Azamat,
You wrote:
"It seems to me that a
noncontradictory position in terms of your conclusion could be: Eternalism
(time as infinite duration) naturally implying Intensionalism [for
individuals and classes]."
Suppose such noncontradictory position in some terms around the
"Extensionalism vs intensionalism" was developed long time ago in the
Classification Theory (CT). I wrote already about some features of the CT. (01)
- http://www.ototsky.mgn.ru/it/21abreast.htm .
For example :
<<
- Any Classification System has two Dual parts - "Taxonomy" and
"Meronomy". The first one is "external" and connected with ordinary set
theory relations (unions, intersections, hierarchy (a subclass of)) etc..
- The second one is "internal" and connected with Properties/Parts
structure (archetype).
...
- A strict hierarchy of Taxons can be described by pure combinations of
Properties.
- "Good sets" ,their members and standard set theory relations are
described by the "Taxonomy", but the dual part "Meronomy" doesn't fix
the sets of objects in principle . Only the "subject areas" with
"open" object types and explicitly defined properties for them. A
"good" classification system must have the both parts but in practice
very often only the taxonomy is used EXPLICITLY .
...
>>
Suppose a modern activity around "a new Web" must take into account the CT
and some other "old ideas" I mentioned in the paper. (02)
Best,
Leonid Ototsky - http://ototsky.mgn.ru/it
-------------
> On Thursday, September 11, 2008 11:33 AM, Matthew wrote:
>
> '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)?
> 2. Extensionalism (or not) in particulars.
> i.e. if particulars coincide, are they the same thing?
> 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?
> 4. Extensionalism in sets/types/classes vs intensionalism
> i.e. if two sets/types/classes have the same membership, are they the
> same.'
>
> Now my choices are:
>> - Temporal Parts
>> - Extensionalism for particulars
>> - eternalism
>> - Extensionalism in sets
>>
>>>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'
>
> Matthew,
>
> Very clear account, as always. But summing up looks not so consistent,
> what
> may be caused by the interpretation of ''eternalism', your or mine. If its
> meaning implies ''eternity'', then this sort of ontology of time would
> deny
> temporal boundaries at all or time itself, and hence any measure or number
> for change and motion.
> In fact, there is eternity as infinite duration, timelessness and
> immutability, and there is time, as a specific whole made of specific
> parts:
> the past, the now, the future. But particulars with their classes are not
> the things partaking of eternity. Its denizens are rather fundamental
> properties and relationships, determining the meanings or intensions of
> things, and their classes, which innumerable members are the instances of
> those essential properties, in some particular world or state of affairs.
> It
> appears that John ontological commitments look more coherent or, say,
> ontological, as far as ontology is about intensional entities and models,
> unlike formal set theory dealing with extensional things and
> interpretations. It is natural that some known ontologists tried to review
> the set theory, where sets and classes would be replaced by properties or
> attributes.
> It must be also noted that in the information sciences and engineering, a
> usual doing is to divide the conceptual model into two complementary
> parts:
>
> A. intensional (intrinsic, underlying, innermost, inherent,
> essential,
> implicit, and constitutional);
>
> B. extensional (extrinsic, external, extraneous, or accidental).
>
> The former implies the generic things and relationships of the world and
> so
> inherently referred to ontology and embodied as a knowledge base schema.
> The
> latter involves particular states and cases of the world, and it deals
> with
> all sorts of specific assertions about specific instances of classes and
> relationships determined by the ontology, and presented as a knowledge
> base
> instance. So, the ontological work consists in providing the general
> entities, as properties, principles, rules, lwas, and underlying meanings,
> which form the base for any particular domain of special classes and
> individual things, or extensional classes. It seems to me that a
> noncontradictory position in terms of your conclusion could be: Eternalism
> (time as infinite duration) naturally implying Intensionalism [for
> individuals and classes].
>
> Thanks again for your inspiring communication.
>
>
>
> Azamat Abdoullaev
>
>
>
> ----- Original Message -----
> From: "Matthew West" <dr.matthew.west@xxxxxxxxx>
> To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
> Sent: Thursday, September 11, 2008 11:33 AM
> Subject: Re: [ontolog-forum] Thing and Class
>
>
>> 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.
>>
>>> 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). 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.
>>>
>>> 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.
>>
>> 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. 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).
>>>
>>> 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.
>>>
>>> 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.
>>
>>> 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.
>>>
>>> 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.
>>>
>>> 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.
>>
>> [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)?
>> 2. Extensionalism (or not) in particulars.
>> i.e. if particulars coincide, are they the same thing?
>> 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?
>> 4. Extensionalism in sets/types/classes vs intensionalism
>> i.e. if two sets/types/classes have the same membership, are they the
>> same.
>>
>> Now my choices are:
>> - Temporal Parts
>> - Extensionalism for particulars
>> - eternalism
>> - Extensionalism in sets
>>
>>>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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