> >
> > 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. (01)
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. (02)
> >
> > 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? (03)
I offered my two pennies' worth on this here:
http://ontology.buffalo.edu/bio/logic_of_classes.pdf
esp. pp. 6ff. (04)
> >
> > Sets are abstract entities, with wonderful mathematical properties,
> > but they are not what, e.g., biologists study.
>
>MW: Interesting how often it is people don't recognise what they are
>looking at. (05)
So you really haven't heard of Charles Darwin! You have some
interesting reading ahead of you. I suggest you start with a book
called 'The Origin of Species'. (06)
> >
> > > > 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. (07)
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). (08)
>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). (09)
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: (010)
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)
BS (012)
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