Azamat,
As a preliminary reply you may look at the original paper about Taxonomy
and Meronomy by Meien and Schreider -
http://ototsky.mgn.ru/it/papers/meien-shreider.htm (in Russian). Also I
may send you a copy of Schreider's paper (in Russian) about the Duality
Principle. (01)
Best,
Leonid (02)
> Privet, Leonid,
>
>
>
> Spasibo za material, very research intensive content. I like your
> assertions
> like: 'A strict hierarchy of Taxons can be described by pure combinations
> of Properties.' What is interesting for me how you manage to reconcile two
> different schemes, call it meronomy and taxonomy, in one framework, or
> they
> just go separately. The first one is ''a logic or calculus of
> individuals'',
> ie, concrete things, and it was initiated as an alternative to ''a logic
> of
> classes'', dealing with a hierarchy of classes, classes of classes, etc.,
> ie, abstract entities. That may depend on how you define a member of
> relation and a part-whole relationship. For instance, Unlike the set
> theory,
> all good dictionaries take at least three senses to 'the member of
> relation':
>
>
>
> a classificatory relation, a subclass-class, taxonomy;
>
> an individual relation, an instance-class; set theory;
>
> a constitutive relation, structural or functional, say, meronomy;
>
>
>
> regards,
>
> Azamat Abdoullaev
>
>
>
>
>
>
>
> Leonid,
> Thanks for your stuff, a research intensive content. I like your
> assertions
> like : 'A strict hierarchy of Taxons can be described by pure
> combinations
> of Properties.' What is interesting for me how you manage to reconcile two
> different schemes, call it meronomy and taxonomy, in one framework. The
> first one is ''a logic or calculus of individuals'', ie, concrete things,
> and it was initiated as an alternative to ''a logic of classes'', dealing
> with a hierarchy of classes, classes of classes, etc., ie, abstract
> entities. That may depend on how you define a member of relation and a
> part-whole relationship. For instance, Unlike the set theory , all good
> dictionaries give at least three senses to the member of relation:
> a classificatory relation, a subclass-class, taxonomy;
> an individual relation, an instance-class; set theory;
> a constitutive, structural or functional, relation, meronomy;
> regards,
> Azamat Abdoullaev
>
>
> Another
> ----- Original Message -----
> From: <leo@xxxxxx>
> To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
> Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
> Sent: Friday, September 12, 2008 9:51 AM
> Subject: Re: [ontolog-forum] Thing and Class
>
>
>> 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.
>>
>> - 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.
>>
>> 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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