind
>> of comparison).
>>
>> Basic principle: the *relation* is fundamental.
>>
>> John
>>
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