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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 11 Sep 2008 11:23:44 -0500
Message-id: <F3617ADC-AA69-4D32-8623-369D54AD7994@xxxxxxx>

On Sep 11, 2008, at 3:33 AM, Matthew West wrote:    (01)

> Dear John,
> I know we usually agree on most things, so here I am going to try to
> tease out what if anything we might disagree about here.    (02)

Matthew, you and I agree on even more than you and John do, so I think  
its important to get one or two points cleared up.    (03)

>> First of all, I strongly endorse the 4-d view, and I believe that
>> it is preferable to a 3-d view for many problems.  However, I don't
>> believe that there is any ontology that is ideal for all problems.
> [MW] Yes, that is my position too.
>> JFS>> Whether you have a 3D or a 4D perspective, change still exists,
>> MW> Not really. 4-Dimensionalism has the effect of making 3D change
>>> seem static, because it is looked at in a different way, in 4
>>> dimensions instead of 3.
>> The basic laws of physics are stated in differential equations, which
>> are "almost" symmetric with respect to the space and time  
>> coordinates.
>> I use the term 'almost' because entropy creates an "arrow of time",
>> which breaks that symmetry.  In relativistic terminology, the arrow
>> of time defines a *light cone* that delimits the causal influences.
>> If you look in the direction of that arrow, you find increasing
>> entropy.  But there is no such distinction in any of the spatial
>> coordinates.
> [MW] Again I agree, but this is not really the root of what is  
> different
> between 3D and 4D. The real difference is that 3D sees that what  
> exists
> now is all that exists, whilst 4D sees the past and the future as  
> part of
> what exists as well as the present. This is what it means to stand  
> outside
> time.
> If you think about it this is necessary when you accept that things  
> have
> temporal parts. If things have temporal parts, then those temporal  
> parts
> must exist, but they are extended in time, so things that are not  
> simply
> "here and now" must exist, i.e. all spatio-temporal extents exist  
> (at all
> times, but strictly independent of time).    (04)

Agreed, and a nice analysis. Putting the same point in logical terms,  
the universe of discourse shouldn't be in a state of flux, if we ever  
expect to be able to write stable ontologies; so the universe of  
things we quantify over needs to be defined outside of time, and  
itself contain temporally extended (or at least temporally located)  
entities.    (05)

> Now when I was saying it was
> natural in 4D that the set of, say cars, was the set of all cars  
> that ever
> existed, that is because it is natural for the set of cars to be the  
> set of
> all cars that exist, and since that is the set of all extents that  
> are cars
> for the whole of their lives, then that is naturally the set of all  
> cars
> that ever existed or will exist (to put it in 3D terms).
>> MW> ... extensionalism in classes is quite natural when you have
>>> dealt with change in the way that 4-dimensionalism does.
>> I'll avoid getting into debates about what is 'natural', but I must
>> emphasize that the distinction is independent of time or change.
>> In my previous note, I made that point by talking about hypothetical
>> issues, but the same point can also be made in terms of modal logic.
> [MW] And interestingly, I again use possible worlds as an alternative
> to modal logic. Not that I object to others using modal logic, but I
> do not see that I am obliged inevitably to do so.    (06)

Again, I agree that this is the best approach. I think this is widely  
accepted, by the way: John McCarthy made the same point many years ago :
http://www-formal.stanford.edu/jmc/modality/modality.html    (07)

>> Second, the distinction can be seen very clearly in examples such as
>> the types HumanBeing and FeatherlessBiped, both of which have the  
>> same
>> extension, but different intensions.  It's irrelevant whether those
>> two types have the same extension in a 4-d universe or for all time
>> in a 3-d universe.  They are not provably equivalent according to
>> the usual definitions of the terms.  Therefore, they are different
>> by intension, and only accidentally the same by extension.
> [MW] Again, I do not object to others choosing to follow this route,
> I only say that I am not inevitably obliged to do so, and in fact do
> not.    (08)

