Matthew, John, Doug,
Pls humor me. Slow learner. However this is about more than data processing.
I have three vehicles (roadster, sedan and SUV) and three activities
(joyriding, grocery shopping and chauffeuring the soccer team).
Which are classes, types or sets?
I think (roadster, sedan and SUV) comprise the set, classes of vehicles,
whereas (joyriding, grocery shopping and chauffeuring the soccer team) comprise
the set, types of usage.
On May 9, 2012, at 11:02 PM, John F Sowa wrote: (02)
> Dear Matthew and Doug,
>> I do not know what distinction you [JR] make between class
>> and type. I make none.
> I sympathize. I would prefer not to use the word 'class' because
> it has been used in so many different ways that any use is an open
> invitation to confusion. In any case, my preferred definition
> determines a one-to-one association between classes and types:
> A class is the set of all x of a given type, where type is
> defined by a monadic predicate.
>> You define a class as "the set of all instances of a given type". In
>> order for a definition of a set to identify a timeless group of things,
>> the definition must yield the same group no matter when its extent
>> is calculated.
> That is why I prefer to avoid the word 'class'. The O-O people wanted
> to apply set-like operators to collections that change their membership
> in different contexts. The word 'type' defined by a monadic predicate
> has that property. You can talk about subtypes and instances in the
> same way that you can talk about sets and members, but the instances
> can change in different contexts.
>> The spatio-temporal extents [in a 4D view] are considered to exist
>> simpliciter independent of time. You can of course also have the class
>> "Persons alive at 2012-05-08 21:52:00".
> I'm happy with that way of talking. But I would prefer to use the word
> 'set' when I focus on the instances and 'type' when I focus on the
> membership criteria. There is never a case when the word 'class' is
> useful -- except when talking about notations that use that word.
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