Privet, Leonid,
I browsed the article on Meronomy and Taxonomy. It is not what i expected.
It is all of the 2 senses of ''member-of relationship'': classificatory and
constitutive. What the authors proposing, as i mentioned earlier, to keep
both schemes running hand by hand. Here are some main points: (01)
[????, ???? ???? ????????, ????????? ? ????????? ????????? ???????? ?
???????????? ??? ??????????????? (?????????????) ?????? - ???????, ?? ?????
???????? ?????????? ? ????????? ? ????????????? ?????????????. ???? ??????
??????? ??????????? ? ???????? ???????-???, ????????????? ????????? ??????
?. ???????????, ??????? ???? ? ???? ?????????? ?????????? ?????? ????????
???????? ?? ?????. ??? ??????, ?? ??? ?????, ???????? ???? ????????
???????????? ?????? ???????? 14. ??? ??? ????????? ???? ???????,
???????????? ??????????, ?? ???? ?? ??????, ?? ?????????????? (? ?????? ?.
????) ?????????-?????????????? ???????? ??????????, ? ?????? ???????????????
?????? ?????????????]. (02)
For whom who is not fluent in Russian, or whose e-reader doesn't support
such characters, adapted translation:
There is intension, and there is extension, a typical meaningful structure
of any concept or notion. Accordingly, there is extensional classification,
called taxonomy, and intensional classification, called meronomy, or
mereology. Unlike mereology of L., we consider meronomy as a Bohr's like
complement to taxonomy. That's it.
In other words it says, if your need to classify, say, a truss, a supporting
structure for roofs, bridges, etc., a framework of beams. You have to
specify its types, from collars to decks to domes to mansards, and its
supertype. At the same time, showing the composition and structure of each
member, as ties, beams, bars, struts, posts, rafters. This is too
intuitive. But still wonder to read the Duality Principle, believing the
name inspired by the Complementarity Principle.
regards,
Azamat (03)
----- Original Message -----
From: <leo@xxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Friday, September 12, 2008 3:16 PM
Subject: Re: [ontolog-forum] Thing and Class (04)
> 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.
>
> Best,
> Leonid
>
>> 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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