But here I think John is right, and that you are obliged, whether you  
like it or not :-), to accept this distinction.
> What you say is very "natural" for someone with a background in logic
> and traditional set theory which has a strong emphasis on predicates
> equating to sets or types, but this is not an inevitable choice.    (09)

Of course, but that is the point. Extensionality *is* the decision to  
identify predicates with sets.    (010)

> For
> example, I prefer to say that sometimes predicates do not refer to a
> set (e.g. Russels paradox), and sometimes more than one predicate  
> refers
> to the same set (e.g. your example above).    (011)

A healthy intensionalist position regarding predicates. However, you  
do need to say what it is they DO refer to, if its not a set. Common  
Logic solves that problem for you, by the way.    (012)

>> JFS>> In any perspective, you must be able to plan for the future,
>>>> talk about what exists NOW, or what exists in some hypothetical
>>>> time or place that might never exist anywhere in the 4D universe.
>> MW> Yes. But in a 4-dimensional world view, all of this can be dealt
>>> with extensionally, so why wouldn't you?
>> You wouldn't in either 3-d or 4-d because it's impossible.  Many more
>> things are planned than are ever implemented, and many things that  
>> are
>> implemented have no little or no resemblance to the plans.   
>> Therefore,
>> you must be able to talk about the *type* of airplane because the set
>> is very likely empty in any or all ontologies.  And there is exactly
>> one empty set:  the set of all unicorns is identical to the set of
>> all airplanes with flapping wings.
> [MW] This is just another case that is covered by possible worlds.  
> Plans
> are about possible worlds you wish to bring about, but often they do  
> not
> coincide exactly with the real world, and they can include entirely
> fictional
> worlds in which unicorns do exist, and then I can quantify across  
> these
> possible worlds and not end up with the empty set.    (013)

True. You can have what IKRIS called a panoptic universe, which  
contains anything anyone might ever want to contemplate or imagine.  
This seems to be the only realistic approach to dealing with  
interoperability between potentially incompatible universes of  
discourse, see the IKL guide for a brief discussion of this point: 
http://nrrc.mitre.org/NRRC/Docs_Data/ikris/IKL_guide.pdf    (014)

>> MW> Well you can do the usual things with possible worlds to deal
>>> with That [hypotheticals], so no great problem there.
>> But we cannot observe, visit, or manipulate possible worlds.
> [MW] But we can talk about them and say "What if?" which is the  
> usual use
> I find for these in practice.    (015)

Quite.    (016)

>> When we reason about possible worlds and entities on our computers,
>> we are actually using intensional descriptions of the hypothetical
>> entities to create 'virtual' extensions.
> [MW] I suggest that using possible worlds is not necessarily  
> restricted
> to this. I see the entities as existing in the possible world, and not
> being hypothetical.    (017)

Exactly. This whole discussion is becoming confused. There are two  
ways to look at modalities: John's way follows Dunn's theory and is  
based on intensional descriptions. The far more commonly used view  
uses Kripke's possible-worlds account of modalities. Kripke's is  
widely accepted as the standard, and certainly gives a more useable  
semantics, which corresponds exactly to your perspective (and has been  
used as the basis of planning systems in AI for the past 30 years)    (018)

>> Even with our actual world, it is impossible to deal with extensions
>> for most of the things we talk about.  Census takers are well aware
>> of the difficulty of enumerating all the people in a single city.
>> Imagine trying to enumerate or reason with the set of all mice,
>> flies, or bacteria in a city.  We must reason with intensional
>> descriptions because it's impossible to deal with the extensions.
> [MW] Ah! OK. Here we need to distinguish between what is and what we
> know. Ontologically, the set of people in a city (at a point in time)
> does exist, but we may not know all the members. That does not make  
> the
> set intensional, nor does it mean the set does not exist, it only  
> means
> we do not have complete knowledge about it.
> This brings some practical problems, but it is not an ontological  
> reason
> for intensionality.    (019)

Exactly.    (020)

