Re: SUO: *Date 13 Mar 2002 -- Changing Membership
Jon,
Very important notes !
Wednesday, March 13, 2002, 10:10:24 AM, you wrote:
JA> 4. Ergo, sets and their elements are not physical objects.
JA> Now, I am perfectly well aware that we very often speak as
JA> if physical objects could be sets, or the elements of sets,
JA> but that just tells me that we very often speak loosely.
JA> No news there.
JA> The confusion arises, I guess, from the fact that we very often
JA> use mathematical systems in the description of physical systems.
JA> And so I would have to classify this as yet another instance of
JA> uncritically and unreflectively projecting the mathematical map
JA> onto the physical territory, and thus confounding both of them.
There are some additions from "The duality principle..." point of
view. They differ a "subject area" from a "classsification field" .
The first one is "not closed" class in principle . The last is a "good
set" when the proper "primary" identifications from real objects to
"minimal" taxons are made already!(This is another very impotant theme).
The minimal taxons "substitute" real
objects in any model. It is important to differ "taxonomical"
properties from more deep "diagnostic" properties . A value of a
taxonomical property may have a complex connection with them.
What about to take this into account in the SUO ?
Leonid
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Leonid Ototsky,
www.mgn.ru/~ototsky/ototskyhome.html
Chief Specialist of the Computer Center,
Magnitogorsk Iron&Steel Works (MMK)- www.mmk.ru
Russia
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JA> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
JA> MW = Matthew West
JA> MW: Being a member of a set is not something that changes over time.
JA> Possessing a property can change over time. This means that
JA> property possession is different from set membership.
JA> Matthew, & All,
JA> Something about this sort of statement really sounds wrong to me.
JA> I have wrestled with it for a couple of days now, and here is the
JA> best that I can work out for the time being.
JA> 1. Sets are mathematical objects.
JA> 2. Elements of sets are mathematical objects.
JA> If you cannot imagine what in the world such statements might mean,
JA> please feel free to interpret them as idiomatic figures of speech,
JA> affording the paraphrase that sets and their elements are objects
JA> of signs of a sort that we call "mathematical". In most settings,
JA> the descriptors "formal" or "logical" will convey the point just
JA> as well as "mathematical". These adjectives are meant to impart
JA> no more than the fact that the meanings of the signs in question
JA> are determined solely by bodies of formal, logical, mathematical
JA> expressions that we know as "theories".
JA> 3. Mathematical objects are not physical objects.
JA> The reason I say this is because the meanings of physical signs,
JA> that is, the sorts of signs that refer to physical objects and
JA> physical phenomena, are not determined solely by theories, as
JA> a large share of their meanings reside in the experiences of
JA> these objects and phenomena themselves. Notice that there
JA> is a difference between being determined by a law, which
JA> we may not know well enough to be able to write down,
JA> and being determined by a theory, at least, of the
JA> sort whose finite axiom set has been written down.
JA> Aside from all of this, as we went through several times before,
JA> it only coronates confusion to describe mathematical objects as
JA> "timeless". The factor of time, as the conventional aspect and
JA> the standardized parameter of a physical process, is simply not
JA> a determinant in the definition of a mathematical object proper.
JA> Nevertheless, we do use mathematical systems to describe
JA> time-evolving physical systems. And when we do this, it
JA> is perfectly possible for a function f : R -> X to give,
JA> for every real time associated with a real number t in R,
JA> the position of the test object in a physical space that
JA> is parameterized by a mathematical space X. In this way,
JA> then, in the only figure of speech that could make sense,
JA> the "associate membership" of the test object in various
JA> subsets of X is indeed something that changes over time.
JA> Anyways, this is kind of tentative,
JA> and may of course change with time.
JA> Jon Awbrey
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