>Dear Matthew, David, Chris, Pat, John,
>MW> So Matthew West the employee of Shell is only the same
> > thing as Matthew West the person if Matthew West is an
> > employee of Shell for the whole of his life.
>Nonetheless, it is always true in both 3-D and 4-D models
>that every instant of time when MW is an employee, MW is
>also a person. Therefore, Employee < Person. (01)
No, that doesn't follow at all. We are quantifying over 4-d entities,
ie 'slices' of a 'history-worm' (using a commonly used way of
ridiculing this POV) which I will write by pairing a name with a
time-interval, eg [PatH, 1997-2007]. That is not a person, it is a
temporal part of a person. The actual person, Pat Hayes, is [PatH,
(lifetimeOf PatH)], which I will not tempt fate by giving a numerical
form for. OK, now, suppose that I was an employee of the State of
Illinois from 1994 to 1999, at which time I left to come to Florida.
Then [PatH, 1994-1999] is an Employee and a temporal part of a
Person, to wit [PatH, (lifetimeOf PatH)]. It is not a Person. So (02)
forall x Employee(x) implies Person(x) (03)
is false: in fact, this is a counterexample. So Employee is not < Person. (04)
>MW> The employee instance is not a person-for-the-whole-of-their-life,
>Of course. But every employee instance is a part of the person
>instance. That is exactly what is implied by Employee < Person. (05)
Your earlier explanation of < didn't mention anything about parts. On
the face of it, that seems to be about employees and people. Usually,
an employee is an instance of a temporal part of a person, not of a
whole person (someone born into servitude might be the only exception
I can think of). All speaking in 4-d language here, of course. (06)
>DD> Simply said, identifying whether something is a 'natural kind'
> > or a role might be very hard in some cases and completely depends
> > on the level of granularity of your ontology or the background
> > of the modeler.
>This is one of many reasons why trying to draw a hard-and-fast
>distinction that holds for every possible case is not easy.
>Therefore, it makes more sense to put all the concept types into
>a single hierarchy and leave it underspecified, if necessary.
>CP> Your notion of employee does not distinguish between employers
> > - and it is also temporalised - one is an employee at a time.
>No. The statement X<Y is about *types*, not about *individuals*,
>and the *definition* of a type is independent of space and time.
>What is time dependent is whether a particular individual is
>an instance of a particular type at a given time.
>CP> It seems that implicitly mean that *at time t1*, X < Y means
> > that every instance of X is an instance of Y. Maybe better to
> > say that X <t1 Y means that at t1 every instance of X is
> > an instance of Y.
>No. To say Employee<Person means that at *every* point in time
>and place, if x is an employee, then x is a person. (07)
That is a 3-d-ish way of talking, however, in which things that
endure through time, retaining their identity, have properties *at a
time*. In a 4-d framework properties are all timeless, and if
something *at a point in time* is a person, then it is a very
unfortunate - because very short-lived - person. (08)
PS. Just for the record, I often talk this 3-d-ish way myself. But I
can speak 4-d when required :-)
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