>> MW> They [differential equations] are just descriptions of 4D
>>> objects, just as a quadratic can describe a line in two dimensions.
>> Yes, indeed.  Those equations are *intensional* characterizations
>> of entities that might or might not exist in any world, independent
>> of whether the ontology happens to be viewed in 3-d or 4-d terms.
> [MW] I see these as properties that all members happen to have. That
> might be why a particular set is interesting, rather than another one.
>> MW> However, a 3D ontology will be predisposed to an intensional
>>> approach, whereas I find with a 4D ontology an extensional approach
>>> is more natural.
>> In all of your examples of hypotheticals and plans, you were talking
>> about the intensional characterizations.  So you were doing what I
>> was suggesting:  talking about intensions.    (021)

John is just plain wrong here. Hypothetical talk does not HAVE to be  
interpreted in intensional terms. The Kripke possible-world  
perspective is simpler and more robust, and does not invoke anything  
intensional (though it CAN do so, if one feels that is absolutely  
necessary.)    (022)

> [MW] I agree I am "talking about" the same things, but in different
> terms.
> Bottom Line
> There are a number of ontological positions that you need to choose
> between, and it seems to me that we have not made all the same  
> choices,
> and this is what is resulting in the differences we have found here.
> The key choices that seem to me to be relevant here are:
> 1. Do particulars have temporal parts or not.
> i.e. are particulars extended in time as well as space (or not)?    (023)

Physical (spatiotemporal) particulars. The number 7 is a particular  
but isn't spatiotemporal.  Here's another way to say it: can something  
occupy space without occupying time? Yes (continuants) or no ("4-d")?    (024)

> 2. Extensionalism (or not) in particulars.
> i.e. if particulars coincide, are they the same thing?    (025)

Do you mean spatiotemporally coincide? LIke a bottle and the glass it  
is made of?    (026)

> 3. Eternalism vs presentism.
> i.e. is everything that exists what exists now, or is everything that
> exists include all that exists in the past and the future?    (027)

Also possibilism: even hypothetical things exist. But this 'exists'  
has to be taken with a pinch of salt, or at least clarified, as it  
really doesn't mean what people ordinarily mean when they talk about  
the world in English. We say things like, "The hadron supercollider  
didn't exist in the sixteenth century."  I suggest a better (less  
confusing and contentious) way to say it is, the logic admits all  
possible, future and past entities in its universe: they all  
*logically exist*. But only a small fraction of the things that  
*logically exist* ACTUALLY exist (i.e. in the actual world, now). So  
actual existence is a predicate (or a type, if you like) in the  
logical description. To 'logically exist' simply means that it is a  
thing that can be referred to, can be discussed, can be given a name.  
So this is really only another way to say that all names refer, which  
is the basic semantic assumption of logic.    (028)

> 4. Extensionalism in sets/types/classes vs intensionalism
> i.e. if two sets/types/classes have the same membership, are they  
> the same.    (029)

That is not a option. Sets with the same members are the same set,  
simply by definition of "set". There is no intensionalist option for  
sets. An intensionalist view of classes says that a class is not a set.    (030)

> Now my choices are:
> - Temporal Parts
> - Extensionalism for particulars
> - eternalism
> - Extensionalism in sets    (031)

I agree except for the second. Don't you want to be able to  
distinguish the bottle from the glass out of which it is made? Or have  
I misunderstood what you mean by this?    (032)

Pat    (033)

>> From the way you are talking you choices would seem to be:
> - Temporal Parts
> - (not clear from these discussions, but probably extensionalism for
> particulars)
> - Presentism (the membership of types changes over time)
> - Intensionalism
> Now none of these choices are a free lunch it seems to me, and various
> combinations
> can make sense, though I think there are some that do not, and there  
> are
> other
> choices to be made beyond these (like possible worlds and modal  
> logic). In
> my mind,
> the most important thing is to be clear about the choices you have  
> made, and
> then
> be consistent, rather than that there is only one "right" choice  
> that can be
> made.
> Regards
> Matthew West
> http://www.matthew-west.org.uk/
>> John
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