Dear Barry, (01)
See below. (02)
Regards (03)
Matthew West
Reference Data Architecture and Standards Manager
Shell International Petroleum Company Limited
Shell Centre, London SE1 7NA, United Kingdom (04)
Tel: +44 20 7934 4490 Mobile: +44 7796 336538
Email: matthew.west@xxxxxxxxx
http://www.shell.com
http://www.matthew-west.org.uk/ (05)
> > >
> > > membership
> > >
> > > 1. the number 4 is a member of the set {4, the moon, Napoleon}
> > > 2. there is no corresponding type
> >
> >MW: Why? Surely a trivial type listing the members can be
> constructed.
>
> Leaving aside administrative domains (e.g. tax collection), types,
> like instances, are discovered. They are out there in reality. They
> form the subject-matter of scientific inquiry. (06)
MW: Well I would say that there is an abundance of sets out there and
some of them have greater significance than others.
>
> > >
> > > 3. Harvey is a member of the set of rabbits
> > > 4. Harvey is also an instance of the type rabbit.
> > > It is in virtue of 4. that 3. is true.
> > >
> > > We see that there are cases of set-membership where there is no
> > > counterpart to 4. Hence set membership is at least a wider notion.
> >
> >MW: Yet membership would not be time indexed whilst instance_of could
> >be (for you at least). Sounds to me as if each is narrower than some
> >common core. Can I assume (correctly) you consider that they have the
> >same properties in terms of transitivity and the like?
>
> I offered my two pennies' worth on this here:
> http://ontology.buffalo.edu/bio/logic_of_classes.pdf
> esp. pp. 6ff. (07)
MW: That was interesting. The only axiom I have to object to is the
one that says there are some particulars that are not instances (of a
class). I can live with some universals that are not classes since
for us relations are universals. I notice there is no empty class,
but that can easily be added in a more specific ontology. (08)
MW: The problem for you as I see it is that you cannot impose your
interpretation of a class to exclude as classes things that you do not
consider to be such, but I might. You can only say you have a different
intended interpretation. (09)
> > >
> > > > > Types have instances.
> > > > > We represent these instances using various means, e.g.
> > > English words
> > > > > ('red', 'bright red') or hexadecimal numbers, or what
> you will.
> > > > > Sometimes our representations are more precise, sometimes
> > > less. They
> > > > > may still all be correct (as it may be equally correct to say:
> > > > > 'animal over there', or 'cat at fifty paces').
> > > >
> > > >MW: I think I have mostly grasped what you mean by a
> type, surprising
> > > >as it has been to me. Just one last clarification here.
> I presume you
> > > >agree there are some types whose membership does not change,
> > > i.e. your
> > > >type and set have the same members, e.g. integers and
> real numbers.
> > >
> > > If integer is a type, then the set of its instances is
> indeed always
> > > identical to the set of its instances. And ditto for
> 'real number'.
> >
> >MW: So one possibility here might be for me to settle for types whose
> >instances didn't change over time, and just forget about the "sets"
> >as uninteresting.
>
> Quine used to talk about desert landscapes. You, it seems, are pining
> for desert landscapes from which all traces of the biological have
> been eliminated (even, I suppose, the oil and gas underneath). (010)
MW: Quite the reverse, I am saying there is every possible set you can
imagine (and probably more) and that you are just identifying some as
useful for some purpose.
>
> >MW: My problem now is that I understand that you want types to be
> >restricted to things like rabbits, not "people with 376
> hairs on their
> >arms" or "4, the moon, and me". Now, whilst I am sympathetic
> >to the idea of natural kinds, it seems to me that these
> three examples
> >actually sit in a spectrum and there is no clear divide between them
> >(though these three being prototypical can be easily distinguished).
>
> There are many terms for which we have clear examples of entities
> which fall under them, clear examples of entities which do not fall
> under them, and then a penumbra of problematic cases in between.
> Responses to this problem for 'type' might be:
>
> 1. it is hard work to find out which types exist (this work is called
> 'science') (BS)
> 2. we should refrain from formulating axioms about what is a type (JS)
> 3. 'type' is redundant; we should talk of sets instead, keeping our
> heads under the desert sand to avoid all sight e.g. of
> anything biological (MW) (011)
MW: Well as usual you indulge in gross misrepresentation when all else
fails. (012)
MW: In a 4D world I am happy to concede that there will be a set of sets
that corresponds to what you would refer to as types. (With an abundance
of sets of course its there). In your 3D world you seem to need these
things to be able to have varying membership over time. That is simply
a problem I don't have. (013)
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