Re: [ontolog-forum] Spatial Extent of Abstract Entities?

[Mike Pool <mikepool@xxxxxxxxx>]

Pat,

In terms of other treatments of this topic, it would be useful to look at Penelope Maddy's excellent "Realism in Mathematics" which attempts to answer the causal epistemic objections to mathematical platonism by positing the physical manifestation of mathematical sets, i.e., contending that pure sets do/can have spatial extent (and that that is how we in fact have knowledge of them). It has been some time since I read the book, but from what I recall she would not argue that abstract mathematical entities depend on physical manifestation for their existence, but they nonetheless do physically manifest themselves whenever we encounter a set of things.

regards,

Mike Pool

On Thu, May 23, 2013 at 12:15 PM, Patrick Cassidy <pat@xxxxxxxxx> wrote:

Name of thread changed to the more specific topic.

I'm curious to know how others have handled the issue of spatial extent of
abstract objects, which Doug and Matthew have been discussing.  Here I
describe my current treatment, open to criticism or modification.

Abstract entities, in particular information such as text or images
(abstracted as pixilated raster objects), do not themselves have mass or
extent, but they may have physical representations (as markings on paper,
solid models, audible sounds, light wave patterns).  So do they can be said
to have physical "location" or "extent".  In COSMO I avoid specifying any
physical 'location', but when necessary, the 'location' is either the
contiguous region in which all physical representations exist, or the
disjoint spatial extent of all of the physical representations.  Neither is
easy to identify.

I haven't yet encountered an occasion to actually *use* the physical
'location'.  It can be problematic.  Anything that sends electromagnetic
waves into space may represent information, and the physical extent of that
information would then be the region in which those electromagnetic waves
exist.  But whether that information is actually recoverable at some
distance from its origin may depend on the size and sensitivity of the
receiver, and the degree of obscuration by background noise.  Very tricky.
If in fact a 'location' must be specified for the information content,
perhaps it is easier just to say that it is in the world (real or possible)
in which it originated.

But one also needs to decide whether it in fact 'exists'.  My treatment
considers abstract entities as 'existing' only as long as there is some
physical representation (which may be , e.g., on paper or in the mind of
some agent).  When the last representation disappears, that abstract entity
no longer 'exists'.  Can it be re-created?  No, not as the same individual.
There may be other individual abstract entities (e.g. a sentence) that are
in every attribute (except time, location,  and origin) identical to
another, but that would be a different individual, just as atoms of some
element are all identical, but are distinct individuals.  Likewise, the same
sentence generated by two different people, existing simultaneously, are
still different individuals, though they may have the same propositional
content.

Other treatments?

