As I understand it, the issue can be seen as what series of architectural
choices one makes. (01)
There is a distinction going back to Aristotle between things that can have
members and things that cannot (phrase this in the way that suits you -
instances, predicables, etc.).
If you choose to make that distinction, then you may then want to tighten up
what kind of things cannot have members, and argue that these must all be
concrete (a kind of abstract object nominalism) - another choice.
If you make this second choice, you can resolve Pat's point about numbers
(at least, natural numbers) with some neo-Fregean approach. Or, maybe a
structuralist approach such as Shapiro's.
If you have made these two choices then a mental shorthand for the
distinction might be that it rests upon a concrete-abstract distinction -
but (architecturally) this is a much weaker and murkier distinction to base
things on, so not such a solid foundation.
So, to make sense of this I think it helps to expose the architectural
choices one had made - and as the discussion shows (a) we often do not do
this and (b) there are a myriad of choices to choose from. (02)
Chris (03)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 18 December 2012 22:24
> To: [ontolog-forum] ; David Price
> Subject: Re: [ontolog-forum] Fwd: Ontologies and individuals
>
>
> On Dec 18, 2012, at 6:13 AM, David Price wrote:
>
> > On 18 Dec 2012, at 13:28, Alexander Titov wrote:
> >
> >> Dear Matthew,
> >>
> >> I would like to ask a few questions to understand you better:
> >>
> >>> MW: Someone mentioned that an individual is something that does not
> have members (in the sense of a set having members) and that is close to
what
> I would mean, but that would make the null set an individual, so it is not
quite
> adequate. My definition of individual is something that exists in space
and
> time. I am not a set (or class or type or kind or sort etc) nor is my car
or this
> email. Nor is Sherlock Holmes to give a more difficult example. All these
things
> can be placed in space and time (even if it is imaginary space and time) .
On the
> other hand, sets/classes/types are generally considered to exist outside
space
> and time.
> >>
> >> I understand that a 'main dichotomy' between an individual and a
> set/class/type is - existence in space and time (rather than having or not
having
> members).
>
> That surely will not work. The natural number five is an individual, but
does not
> exist in space and time, even imaginary space and time. Does Moby Dick,
the
> work, exist in space and time? (Where?) Some people think that sets exist
in
> time. There is hardly any position on these debates that has not been held
and
> defended by someone.
>
> Pat
>
>
> >
> > This depends on the metaphysics and language you've adopted. As Pat
said,
> Individual means 'member of set' in logic and has nothing to do with space
and
> time. Matthew's comments are couched in 4-dimensionalism so Individual is
> "Thing that exists in some possible world" and so is entirely about space
and
> time. In 4-D, a Class can be a member of a Class, yet Classes are not
Individuals.
> >
> > So, without couching discussions into the approach/background that is
the
> context, even Individual is not a clearly defined term.
> >
> >>
> >>> MW: On the other hand, sets/classes/types are generally considered to
> exist outside space and time.
> >>
> >> Can we consider opposite - sets/classes/types do exist within space and
> time as well? For example, as a collection/set of space and time
extensions of
> all their members?
> >>
> >> What will happen if the criteria is joined: 'does not have members'
> >> and 'exists in space and time'? Not sure if it is better... We have
> >> now another (at least three) cases to think about.
> >
> > As Classes are things of which Individuals are members based on some
> criteria so, by definition, Classes in 4D are not in space time. Classes
are
> identified by their extension, but that does not put them into space/time
> either.
> >
> > Cheers,
> > David
> >
> >
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