Nominalist?
Dear Colleagues,
> Nicola wrote
>
> >By the way, better talking of "properties" rather than "classes". A
> >property can correspond to multiple classes (its extensions) in
> >different worlds/situations. This is related to the modality
> >discussion, however (different thread).
John Sowa replied:
>
> I agree. Nominalists try to avoid talking about any kind of universals,
> but they sometimes admit sets or classes as the least objectionable
> kinds of abstract entities.
I might infer from this that you consider me a nominalist. In which case I
would like to take the opportunity to deny it. I consider sets, classes and
tuples to be essential to be able to say anything useful. On the other hand
I am not sure there are any "properties" that cannot be reduced to some
combination of sets classes and tuples.
Indeed when I look at languages such as KIF and Conceptual Graphs, one of my
main criticisms is that they do not (or so it seems to me) explicitly
recognise classification as a primitive, although it is still and implicit
primitive.
I would describe myself as minimalist, by which I mean that I try not to
have pre-conceived ideas about what is primitive (cannot be derived from
other concepts) but seeking to minimise what is primitive. There is no
problem with any number of derived concepts provided their derivation is
clear and complete.
So amongst what are known as universals, I find 2 primitives, set and tuple
(together with the concepts of set membership and order in tuple). I find
class a derivative of set (a set whose members have some properties in
common). A relation is the classification of a tuple. From here it is a
short step to functions, numbers and the rest of mathematics as John pointed
out.
In relations amongst sets, I find two types, transitive - these always (so
far) turn out to be subtype-supertype, and intransitive - these always (so
far) turn out to be set membership/classification relations, (though
sometimes there is something more complex in addition). Other "relations"
really are between variables who are members of some set. This is usually
clear in logic, but in data models (Entity Relationship models lack
variables) this is not true, and pseudo-relations are often used where
variables are really required.
I am always interested in counter examples.
Regards
Matthew
============================================
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============================================
> -----Original Message-----
> From: John F. Sowa [mailto:sowa@west.poly.edu]
> Sent: 04 July 2000 14:45
> To: West, Matthew MR SSI-GPEA-UK; Nicola.Guarino@ladseb.pd.cnr.it;
> sowa@west.poly.edu; standard-upper-ontology@ieee.org
> Subject: Re: Rigid Properties
>
>
> Nicola et al.,
>
> The distinction between rigid and non-rigid is one aspect of the triad
> that Peirce (and I) have been trying to get across (with
> limited success)
> for many years. The various problems that have been discussed in the
> "rigid properties" thread illustrate how important and all-pervasive
> that triad is.
>
> During the Heidelberg meeting, Husserl's distinction of dependent vs.
> independent was accepted by everyone as an important distinction, but
> I kept insisting that it represented only the first two parts
> of a triad.
> Some people suggested that the third part might be defined as
> "dependent
> on more than one other", but that trivializes the third to the point
> where it has lost the most significant aspect: mediation between the
> others.
>
> Peirce introduced a fundamental distinction between the ontological
> categories and the phenomenological categories. An ontological
> category arises from the attempt to classify something as it is
> by itself independent of any observer. A phenomenological category
> arises from the attempt to classify something as it appears to
> some mind (human, animal, robot, plant, or even bacterium).
>
> The example of a hammer illustrates the point: a rock is a naturally
> occurring entity that can be described ontologically by its matter
> and form. It can be described phenomemologically by the way it is
> perceived: how it looks, what use it can serve the viewer, and what
> it can tell the viewer -- about its origin, its previous use by humans
> as a hammer or by insects as a shelter, and its effects on
> the environment
> by scraping a tree, deflecting the pathway for deer and hikers, or
> providing a hiding place for creepy crawly things.
>
> The distinction between naturally occurring vs. human
> artifacts is another
> sometimes helpful, but more often confusing distinction. A
> rock doesn't
> lose its ontological status as a rock by how it may be used
> or perceived.
> And there is nothing fundamentally different between being used by a
> human or by an ant or even a bacterium. Our provincial,
> species-related
> preferences may be the first things we think about and talk about, but
> there is no fundamental difference between a human house and a beaver
> dam or a termite mound. And once you allow beavers or termites to
> have the status of "artifact makers", you can't rule out plants
> that form mangrove swamps or single cells that "decide to" or are
> somehow "induced to" form slime molds.
>
> Nicola wrote
>
> >By the way, better talking of "properties" rather than "classes". A
> >property can correspond to multiple classes (its extensions) in
> >different worlds/situations. This is related to the modality
> >discussion, however (different thread).
>
> I agree. Nominalists try to avoid talking about any kind of
> universals,
> but they sometimes admit sets or classes as the least objectionable
> kinds of abstract entities. However, once you admit enough ontology
> to build up mathematics, you have all the shapes, forms, and patterns
> of any kinds of universals anyone has ever dreamed about. I admit all
> of mathematics into my ontology, and that provides plenty of
> predicates
> (properties, relations, types).
>
> >Indeed all examples with artifacts are tricky. I agree that in many
> >cases is useful to take the intended role as an essential
> property of
> >artifacts. So we may postulate a difference between a stone
> >intentionally shaped to be used as a hammer and a stone that
> >accidentally has that shape. Saying that "hammer" is rigid
> means that
> >no accidental hammer exists.
>
> The "trickiness" of artifacts indicates that the rigid/nonrigid
> distinction is too limited. I don't postulate any difference,
> ontologically, between a stone used in any way. But there is,
> of course, a big difference phenomenologically. However, that
> same difference applies to everything. Everything we encounter
> has aspects of quality, reaction, and mediation -- Peirce's three
> phenomenological categories. There are no accidental beaver dams,
> termite mounds, mangrove swamps, or even rocks.
>
> >In the case of the bomb, I agree that it is essentially intended to
> >blow things up, but in my example I imagined that something that
> >blows things up may not be essentially a weapon: so "being a bomb"
> >may be a rigid property, and "being a weapon" a non-rigid one...
> >Another example is a knife: it may be a weapon, it may not (while
> >remaining essentially a knife).
>
> The word "essentially" in this context simply means "its current
> form is the result of...." But every object has a form that results
> from its previous history. We could replace the word "artifact"
> by the phrase "shaped by human intention", which we could generalize
> to "shaped by the intention of species X". But then the crucial term
> to be explained is "intention", which is one aspect of Peirce's
> mediation.
>
> >These reflect only particular points of view, of course. The
> >important thing is that these points of view can be clarified by
> >using the rigid/non-rigid distinction.
>
> The most important thing to clarify is the phrase "points of view".
> That is precisely what Peirce was doing with his phenomenological
> categories.
>
> John
>
> :wq
>