Pat

Patrick Cassidy
MICRA Inc.
cassidy@xxxxxxxxx
908-561-3416


> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Matthew West
> Sent: Thursday, May 23, 2013 9:25 AM
> To: doug@xxxxxxxxxx
> Cc: '[ontolog-forum] '
> Subject: Re: [ontolog-forum] What is the role of an upper level
> ontology?
>
> Dear Doug,
>
> > >> In 4D, i would too.  But i would consider the organization an
> object
> > >> with a temporal, but not a spatial dimension.
> > >
> > > MW: That is a rather half hearted 4 dimensionalism. I go for strong
> 4D
> > > which has the 4D extent as the identity of any individual (not a
> set
> > > or relationship). So I do not even know what it means to exist if
> you
> > > have a temporal but not a spatial extent.
> >
> > At work i have a sick leave account and a vacation leave account.
> > Such accounts (as well as bank accounts, credit card accounts) are
> useful
> to
> > model in an ontology.
> > They certainly have temporal existence.  But it seems
> > to me quite a stretch (not that Rose Mary Wood couldn't do it 8)# )
> to
> claim
> > that they have a spatial extent.
>
> MW: The question is what is the root of a day's leave? It is you for
> the day
> in a vacation state. That is a spatio-temporal extent, and any account
> of it
> is some representation of that, or an aggregate of similar objects.
> >
> > Permission to do something has a temporal extent.  Claiming that its
> spatial
> > extent it the area in which the thing may be done seems specious to
> me.
>
> MW: Not at all. You only need to bring possible worlds into the
> equation to
> cover the future activity (a spatio-temporal extent) that is the
> execution
> of that permission.
>
> > A
> > patent is temporal, and is different from the sheet of paper (or
> group of
> all
> > sheets of paper that document the
> > patent).   Claiming that it has a spatial extent of the territory of
> > the issuing country also seems a stretch.
>
> MW: A patent is about (generally) a design - that is universal, and
> placing
> restrictions on its use. Again we need possible worlds and activities,
> but
> not objects with temporal but no spatial boundaries.
> >
> > What would the physical extent of an ontology be?
>
> MW: An ontology, is an aggregate of signs of classes, individuals,
> relationships, and rules. The signs are spatio-temporal extents of some
> sort, even if they are bits in computers.
> >
> > What is the physical extent of an hour, a day, a year, a century be?
>
> MW: The whole universe. That is actually obvious if you really think in
> 4D.
>
> > A time zone, the Earth, the observable universe, an
> expanding/contracting
> > sphere around the time zone/Earth with its radius being in light-
> units of
> > time, the instantaneous greatest distance in time from the specific
> time
> to
> > the time of the sphere?
>
> MW: It actually makes a lot more sense when you add the spatial
> dimensions
> in. I suggest you try drawing a space-time diagram for this problem.
> >
> > I accept 4D models of physical objects, situations, and events, but
> also
> > accept the existence of temporal non-physical objects.
>
> MW: I consider that unnecessary, and therefore to be avoided.
> >
> > > In the strong 4D that I use, an organization consists of the
> temporal
> > > parts of the people involved in it, whilst they are in an
> > > organizational role.
> >
> > Then in any KB using that model, Apple, Inc., didn't have a presence
> in
> the
> > countries in which it rented post office box numbers, but had no
> employees?
>
> MW: It is actually an interesting question what exactly is the
> constitution
> of an organization. Is it just the people? Or does it include what the
> organization owns/rents as well? The answer is a matter of law, which
> may
> vary from place to place.
>
> MW: If there was a company set up, and it had a PO box, then there are
> officers of the company, and even if they are not resident in the
> country,
> then the company exists (there is not a restraint on companies to
> operate
> only within their country). Whether just a PO box counts as a
> "presence" is
> interesting. I would look for legal precedence. However, the
> consequence
> determines what spatio-temporal extents count as part of a company, not
> whether or not a company is a spatio-temporal extent.
> >
> > Such a model may be consistent and useful for your purposes.  But
> there
> seems
> > to me to be no reason to impose it on everyone who
> > wishes to use any ontology.
>
> MW: I carefully declare that this is a 4D view of the world. I quite
> agree
> that this does not require everyone else to take the same view. I only
> argue
> that it is a valid, compact and rigorous view.
>
> > I'd accept it as an upper-level microtheory,
> > but not as part of an upper level ontology designed for general use.
>
> MW: It is perfectly suitable for general use. I have not yet found
> something
> (together with the other elements I mentioned, a basic set theory,
> mathematical objects, and possible worlds) that it cannot cover.
> >
> > > Note that I have no problem constructing one kind of object out of
> the
> > > temporal parts of another kind (or kinds) of object.
> > > In any case, given the nature of space-time, I don't know what it
> > > means to exist with a temporal extent, but no spatial extent.
> > > I therefore reject abstract individuals as an unnecessary
> commitment.
> >
> > Some people would reject a 4D model as an unnecessary commitment.
>
> MW: If you do not commit to 4D you  have to commit to something else.
> It is
> a choice you have to make, not an unnecessary one. There are of course
> people who make alternative choices, such as 3D + time, or even as
> Barry
> does, 4D for activities and 3D + time for physical objects.
>
> > It seems to me that enforced 4D (or 3D+1) models as well as there
> being
> > subclasses of abstract individual should be stated in microtheories
> that
> users
> > can accept/reject/ignore according to their needs.
>
> MW: If you are trying to build a tower of Babel that contains all
> possible
> theories, then you should certainly include alternatives. Most of my
> work
> has been in data integration. Here the objective is to bring different
> ways
> of looking at the world together in one place using one way of looking
> at
> the world. I have found 4D unsurpassed for that because of its rigour.
> >
> > >> Would you say, "Part of the Red Sox has a daughter named Sue."?
> >
> > > MW: That strikes me as rather unlikely, but not impossible. Let us
> > > look at the case. Presumably you do not mean any part of the Red
> Sox
> > > (say all the pitchers, or the right arm of one of them) but a
> particular
> > player.
> >
> > Isn't a temporal part of a particular player a part of the Red Sox,
> if
> that
> > player is part of the Red Sox?
> >
> > From the above comment, it seems you would have the same objection
> to
> these
> > two sentences.
> > + A Red Sox player has a daughter named Sue.
> > * Part of the Red Sox has a daughter named Sue.
> >
> > I'd guess that most English speakers would find the first statement
> > acceptable, but not the second.
>
> MW: Yes, the second statement is not sufficiently precise to be
> meaningful,
> though not actually wrong.
> >
> > > Of course, a particular player is not the whole life of the person,
> > > but the temporal part of the person whilst they are a player for
> the
> > > Red Sox. Now what has a daughter is a father (or mother - but I am
> > > going to presume that there are no women players for the Red Sox).
> >
> > > The father is the temporal part of the person from when the
> daughter
> > > is born until they die
> >
> > By "they", it appears you mean the father,
>
> MW: Yes.
>
> > not both the father and the
> > daughter.  Do you use "they" instead of "he", to accept the
> possibility of
> the
> > father changing gender?
>
> MW: No. But I am assuming that if he did change gender that would not
> stop
> him being a father (though that might make a mess of some databases).
> >
> > > (I presume that you remain a father until your death, even if your
> > > daughter dies before you - you could make other choices).
> >
> > This means that there is only one father -- only one specific
> temporal
> part of
> > the person who is a father.  Which means that I, today, am not a
> father,
> > although there is a temporal part of me (of which I, today, am a
> temporal
> > part) that is.
>
> MW: Yes, but it is a state extended in time, not a series of time
> slices. I
> take a perdurant view. That means I am a father from when a child is
> born
> until my death.
> >
> > > Now it is true that a Red Sox player has a daughter if the temporal
> > > part of the person is identical to (has the same spatio-temporal
> > > extent) as the father of the daughter.  That is unlikely,
> >
> > ... and very counter-intuitive.  If you told a Red Sox fan that none
> of
> the
> > Red Sox players were fathers, you would find that s/he disagreed with
> you.
> > Your ontology might work for your purposes, but has little agreement
> with
> the
> > human world.
>
> MW: That is because what you have stated includes several short cuts.
> If you
> expand it fully, you could say, the person (for the whole of their life)
> that is currently a Red Sox Player (a state of the person whilst they
> are a
> Red Sox Player) is currently father (a temporal part of the person) to
> Sue.
>
> >
> > > but if the person who had a temporal part that was a Red Sox Player,
> > > and had a temporal part that was a father and the daughter was born
> > > exactly when they joined the Red Sox and they died whilst still a
> Red
> > > Sox player,
> >
> > > then indeed, a part of the Red Sox would have a daughter.
> >
> > The conclusion here is that then a Red Sox player would have a
> daughter.
> > According to your logic, if a person became a father while playing
> for the
> Red
> > Sox, and he died while still being a Red Sox player, then a part of
> the
> Red
> > Sox, more specifically a temporal part of one of its player parts,
> would
> have
> > a daughter.
> >
> > Such reasoning is consistent and mathematically valid, but seems to
> me to
> be a
> > model of reality that most would reject.
>
> MW: That seems inconsistent to me, when it seems you wanted to be able
> to
> say that a Red Sox player had a daughter.
>
> > By all means create an ontology
> > (microtheory) that encompasses it and can be used for reasoning in
> conjunction
> > with a knowledge base that does not reject its assumptions.  But be
> aware
> that
> > many people would use contradictory microtheories, and they might be
> > interested in the same KBs that you are.  So i suggest avoiding
> having a
> KB
> > inherit such an ontology, instead use it for your reasoning modules.
>
> MW: Of course. If you want to be precise, you have to translate things
> into
> 4D before you start reasoning. 3D and 4D mixed together will give odd
> results, and possibly inconsistent ones. I find the translation brings
> out
> details and issues that are otherwise left hidden.
>
>
> Regards
>
> Matthew West
> Information  Junction
> Tel: +44 1489 880185
> Mobile: +44 750 3385279
> Skype: dr.matthew.west
> matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
> http://www.informationjunction.co.uk/
> https://sites.google.com/site/drmatthewwest/
> This email originates from Information Junction Ltd. Registered in
> England
> and Wales No. 6632177.
> Registered office: 8 Ennismore Close, Letchworth Garden City,
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>
> >
> > -- doug foxvog
> >
> > > Regards
> > >
> > > Matthew West
> > > Information  Junction
> > > Tel: +44 1489 880185
> > > Mobile: +44 750 3385279
> > > Skype: dr.matthew.west
> > > matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
> > > http://www.informationjunction.co.uk/
> > > https://sites.google.com/site/drmatthewwest/
> > > This email originates from Information Junction Ltd. Registered in
> > > England and Wales No. 6632177.
> > > Registered office: 8 Ennismore Close, Letchworth Garden City,
> > > Hertfordshire,
> > > SG6 2SU.
> > >
> > >
> > >
> > >>
> > >> -- doug foxvog
> > >>
> > >> > Regards
> > >> >
> > >> > Matthew West
> > >> > Information  Junction
> > >> > Tel: +44 1489 880185
> > >> > Mobile: +44 750 3385279
> > >> > Skype: dr.matthew.west
> > >> > matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
> > >> > http://www.informationjunction.co.uk/
> > >> > https://sites.google.com/site/drmatthewwest/
> > >> > This email originates from Information Junction Ltd. Registered
> in
> > >> > England and Wales No. 6632177.
> > >> > Registered office: 8 Ennismore Close, Letchworth Garden City,
> > >> > Hertfordshire,
> > >> > SG6 2SU.
> > >> >
> > >> >
> > >> >
> > >> >
> > >> >
> > >>
> > >>
> > >>
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